# Big Ideas Math Answers Grade 5 Chapter 1 Place Value Concepts

## Big Ideas 5th Grade Chapter 1 Place Value Concepts Math Book Answer Key

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Lesson 1: Place Value Patterns

Lesson 2 Place Value with Whole Numbers

Lesson 3 Patterns and Powers of 10

Lesson 4 Decimals to Thousandths

Lesson 5 Place Value with Decimals

Lesson 6 Compare Decimals

Lesson 7 Round Decimals

### Lesson 1.1 Place Value Patterns

Explore and Grow

Write the whole number represented by each base ten block. Then use the base ten blocks to complete the table.

Rod is 10 times as much as Unit

The flat is 10 times as much as Rod

Cube is 3 times as much as Flat

Unit is 1/10 of Rod

Rod is 1/10 of Flat

The flat is 3/10 of Cube

Reasoning
Describe the patterns you see in a number as you move from one place value position to another place value position.

Answer: As we move from one place value position to another value position, The place value of a digit increase by ten times as move from the left.

Think and Grow: Place Value Patterns

You can use a place value chart to help write numbers that are 10 times as great as a number or $$\frac{1}{10}$$ of a number.

Show and Grow

Question 1.
Complete the statements.

Apply and Grow: Practice

Use a place value chart to answer the question.
Question 2.
What number is 10 times as great as 6,000?

If 6,000 is multiplied by 10 times it becomes 60,000

Question 3.
What number is $$\frac{1}{10}$$ of 300?

300 x 1/ 10 is 30

Question 4.
80 is 10 times as great as what number?

if 8 is multiplied by 10 times it becomes 80

Question 5.
40,000 is $$\frac{1}{10}$$ of what number?

4,00,000 x 1/10 is 40,000

The number is 4,00,000

Complete the table.
Question 6.

1. 100 ,1 ,

10,  10 times as number is 10 x 10 = 100

1/10 of 10 is 1

2. 4000,40

400, 10 times as number is 400 x 10 = 4000

1/10 of 400 is 40

3. 70,000,700

7,000, 10 times as number is 7,000 x 10 =70,000

1/10 of 7,000 is 700

4. 500,000,    5,000

50,000,10 times as number is 50,000 x 10 = 5,00,000

1/10 of 50,000 is 5,000

Question 7.

1. 2,000, 20

200,  10 times as number is 200 x 10 = 2,000

1/10 of 200 is 20

2. 3,00,000,   3,000

30,000,  10 times as number is 30,000 x 10 = 3,00,000

1/10 of  30,000 is 3,000

3. 900, 9

90, 10 times as number is 90 x 10 = 900

1/10 of 90 is 9

4. 80,000, 800

8,000,  10 times as number is 8,0,0 x 10 = 80,000

1/10 of 8,000 is 800

Question 8.
Patterns
Describe the relationship between any place value position and the next greater place value position.

The relation between any place value position and next greater place value position increases ten times as we move.

Number Sense
Write whether the statement is true or false. If false, explain why.
Question 9.
600 is 100 times as great as 60,000.
______

600 X 100 = 60,000

Question 10.
9,000 is 1,000 times as great as 9.

_____

9 X 1,000 = 9,000

Think and Grow: Modeling Real Life

Example
Which state is about 10 times larger than Georgia?
The approximate land area of Georgia is 60,000 square miles.
Use a place value chart to find the number that is 10 times as great as 60,000.

6,000_____ is 10 times as great as 60,000.

Show and Grow

Use the table above.
Question 11.
Which state is about 10 times larger than Hawaii?
Answer: Georgia is 10 times larger than Hawaii

Question 12.
Which state is about $$\frac{1}{10}$$ the size of Wyoming?
Answer: Maryland is 1/10 the size of Wyoming

Question 13.
DIG DEEPER!
Which state is about 100 times larger than the District of Columbia?

District of Columbia = 60

100 times larger than the District of Columbia 60 X 100 = 6,000 is Hawaii

Question 14.
DIG DEEPER!
A mother rhinoceros weighs 2 tons. Her baby weighs $$\frac{1}{10}$$ as much as her. What is the weight of the baby rhinoceros, in pounds.

Answer: The weight of the baby rhinoceros is 20 Pounds.

2 tons Mother

Baby = 200 x 1/10 = 20 Pounds

### Place Value Patterns Homework & Practice 1.1

Complete the statements.

Question 1.
______ is 10 times as great as 2,000.

2,000 x 10 = 20,000

Question 2.
_____ is $$\frac{1}{10}$$ of 2,000.

2,000 x 1/ 10 = 200

Use a place value chart to answer the question.
Question 3.
What number is 10 times as great as 50?

50 x 10 = 500

Question 4.
What number is $$\frac{1}{10}$$ of 4,000?

4,000 x 1/10 = 400

Question 5.
800 is $$\frac{1}{10}$$ of what number?

8,000 x 1/10 = 800

Question 6.
60,000 is 10 times as great as what number?

6,000 is 10 times means 6,000 x 10 =60,000

Complete the table.
Question 7.

1. 400, 4

40, 10 times as number is 40 x 10 = 400

1/10 of 40 is 4

2. 5,000, 50

500, 10 times as number is 500 x 10 = 5,000

1/10 of 500 is 50

3. 10,000  ,  100

1,000, 10 times as number is 1,000 x 10 = 10,000

1/10 of 1,000 is 100

4.8,00,000   , 8,000

80,000, 10 times as number is 80,000 x 10 = 8,00,000

1/10 of 80,000 is 8,000

Question 8.

1. 7,00,000   ,   7,000

70,000, 10 times as number is 70,000 x 10 = 7,00,000

1/10 of 70,000 is 7,000

2. 200 ,  2

20, 10 times as number is 20 x 10 = 200

1/10 of 20 is 2

3. 30,000, 300

3,000, 10 times as number is 3,000 x 10 = 30,000

1/10 of 3000 is 300

4. 1,000 ,  10

100, 10 times as number is 100 x 10 = 1,000

1/10 of 100 is 10

Question 9.
Patterns
Describe the relationship between any place value position and the next lesser place value position.

The relation between any place value position and next lesser place value position decreases ten times as we move.

Question 10.
YOU BE THE TEACHER
Your friend says 6,700 is $$\frac{1}{10}$$ of 67,000. Is your friend correct? Explain.
Answer: Yes My friend is correct, because if we divide 67,000 by 10 we get the result as 6,700 only.

Use the table.

Question 11.
Modeling Real Life
Which city’s population is about 10 times the population of Newark?

Newark=40,000

40,000 x 10 = 4,00,000 is Oakland

Question 12.
Modeling Real Life
Which city’s population is about $$\frac{1}{10}$$ the population of Marina?
Answer: Population of Del Ray Oaks.

Marina = 20,000

20,000 x 1/10 = 2,000=Del Ray Oaks

Question 13.
DIG DEEPER!
An archaeologist finds a ceramic bowl that is about 400,000 years old. He finds different artifact that is $$\frac{1}{100}$$ times as old as the 100ceramic bowl. How much older is the ceramic bowl than the other artifact?
Answer: The Ceramic bowl is 4000 years old.

4,00,000 x 1/100= 4,000

Review & Refresh

Find the factor pairs for the number.
Question 14.
9
Answer: 1,3,9 are factor pairs of 9

Question 15.
24
Answer:  (1,24), (2,12) (3,8) and (4,6) are factor pairs of 24

Question 16.
15
Answer:(1,3,5,15) are factor pairs of 15

### Lesson 1.2 Place Value with Whole Numbers

Model the number. Draw your model.
Then write the value of each digit.

Compare the values of the 4s.
Answer: Thousands-4, Hundreds -4 , Tens – 4 and Ones- 2

4 is in thousand, 4 is in Hundreds and 4 is at tens value.

Repeated Reasoning
Is the value of the 4 in the tens place 10 times as much as the value of the 2 in the ones place? Explain.
Answer: No, Why means 4 in tens place means its value is 40 and 2 in ones place means only 2so 4 in the tens place is not 10 times as the value of 2.

Think and Grow: Place Value with Whole Numbers

Key Idea
A place value chart shows the value of each digit in a number. It also shows how the place values are grouped. Each group of three digits is called a period. Ina number, periods are separated by commas.

Example
Write the number in standard form, word form, and expanded form.
Standard form:4,66,900
Word form: Four hundreds sixty six thousand and nine hundred
Expanded form:
4 × 1,00,000 + __6___ × 10,000_____ + ___6__ × _1,000_____ + _9____ × __100____

Show and Grow

Write the number in two other forms.
Question 1.
Standard form: 78,300
Word form:
Expanded form:

Word Form : Seventy -Eight Thousand, Three Hundred.

Expanded Form : 7 x 10,000 + 8 x 1000 + 3 x 100=78,300

Question 2.
Standard form:
Word form: three hundred fifty thousand, fifty-eight
Expanded form:

Standard Form : 300,50,058

Expanded Form : 3 x 10,00,000+ 5 x 10,000 + 5 x 10 +8=300,50,058

Question 3.
Compare the values of the 6s in the number 466,900.

the values of the 6 s are one is in 60 thousand’s place and other is at 6 thousands place.

Apply and Grow: Practice

Write the number in two other forms.
Question 4.
Standard form:
Word form:
Expanded form: 6 × 100,000 + 8 × 1,000 + 4 × 100 + 5 × 10 + 9 × 1

Standard Form : 6,08,459

Word Form : 6 hundred / six lakh, eight thousand , four hundred  fifty nine.

Question 5.
Standard form: 45,006,702
Word form:
Expanded form:

Word form: forty five lakh ,six thousand seven hundred and two.

Expanded form:4 x 10000000 + 5 x 1000000 + 6 x 1000 +

7 x 100 +2

Question 6.
Compare the values of the 7s in the number 4,877,034.

The value’s of 7s is at seventy thousand,(70,000) and again at  seven thousand(7,000).

Question 7.
Compare the values of the 3s in the number 5,338.

The values of 3s is at 3-Hundred(300) and at thirty (30)[3 tens)]

or

3 at hundreds and 3 at tens place.

Compare.
Question 8.

In 8,046 The value of 4 is in Ten’s place and 6 is in one’ s place

and in 8,460 the value of 4 is in hundreds place and 6 in ten’s place.

Question 9.

In 28,517 the value of 2 is at twenty thousand place, 8 at thousands and 5 at hundreds, 1 at tens and 7 at one’s place.

and 28,509 the value of 2 is at twenty thousand place, 8 at thousands and 5 at hundreds, zero at tens and 9 at one’s place.

Question 10.

In 5,854,331- Fifty Lakhs , 8 at lakhs, Five at ten thousand, 4 at thousand,3 at hundred, 3 at ten’s and 1 at one’s place.

and in 5,854,231 – Fifty Lakhs , 8 at lakhs, Five at ten thousand, 4 at thousand,2 at hundred, 3 at ten’s and 1 at one’s place.

Question 11.
The white truffle is the world’s most expensive edible fungus, which costs up to three thousand dollars per kilogram. Write this number in standard form.

Standard Form: 3000$per Kg. the white truffle is 3000$ per kg.

Question 12.
YOU BE THE TEACHER
Your friend says that in the number 45,951, one 5 is 10 times as great as the other 5. Is your friend correct? Explain.

Yes,  because  at first the 5 is at tens place and in next time 5 is at thousands place so friend is right 5 is 10 times greater as the other 5 . As we move from right value to left twice tens value place becomes thousand value place.

Question 13.
Logic
Newton is thinking of a 6-digit number in which all of the digits are the same. The value of the digit in the thousands place is 8,000. What is Newton’s number?

8,88,888

8 x 1,00,000 + 8 x 10,000+8 x 1,000+8 x 100 + 8 x 10 + 8 x 1

Think and Grow: Modeling Real Life

Example
Compare the values of the 3sin Jupiter’s average distance from the Sun.

Use a place value chart to help you find the value of each 3.

Each place value is 10 times as great as the place value to its right. The digits are two places apart. So, multiply 30,000 by 10 × 10 = 100.
So, the value of the 3 in the millions place is _______ times the value of the 3 in the ten thousands place.

Show and Grow

Use the table above.
Question 14.
Compare the values of the 7s in Mars’s average distance from the Sun.

the value of 7 s in first is in thousands place and next 7 s is at hundreds place, the digits are one place apart, so the value of first 7 is in thousands place is 10 times the value of the next 7s in hundreds place.

Question 15.
Compare the values of the 4s in Saturn’s average distance from the Sun.

the value of 4 s in first is in four hundred thousands place and next 4 s is at hundreds place, the digits are two places apart, so the value of first  4 is in hundred thousands place is 100 times the value of the next 4s in hundreds place.

Question 16.
DIG DEEPER!
An organization wants to donate all of the money raised through fund raisers and raffles to a children’s charity. Complete the donation check.

1.

$194,918 +$ 35,187 = $230,005 Word Form : Two Hundred, Thirty thousand and Five dollars. Standard Form :$ 230,005

### Place Value with Whole Numbers Homework & Practice 1.2

Write the value of the underlined digit.
Question 1.
740,225

4 is at Forty thousand place

Question 2.
604,197,872

6 is at Six Hundred Lakh place

Question 3.
12,405,287

2  is at  twenty Lakh or twenty hundred thousand place

Question 4.
392,183

3 is at 3 lakhs or 3 hundred thousand place

9  is at ninety thousand place

2 is at 2 thousand place

1 is at one hundred place

8 is at eighty place

3 is at ones place place

Write the number in two other forms.
Question 5.
Standard form: 450,014
Word form:
Expanded form:

Word Form : 4 lakhs or 4 hundred thousand ,  fifty thousand and fourteen

Expanded  Form : 4 x 1,00,000 +5 x 10000 + 1 x 10 + 4

Question 6.
Standard form:
Word form: fourteen thousand, two hundred one
Expanded form:

Standard Form : 14,201

Expanded Form : 1 X 10000 + 4 X 1000 + 2 X 100 +1

Question 7.
Compare the values of the 9s in the number 537,499.

First 9 is at ones place, and second 9 is at tens place.

Question 8.
Compare the values of the 5s in the number 78,550,634.

First 5 is at Ten Thousands place,

Second 5 is at Five Hundred Thousands place.

Compare.
Question 9.

67,893 < 67,943

6 at sixty thousand place ,6 at sixty thousand place

7 at thousand place, 7 at thousand place

8 at eight hundred place,9 at nine hundred is great

9 at tens place and 4 at four at tens place is less

and 3 at ones place and 3 at ones place is same

Question 10.

450,823 > 405,823

4 at Four hundred thousand,

5 at fifty thousand and 0 is smaller at ten thousands place

0 at thousands place is smaller than 5 at thousands place

8  at hundreds place is same as 8 at hundreds place

2 at tens place is same as 2 at tens place

and 3 at ones place is same as 3 at ones place

Question 11.

176,994 = 176,994

1 at one hundred thousand, is same at 1 at One Hundred Thousand place

7 at Seventy thousand is same at 7 at Seventy Thousand place

6 at six thousand is same at 6 at six thousand place

9 at hundreds place is same at 9 at hundreds place

9 at ninety or 9 tens place is same as 9 at Ninety or 9 Tens place

and 4 at ones place is same as 4 at Ones place

Question 12.

Your body contains about 60,000 miles of blood vessels. Write this number in word form.

60,000 miles of blood vessels in  Word Form : Sixty Thousand miles.

Question 13.
Which One Doesn’t Belong?
Which number does belong with the other three?
1 × 10,000 + 4 × 1,000 + 2 × 100 + 6 × 1 fourteen thousand, two hundred six
140,206

No number is repeated, so no number belongs to other

one at tens place

4 at ones place

2 at hundredths place

and 6 at thousandths place.

Question 14.
DIG DEEPER!
Find the difference in the values of the underlined digits.
856,092 37,841

8 is at 80 Million,

and

8 is at hundreds value

the difference is 8 X 1,00,00,000 times the other  8 value.

Use the table.

Question 15.
Modeling Real Life
Compare the values of the 3s in the music cost.
Answer: 3 is at 3 millions place and other 3 is at 3 hundreds place.

Question 16.
Modeling Real Life
Compare the values of the 2s in the cost.

Costs Places

In cast 2 is at two hundred thousands place and 2 at thousands place.

In Director 2 is at 2 millions place and 2 at thousands place.

In Editing 2 value is not there.

In Music also 2 is not there

In Producers 2 value is at 2 millions place

In Visual effects 2 place is first at thousands place and 2 is in ones place

Question 17.
DIG DEEPER!
What is the total cost for the director and producers? Write your answer in word form.

Year 2 $6 x 105= 6 x 10 x 10 x 10 x 10 x 10 = 6,00,000  10,000 + 6,00,000 = 6,10,000 there fore total sales for Year 1 and Year 2 combined is is 6,10,000 . Question 18. Which migration is farther? About how much farther is it? Answer: Chinook Salmon about 4 x 103km 4 X 10 x 10 x 10 = 4000 km and Leatherback Turtle about 2 X 104 km 2 x 10 x 10 x 10 x 10 = 20,000 km So Leatherback Turtle is farther and 20,000 km – 4000 km = 16,000 km it is 16,000 km farther Question 9. DIG DEEPER! A human has about 104 taste buds. A cow has about 3 times as many taste buds as a human. About how many taste buds does a cow have? Write your answer as a whole number multiplied by a power of 10. Answer: (104) 3 time means (104) as per the law powers are multiplied 4 x 3 (104×3) = (1012) (104×3)= 1 X (104) x (104) x (104) (1012)= 1 x (10 x 10 x 10 x 10 ) x (10 x 10 x 10 x 10 ) x (10 x 10 x 10 x 10) ### Patterns and Powers of 10 Homework & Practice 1.3 Question 1. Identify the base, exponent, and power for the expression 103. Answer: base: 10 exponent: 3 power : 103= 10 x 10 x 10 Question 2. Write 10 × 10 × 10 × 10 a power. Answer: 10 x 10 x 10 x 10 = 104 Find each product. Use patterns to help. Question 3. 6 × 10 = ______ 6 × 100 = _____ 6 × 1,000 = _____ 6 × 10,000 = _____ Answer: 6 x 10=6 × 101 = 60 6 x 100 =6 × 102 = 600 6 X 1,000=6 × 103 = 6,000 6 x 10,000 = 6 × 104= 60,000 Question 4. 8 × 10 = ______ 8 × 100 = _____ 8 × 1,000 = _____ 8 × 10,000 = _____ Answer: 8 x 10=8 × 101 = 80 8 x 100 =8 × 102 = 800 8 X 1,000=8 × 103 = 8,000 8 x 10,000 = 8 × 104= 80,000 Question 5. 4 × 10 = ______ 4 × 100 = _____ 4 × 1,000 = _____ 4 × 10,000 = _____ Answer: 4 x 10=4 × 101 = 40 4 x 100 =4 × 102 = 400 4 X 1,000= 4× 103 = 4,000 4 x 10,000 = 4 × 104= 40,000 Find the value of the expression. Question 6. 103 Answer: 103 = 10 x 10 x 10 = 1,000 Question 7. 2 × 104 Answer: 2 × 104 = 2 x 10 x 10 x 10 x 10 = 20,000 Question 8. 9 × 105 Answer: 9 × 105 = 9 x 10 x 10 x 10 x 10 x 10 = 9,00,000 Question 9. 3 × 102 Answer: 3 × 102 = 3 x 10 x 10 = 300 Rewrite the number as a whole number multiplied by a power of 10. Question 10. 100,000 Answer: 100,000 = 1 x 10 x 10 x 10 x 10 x 10 = 1 × 105 Question 11. 70 Answer: 70 = 7 x 10 = 7 x 101 Question 12. 6,000 Answer: 6,000 = 6 x 10 x 10 x 10 = 6 x 10 Number Sense Write the number in standard form. Question 13. (3 × 102) + (8 × 101) Answer: (3 × 102) + (8 × 101) = 3 x 10 x 10 + 8 x 10 3 x 100 + 80 300+ 80 = 380 Question 14. (2 × 103) + (5 × 102) + (4 × 101) Answer: (2 × 103) + (5 × 102) + (4 × 101) = 2 x 10 x 10 x 10 + 5 x 10 x 10 + 4 x 10 2,000 + 500 + 40 2,540 Question 15. YOU BE THE TEACHER Newton 6 says 106 = 10 × 6. Is he correct? Explain Answer: No he is wrong because 106 ≠ 10 × 6 it is 10 is to be multiplied by 6 times , 106 = 10 x 10 x 10 x 10 x 10 x 10=10,00,000 is correct Question 16. Which One Doesn’t Belong? Which one does not belong with the other three? Answer: Both are different blocks , in first block it is square and next it is cube. Question 17. Modeling Real Life Each student at an elementary school votes once on this year’s field trip. How many students voted in all? Answer: Aquarium = 7 x 102 = 7 x 10 x 10 = 700 Amusement Park = 103 = 10 x 10 x 10 = 1000 700 + 1000 = 1,700 So total number of students voted are = 1,700. Question 18. Modeling Real Life On which day did more people attend the event? How many more people? Answer: Friday = 10 x 10 x 10 = 1,000 Saturday = 5 x 102 = 5 x 10 x 10 = 500 on Friday more people attend the event and more are 1,000 – 500 = 500 , s0 500 more people attended. Review & Refresh Divide. Then check your answer Question 19. Answer: Step 1) Start by dividing 65 by 6 to get the decimal answer as illustrated below. Note that we round the answer if necessary, but don’t worry, the final answer will still be exact. 65 / 6 = 10.83 Step 2) Next we take the Whole part of the answer in Step 1 and multiply it by the Divisor. As you can see, it does not matter if we rounded in the previous step because the Decimal part is ignored. Furthermore, the Divisor in 65 divided by 6 is 6. Thus, the Whole multiplied by the Divisor is: 10 x 6 = 60 Step 3) Finally, we will subtract the answer in Step 2 from the Dividend to get the answer. The Dividend in 65 divided by 6 is 65. Thus, our final calculation to get the answer is: 65 – 60 = 5 the answer is 5. Question 20. Answer: Step 1) Start by dividing 50 by 4 to get the decimal answer as illustrated below. Note that we round the answer if necessary, but don’t worry, the final answer will still be exact. 50 / 4 = 12.50 Step 2) Next we take the Whole part of the answer in Step 1 and multiply it by the Divisor. As you can see, it does not matter if we rounded in the previous step because the Decimal part is ignored. Furthermore, the Divisor in 50 divided by 4 is 4. Thus, the Whole multiplied by the Divisor is: 12 x 4 = 48 Step 3) Finally, we will subtract the answer in Step 2 from the Dividend to get the answer. The Dividend in 50 divided by 4 is 50. Thus, our final calculation to get the answer is: 50 – 48 = 2 the answer is 2. Question 21. Answer: Step 1) Start by dividing 45 by 3 to get the decimal answer as illustrated below. Note that we round the answer if necessary, but don’t worry, the final answer will still be exact. 45 / 3 = 15 the answer is 0. ### Lesson 1.4 Decimals to Thousandths Explore and Grow Divide the square into10 equal parts. Shade one part. What part of the whole is shaded? Fraction: Decimal: Divide each of the 10 parts into 10 equal parts. Shade one part using a different color. What part of the whole is shaded with the second color? Fraction: Decimal: If you divide each of the 100 equal parts into10 equal parts, how many parts will the model have? If you shade one of those parts, what part of the whole is shaded? Fraction: Decimal: Answer: the model will have 10 parts , only 1/ 10th part is shaded, 0.1 Structure Compare the number of hundredths to the number of tenths. Compare the number of hundredths to the number of thousandths. What do you notice? Answer: number of hundredths to the number of tenths is 10 to 100 , 10/100=1/10 = 0.1 number of hundredths to the number of thousandths is 100 to 1000, 100/1000 =1/10= 0.1 both has equal values 1/10 = 0.1 the number of hundredths to the number of tenths is equal to the number of hundredths to the number of thousandths Think and Grow: Thousandths Key Idea In a decimal, the third place to the right of the decimal point is the thousandths place. You can write thousandths as fractions or decimals. Show and Grow Write the decimal as a fraction. Question 1. 0.009 Answer: 0.009= 9 / 1,000 = 9 x 1/1,000 Question 2. 0.063 Answer: 0.063 = 63 / 1,000= 63 x 1/1,000 Question 3. 0.194 Answer: 0.194 = 194 / 1,000= 194 x 1/1,000 Write the fraction as a decimal Question 4. $$\frac{3}{1,000}$$ Answer: $$\frac{3}{1,000}$$= 3 x 1/ 1,000= 0.003 Question 5. $$\frac{91}{1,000}$$ Answer: $$\frac{91}{1,000}$$= 91 x 1/ 1,000 = 0.091 Question 6. $$\frac{607}{1,000}$$ Answer: $$\frac{607}{1,000}$$= 607 x 1/1,000= 0.607 Apply and Grow: Practice Write the decimal as a fraction. Question 7. 0.645 Answer: 0.645= 645x 1/1,000= 645/1,000 Question 8. 0.002 Answer: 0.002=2 x 1/1,000= 2/1,000 Question 9. 0.98 Answer: 0.98= 98 x 1/ 1,000= 98/1,000 Question 10. 0.6 Answer: 0.6 = 6 x 1/10= 0.6/10 Write the fraction as a decimal. Question 11. $$\frac{884}{1,000}$$ Answer: $$\frac{884}{1,000}$$= 884x 1/1,000= 0.884 Question 12. $$\frac{8}{1,000}$$ Answer: $$\frac{8}{1,000}$$= 8 x 1/1,000= 0.008 Question 13. $$\frac{39}{100}$$ Answer: $$\frac{39}{100}$$= 39 x 1/ 100= 0.39 Question 14. $$\frac{1}{10}$$ Answer: $$\frac{1}{10}$$= 1 x 1/10 = 0.1 Question 15. 0.4 is $$\frac{1}{10}$$ of what number? Answer: $$\frac{4}{10}$$ is 0.4 Question 16. 0.52 is 10 times as great as what number? Answer: 0.52 is 10 times as great as 0.052 Question 17. You use 47 of the cotton balls for an art project. What portion of the bag of cotton balls do you use? Write your answer as a decimal. Answer: 47/100= 47 x 1/100= 0.47 Question 18. Which One Doesn’t Belong? Which number does not belong with the other three? Answer: 0.29 does not belongs to other three Question 19. YOU BE THE TEACHER Your friend says the value of the 7 in the hundredths place of 0.877 is 10 times as great as the 7 in the thousandths place. Is your friend correct? Explain. Answer: Yes , because the value of 7 in the hundredths place as compared is 10 times as great as the 7 in the thousands place. Question 20. Write each fraction as a decimal. What do you notice? $$\frac{4}{10}$$, $$\frac{40}{100}$$ and $$\frac{400}{1,000}$$ Answer: $$\frac{4}{10}$$=0.4 $$\frac{40}{100}$$ =0.4 $$\frac{400}{1,000}$$=0.4 number of tenths, tenths number of hundredths and hundredths number of thousandths are same. Think and Grow: Modeling Real Life Example You put together 156 pieces of the puzzle before lunch and 148 pieces of the puzzle after lunch. What portion of the puzzle did you put together? Write your answer as a decimal. Write the fraction as a decimal. You put together ____0.304__ of the puzzle. Show and Grow Question 21. You make flash cards out of index cards. You use 50 index cards for social studies and 25 index cards for science. What portion of the pack of index cards do you use? Write your answer as a decimal. Answer: 50 for social studies, 25 for science total is 50 + 25 = 75, total number of flash cards is 1,000 , 75 / 1,000 or 75 by 1,000 or 75 x 1/1,000= 0.075 Question 22. There are 458 knock-knock jokes in the book. not What fraction of the jokes in the book are knock-knock jokes? Answer: 458/1,000 or 458 x 1/1,000 of jokes books in knock- knock jokes. Question 23. DIG DEEPER! A newly hatched caterpillar was 0.02 inches long. After 2 weeks, the caterpillar grew 10 times as long as its length when it hatched. After another 2 weeks, the caterpillar grew 10 times as long as its length after 2 weeks. How long is the caterpillar now? Answer: First week it is 0.02 inches, in two weeks -2 weeks-0.02 x 10 = 0.2 inches again after 2 weeks -0.2 x 10 = 2 inches ### Decimals to Thousandths Homework & Practice 1.4 Write the decimal as a fraction. Question 1. 0.735 Answer: 0.735= 735 / 1,000= 735 x 1/1,000 Question 2. 0.051 Answer: 0.051= 51 / 1,000= 51 x 1/1,000 Question 3. 0.804 Answer: 0.804 = 804 / 1,000= 804 x 1/ 1,000 Question 4. 0.2 Answer: 0.2 = 2 / 10= 2 x 1/10 Write the fraction as a decimal. Question 5. $$\frac{98}{1,000}$$ Answer: $$\frac{98}{1,000}$$=98 x 1/1,000= 0.098 Question 6. $$\frac{67}{100}$$ Answer: $$\frac{67}{100}$$= 67 x 1/100=0.67 Question 7. $$\frac{4}{100}$$ Answer: $$\frac{4}{100}$$= 4 x 1/100=0.04 Question 8. $$\frac{9}{10}$$ Answer: $$\frac{9}{10}$$= 9 x 1/10= 0.9 Question 9. 0.08 is 10 times as great as what number? Answer: 0.008 if 0.008 is multiplied by 10 times it becomes 0.08 Question 10. 0.001 is $$\frac{1}{10}$$ of what number? Answer: 0.0001 if 0.0001 is $$\frac{1}{10}$$ equals to 0.001 Question 11. YOU BE THE TEACHER Your friend says that $$\frac{16}{1,000}$$ can be written as 0.16. Is your friend correct? Explain. Answer: No, because if 16 / 1,000 or 16 x 1/1,000 is 0.016 not 0.16, 0.016 ≠ 0.16 so he is incorrect. Question 12. Precision Thirteen unit cubes are taken from the thousand cube. Write a fraction and a decimal to represent how many unit cubes are left. Answer: 13 units cubes are taken Total number of units are 1000 left are from 1,000-13/1,000=87/1000 87 / 1,000 and 0.087 cubes are left Question 13. DIG DEEPER! Write the number represented by each point on the number line. Point X: _____ Point Y: ___ Answer: on the number line Point X = 7.633 as we move from 7.63 to three places forward so Point X is 7.633 on the number line Point Y = 7.638 as we move from 7.63 its eighth place forward and Point Y is 7.638 Question 14. Modeling Real Life A restaurant owner has a 1,000-count box of napkins. She puts 125 of the napkins on tables. What portion of the box of napkins does she use for the tables? Write your answer as a decimal. Answer: Restaurant has 1,000 count box of napkins and keeps 125 on table so portion of the box she uses is 125/1,000= 125 x 1/ 1,000= 0.125 Question 15. DIG DEEPER! Your friend has a recipe book with 1,000 recipes. She wants to try two new recipes each week. What fraction of the recipes in the book will she have tried after 1 year? Answer: In a year there are almost 52 weeks. Each week 2 means 2 x 52 =approximately 104 recipes in a year. so in a year she would have tired 104 / 1,000= 104 x 1/1,000 = 0.104 recipes. Review & Refresh Question 16. Extend the pattern of shapes by repeating the rule “square, octagon, pentagon, octagon ”What is the 48th shape in the pattern? Answer: ” square, octagon, pentagon, octagon, hexagon, octagon , heptagon , octagon, octagon, octagon, nonagon, octagon , decagon, octagon,  11 hendecagon Octagon 12 dodecagon Octagon 13 tridecagon Octagon 14 tetradecagon Octagon 15 pentadecagon Octagon 16 hexadecagon Octagon 17 heptadecagon Octagon 18 octadecagon Octagon 19 enneadecagon Octagon 20 icosagon Octagon 21 icosikaihenagon Octagon 22 icosikaidigon Octagon 23 icosikaitrigon Octagon 24 icosikaitetragon Octagon 25 icosikaipentagon Octagon 26 icosikaihexagon Octagon 27 icosikaiheptagon Octagon 28 icosikaioctagon Octagon 29 icosikaienneagon Octagon 30 triacontagon Octagon 31 triacontakaihenagon Octagon 32 triacontakaidigon Octagon 33 triacontakaitrigon Octagon 34 triacontakaitetragon Octagon 35 triacontakaipentagon Octagon 36 triacontakaihexagon Octagon 37 triacontakaiheptagon Octagon 38 triacontakaioctagon Octagon 39 triacontakaienneagon Octagon 40 tetracontagon Octagon 41 tetracontakaihenagon Octagon 42 tetracontakaidigon Octagon 43 tetracontakaitrigon Octagon 44 tetracontakaitetragon Octagon 45 tetracontakaipentagon Octagon 46 tetracontakaihexagon Octagon 47 tetracontakaiheptagon Octagon 48 tetracontakaioctagon Octagon ### Lesson 1.5 Place Value with Decimals Explore and Grow Model the number. Draw your model. Then write the value of each digit. Answer: from the model 3.33 = 0nes digit is – 3 tenths digit is 3/10 =0.3 hundredths digit is 3/ 100 = 0.03 Repeated Reasoning Compare the value of the ones digit to the value of the tenths digit. Then do the same with the tenths and the hundredths digits. Explain why you can use base ten blocks to model ones, tenths, and hundredths. Answer: a digit in one place represents one and 10 times more what it represents in the place to its right and that is tenths digit. Similarly a digit in tenths place represents tenth and 10 times more what it represents in the place to its right and that is hundredths digit. Each place to the left is 10 times the size of the place to the right, and base 10 blocks are the best way to model ones, tenths, and hundredths. Think and Grow: Place Value with Decimals Key Idea In a place value chart, whole numbers are to the left of the decimal point. Decimals are to the right of the decimal point. Standard form:2.557 Word form:” Two and five hundred fifty-seven thousandths” Expanded form: 2 × 1 + __5__ ×$$\frac{1}{10}$$____ + 5 × $$\frac{1}{100}$$ + _7_ × $$\frac{1}{1000}$$__ Show and Grow Write the number in two other forms. Question 1. Standard form: 0.398 Word form: Expanded form: Answer: Word form: “Three hundred ninety – eight thousandths” Expanded form: 3 x (1/10) + 9 x (1/100) + 8 x (1/1,000) Question 2. Standard form: Word form: eight and forty-six thousandths Expanded form: Answer: Standard form:8.046 Expanded form: 8 x 1 + (4 /100) + (6 / 1,000) Question 3. Compare the values of the 5s in the number 2.557. Answer: at first 5s place value is at tenths and next its place value is at hundredths . Apply and Grow: Practice Write the value of the underlined digit. Question 4. 0.418 Answer: 4 is at tenths value place Question 5. 5.296 Answer: 9 is at hundredths value place Question 6. 3.806 Answer: 8 is at tenths value place 6 is at thousandths value place Question 7. 0.547 Answer: 7 is at thousandths value place Write the number in two other forms. Question 8. Standard form: Word form: Expanded form: 4 × 1 + 9 × $$\frac{1}{10}$$ + 8 × $$\frac{1}{1,000}$$ Answer: Standard form: 4.908 Word form:” Four and nine hundredth – eight thousandths” Question 9. Standard form: 0.125 Word form: Expanded form: Answer: Word form: “one hundred twenty – five thousandths” Expanded form: 1 x (1/10) + 2 x (1 /100) +5 x (1 / 1,000) Question 10. Compare the values of the 4s in the number 0.844. Answer: at first 4s place value is at hundredths and next 4s place value is at thousandths Question 11. Compare the values of the 3s in the number 3.367. Answer: at first 3s place value is at ones place and next 3s place value is at tenths place Question 12. A pygmy jerboa weighs one hundred thirty-two thousandths pound. Write this number in standard form. Answer: The Standard Form of pygmy jerboa’s -one hundred thirty-two thousandths pound weighs is 0.132 pound Question 13. Reasoning Is 9.540 equivalent to 9.54? Explain. Answer: Yes. 9.540 is equivalent to 9.54 because at thousandths value its 0, so zero multiplied by any number is zero. Therefore both are equivalent. Question 14. DIG DEEPER! Write three decimals that are equivalent to 6 × 1 + 4 × $$\frac{1}{10}$$ . Answer: the three equivalent decimals are of 6 .04 are 6.040, 6.0400, 6.04000 Think and Grow: Modeling Real Life Example How do the values of the 3s in the masses of the fruits compare? Use a place value chart to help you find the value of each 3. The value of the 3 in the mass of the tomato is _one_____ . The value of the 3 in the mass of the chili pepper is __tenths___. So, the value of the 3 in the mass of the tomato is __10_____ times the value of the 3 in the mass of the chili pepper. Also, the value of the 3 in the mass of the chili pepper is ___1/10__ the value of the 3 in the mass of the tomato. Show and Grow Question 15. Two baseball players have batting averages of 0.358 and 0.345. How do the values of the 5s in the batting averages compare? Answer: In 0.358 the place value of 5s is at tenths place and in 0.345 the place value of 5s is at thousandths place. Question 16. The stopwatch shows a runner’sritethe100-meter dash time. Write the time in words. Answer: 15.76 seconds time in words is Fifteen and seven tenths and six hundredths Question 17. DIG DEEPER! You exchange 1 U.S. dollar for Australian dollars and 1 U.S. dollar for Kuwaiti dinars. Do you have 10 times as many Australian dollars as Kuwaiti dinars? Explain. Answer: Yes, Because 1 Australian dollars = 1.302 of 0.302 of Kuwaiti dinars, if we multiply 0.302 by 10 it becomes 1.302 which is equal to 1 Australian dollars. [0.302 x 10 = 1.302] so 1 Australian dollars is 10 times more than the 1 Kuwaiti dinars. ### Place Value with Decimals Homework & Practice 1.5 Write the value of the underlined digit. Question 1. 5.437 Answer: 5 at ones place 4 at tenths place 3 at hundredths place 7 at thousandths place Question 2. 0.852 Answer: the underlined digit is 2 at thousandths place, its value is 2 x 1/1000= 2/1000 Question 3. 0.962 Answer: the underlined digit is 6 at hundredths place its value is 6 x 1/100= 6 /100 Question 4. 4.165 the underlined digit is 1 at tenths place its value is 1x 1/10 = 1/10 Answer: Write the number in two other forms. Question 5. Standard form: 9.267 Word form: Expanded form: Answer: Word form: nine and two tenths six hundredths seven thousandths. Expanded form : 9+ 2 x 1/10 + 6 x 1/100 + 7 x 1/1000 Question 6. Standard form: Word form: two and forty-three thousandths Expanded form: Answer: Standard form : 0.243 Expanded form: 2 x 1/10+4 x 1/100+3 x 1/1000 Question 7. Compare the values of the 6s in the number 1.668. Answer: first 6s at tenths place and next 6s at hundredths place Question 8. Compare the values of the 7s in the number 7.704. Answer: first 7s at ones place and next 7s at tenths place Question 9. A pygmy possum weighs 0.097 pound. Write this number in word form. Answer: pygmy weighs 0.097 pound and its word form is nine hundredths and seven thousandths Questio 10. Which One Doesn’t Belong? Which one does not belong with the other three? Answer: no number belongs to other three because 5 is at tenths place one at hundredths place and 4 at thousandths all are at different places. Question 11. Reasoning Which number cards are equal to the value of the underlined digit? Answer: 2 x 1/1,000 , two thousandths and 0.002 are equal to the value of the underlined digit. Question 12. Modeling Real Life How do the values of the 5s in the heights of the plants compare? Answer: In Peace lily the 5s place is at thousandths and in Venus flytrap the 5s place is at hundredths Question 13. Modeling Real Life The world’s largest gold nugget is located in Las Vegas, Nevada. It has a mass of about 27.247 kilograms. Write how to say the nugget’s mass in words. Answer: the mass of gold nugget in Las Vegas is 27.247 kilograms given In Words form it is twenty seven and two tenths four hundredths and seven thousandths Review & Refresh Compare. Question 14. Answer: 8/10 =0.8 80/100=0.8 both are equal 8/10 = 80/100 Question 15. Answer: 5/8 = 0.625 3/6= 0.5 0.625 > 0.5, 5/8 > 3/ 6, 5/8 is greater than 3/6 Question 16. Answer: 7/2= 3.5 10/8=1.25 so 7/2 is greater than 10/8. 7/2 > 10/8 ### Lesson 1.6 Compare Decimals Explore and Grow Use models to compare the decimals. Answer: 0.62 >0.26, 0.62 is greater than 0.26, 0.6 is greater than o.2 0.80= 0.8, 0.80 both are equal 3.5 < 3.55, 3.55 is greater than 3.50 Reasoning How can you use a place value chart to compare two decimals? Use a place value chart to check your answers above. Answer: we use another table to compare with the previous and write the answer. Think and Grow: Compare Decimals Example Compare 3.769 and 3.749. Use a place value chart. Start at the left. Compare the digits in each place until the digits differ. The digits in the ones place and the tenths place are the same. Compare the hundredths. Example Compare 2.4 and 2.405. Use place value. Line up the decimal points. Start at the left. Compare the digits in each place until the digits differ. 2.4<2.405 Show and Grow Compare Question 1. Answer:  Ones . Tenths Hundredths Thousandths 9 . 0 6 3 9 . 0 6 7 Same . Same Same Greater So 9.063 < 9.067 Question 2. Answer:  Ones . Tenths Hundredths Thousandths 0 . 8 9 0 0 . 8 0 9 Same . Same Greater Greater So 0.89 > 0.809, Apply and Grow: Practice Compare. Question 3. Answer:  Ones . Tenths Hundredths Thousandths 8 . 5 3 7 8 . 5 4 1 Same . Same Greater Greater 8.537 < 8.541 Question 4. Answer: 6.401 < 6.409, since 0.009 is greater than 0.001 Question 5. Answer: 7.409 > 7.049 since 7.4 is greater than 7.0 Question 6. Answer: 0.25 = 0.250 Both are equal Question 7. Answer: 2.701 >2.700, since 0.001 is greater than 0.000 Question 8. Answer: 4.006 < 4.61, since 4.6 is greater than 4.0 Question 9. Answer: 0.041 < 41.6, 41 is greater than 0 Question 10. Answer: 0.007 < 0.7 as 0.7 is greater than 0.007 Order the decimals from least to greatest. Question 11. 321.499, 325.499, 321.489 Answer: 321.499, 325.499, 321.489 from least to greatest as 321.489 is smaller than 321.499 and 321.499 is smaller than 325.499 so 321.489 , 321.499 , 325.499 Question 12. 9.7, 9.64, 9.78 Answer: 9.7, 9.64, 9.78 from least to greatest 9.64 is smaller than 9.7 and 9.7 is smaller than 9.78 so 9.64, 9.7 , 9.78 Open-Ended Complete the number to make the statement true. Question 13. Answer: 10.321 > 10.311 as 10.311 is smaller than 10.321 Question 16. Answer: 28.60 = 28.600 Both are equal Question 15. Number Sense Is 0.472 greater than or less than $$\frac{47}{1,000}$$? Explain. Answer: 0.472, 0.047 0.475 is greater than 0.047, as 4 in the tenths place is greater than 0 in the others tenth place Question 16. YOU BE THE TEACHER Your friend says that 45.6 is less than 45.57 because 6 is less than 57. Is your friend correct? Explain. Answer: Friend says 45.6 is less than 45.57 No ,he is wrong as the 6th in tenths place is greater than 5, in the tenths place so he is wrong 45.60 > 45.57 not less Think and Grow: Modeling Real Life Example You, your friend, and your cousin compete at a gymnastics competition. Your floor routine score is 15.633. Your friend’s score is 15.533, and your cousin’s score is 15.635. Order the scores from least to greatest. Use a place value chart. Compare the digits in each place until the digits differ. _15.533______ is the least Write the remaining numbers in the place value chart. Compare the digits in each place until the digits differ. 15.633 ,15.635 as 15.533 is less than 15.633 as 5 at tenths place is less than 6 at tenths place and 15.633 is less than 15.653 as 3 at hundredths place is less than 5 at hundredths place So, the scores from least to greatest are 15.533, 15.633 and 15.635 Show and Grow Question 17. You stand on one leg for 2.75 minutes, your friend stands on one leg for 2 minutes, and your cousin stands on one leg for 2.25 minutes. Order the amounts of time from least to greatest. Answer: You – 2.75 min , Friend – 2.00 min and cousin for 2.25 min 2.00< 2.25 ,2.00 is less than 2.25 as 0 at tenths place is less than 2 at tenths place 2.25 < 2.75, 2.25 is less than 2.75 as 2 at tenths place is less than 7 at tenths place so From Least to Greatest : 2.00 min, 2.25 min, 2.75 min Question 18. DIG DEEPER! You, Newton, Descartes, and your friend each have a tablet. The table shows the screen display sizes. Your friend’s tablet has the greatest display size. Your tablet’s display size is greater than Newton’s but less than Descartes’s. What is the display size of your tablet. Answer: Y-Your, N-Newton’s ,F-Friend- 12.9, D-Descartes Given Friend has greatest display size F= 12.9 Y – N ,given Your tablet’s display size is greater than Newton’s, N< Y and yours is less than Descartes’s Y < D therefore N < Y <D < F, Newton’s< Yours<Descartes’s<Friend so N-Newton’s- 7.9, Y-Your-9.7,D-Descartes-10.5,F-Friend-12.9 ### Compare Decimals Homework & Practice 1.6 Write which place to use when comparing the numbers. Question 1. 0.521 0.576 Answer: 2 at hundredths place is smaller than 7 at hundredths place so 0.521 < 0.576 Question 2. 17.422 17.946 Answer: 4 at tenths place is small than 9 at tenths place so 17.422 < 17.946 Question 3. 9.678 9.67 Answer: 8 at thousandths place is greater than 0 at thousandths place 9.678 > 9.670 Compare. Question 4. Answer: 4 at hundredths place is smaller than 7 at hundredths place so 3.445 is smaller than 3.472 3.445 < 3.472 Question 5. Answer: 0 at tenths place is smaller than 4 at tenths place so 23.049 < 23.409 Question 6. Answer: 4 at tenths place is greater than 3 at tenths place 75.4 > 75.391 Question 7. Answer: All given place values are same so 14.100 or 14.10 = 14.100 Question 8. Answer: the value of 5s at hundredths place is more than 0 in other hundredths place 4.05> 4.005 Question 9. Answer: 15.2, 15.002 2 at tenths place is greater than 0 at tenths place 15.2 > 15.002 Question 10. Answer: 0.021, 0.026 1 at thousandths is smaller than 6 at thousandths place 0.021 < 0.026 Order the decimals from least to greatest. Question 11. 2.75, 0.2, 0.275 Answer: 0.2 < 0.275 as 0 at hundredths place is less than 7 at hundredths place 0.275<2.75 as 0 at ones place is less than 2 at at ones place so from least to greatest 0.2, 0.275, 2.75 Question 12. 56.01, 56.1, 56.001 Answer: 56.001 < 56.01 as 0 at hundredths place is less than 1 at hundredths place 56.01 < 56.1 as o at tenths place is less than 1 at tenths place 56.001 , 56.01, 56.1 Open-Ended Complete the number to make the statement true. Question 13. Answer: 29.030 = 29.030 both the place values are same Question 14. Answer: 3.562 <3.562 as the value of 6 is at hundredths place so the other value at hundredths place is 6. Question 15. YOU BE THE TEACHER Newton says 8.51 is less than 8.492 because 8.51 has fewer digits after the decimal point than 8.492. Is he correct? Explain. Answer: No, he is not correct its not the digits after the decimal point is fewer but the 5s at tenths place is greater than 4 at the tenths place so 8.51 is greater than 8.492, 8.51 > 8.492 Question 16. Open-Ended Descartes is thinking of a number less than 46.922 and greater than 46.915. What could Descartes’s number be? Answer: The numbers can be 46.916, 4 6.917, 46.918, 46.919, 46.920 or 46.921 and all these numbers are less than 46.922 and greater than 46.915. Question 17. Modeling Real Life Player A’s batting average is 0.300, Player B’s batting average is 0.333, and Player C’s batting average is 0.313. Order the batting averages from greatest to least. Answer: B- 0.333, C-0.313 , A – 0.300 0.333 is great than 0.313 as 3 at hundredths place is great than 1 at hundredths place so 0.333>0.313 0.313 is greater than 0.300 as 1 at hundredths place is great than 0 at hundredths place 0.313 > 0.300 the batting averages from greatest to least are B> C> A=0.333 > 0.313 >0.300 batting averages from greatest to least 0.333,0.313,0.300 Question 18. Modeling Real Life A gasoline station customer pumps more than 9.487 gallons of gasoline but less than 10 gallons. Which display could be his? Answer: Given A gasoline station customer pumps more than 9.487 gallons but less than 10 gallons as 9.003 is less than 9.487 so not 9.003 as 9.499 is greater than 9.487 and even less than 10.000 so it is 9.499 as 9.406 is less than 9.487 so it cannot be 9.406 as 9.872 is greater than 9.487 and even less than 10.000 so it can be 9.872 so the displays can be 9.499 or 9.82 as both are more than 9.487 gallons and less than 10 gallons Review & Refresh Round the number to the place of the underlined digit. Question 19. 7,851 Answer: the round place of 5 is 7,850 Question 20. 9,462 Answer: the round place of 9 means 10,000 or 9,500 Question 21. 4,983 Answer: the round place of 9 – 5,000 Question 22. 51,504 Answer: the round place of 1- 52,504 ### Lesson 1.7 Round Decimals Explore and Grow Plot the numbers on the number line. Which numbers round to 3? Which numbers round to4? How do you know? Answer: 3, 3.09, 3.5, 3.51, 3.6, 3.77, 3.9 , 4 The numbers round to 3 are 3.09 The numbers round to 4 are 3.51, 3.6, 3.77 , 3.9 Repeated Reasoning Show how you can use a number line to round 3.09, 3.51, and 3.77 to the nearest tenth. Answer: 3.09 to the nearest tenth is 3.10 3.51 to the nearest tenth is 3.50 3.77 to the nearest tenth is 3.80 Think and Grow: Round Decimal Number Example Use a number line to round 7.36 to the nearest tenth. 7.36 is closer to 7.4 than it is to 7.3. So, 7.36 rounded to the nearest tenth is __7.40____. Example Use place value to round 2.185 to the nearest whole number and to the nearest hundredth. So, 2.185 rounded to the nearest whole number is __2.2_____. 2.185 rounded to the nearest hundredth is ___2.200___. Show and Grow Round the number to the place of the underlined digit. Question 1. 12.67 Answer: the round place of digit 6 is 12.70 Question 2. 0.439 Answer: the round place of digit 4 is 0.5 the round place of digit 3 is 0.44 the round place of digit 9 is 0.440 Question 3. 2.555 Answer: the round place of digit 2 is 3.000 Question 4. 5.409 the round place of digit 4 is 5.400 Question 5. Round 0.68 to the nearest tenth. Answer: 0.68 to the nearest tenth is 0.70, 6 at tenths place becomes 7 Question 6. Round 1.715 to the nearest hundredth. Answer: 1.715 to the nearest hundredth is 1.720, 1 at hundredths place becomes 2 Question 7. Round 4.07 to the nearest whole number. Answer: 4.07 to the nearest whole number becomes 4.00 or 4 Question 8. Round 0.289 to the nearest tenth. Answer: 0.289 to the nearest tenth is 0.300 as 2 becomes 3 at tenths place. Apply and Grow: Practice Round the number to the place of the underlined digit. Question 9. 1.482 Answer: the underlined digit is 8 ,so its value becomes 1.490 Question 10. 5.093 Answer: the underlined digit is 0 so its value becomes 5.100 Question 11. 8.502 Answer: the underlined digit is 8 so its value becomes 9.000 Question 12. 34.748 Answer: if it is underlined at 3 it becomes 35.000 if it is underlined at 4 it becomes 35.000 if it is underlined at 7 it becomes 35.000 if it is underlined at 4 it becomes 34.800 if it is underlined at 8 it becomes 34.750 Question 13. Round 2.619 to the nearest whole number. Answer: the value of 2.619 becomes 3.000 Question 14. Round 7.825 to the nearest tenth. Answer: the value of 7.825 to the nearest tenth is 7.900 Question 15. Round 92.701 to the nearest ten. Answer: the value of 92.701 to the nearest ten 93.000 Question 16. Round 4.263 to the nearest hundredth. Answer: the value of 4.263 to the nearest hundredth is 4.270 Question 17. Round 0.829. Nearest whole number: Nearest tenth: Nearest hundredth: Answer: Round 0.829 Nearest whole number:0.900 Nearest tenth:0.830 Nearest hundredth:0.830 Question 18. Round 18.062. Nearest whole number:18.100 Nearest tenth:18.070 Nearest hundredth:18.063 Answer: Question 19. A baby harp seal weighs 25.482 pounds. Round this weight to the nearest tenth of a pound. Answer: Given a baby harp seal weighs 25.482 pounds and the nearest tenth is 25.000 pounds So the weight of baby harp seal is 25.000 pounds. Name the place value to which the number was rounded. Question 20. 8.942 to 8.94 Answer: It was rounded at hundredths value place Question 21. 0.164 to 0.2 Answer: It was rounded at tenths value place Question 22. 15.826 to 16 Answer: It was rounded at whole value place Question 23. Writing Explain what happens when you round 2.999 to the nearest tenth. Answer: 2.999 round value becomes 3.000 as all value places at tenths, hundredths, thousandths are 9 it becomes increased as we move so it ones value increases by 1 and becomes round 3.000. Question 24. DIG DEEPER! To what place should you round 23.459 to get the greatest number? the least number? Explain. Answer: To make 23.459 to greatest number the value of 4s at tenths becomes 5, 23.500 and to make 23.500 round make 5 at tenths value increased and make ones value 3 as 4 so we get 24.000 and to make 23.459 to least number the value at hundredths 5 becomes 0 , 23.400 and to make 23.400 round make 4 at tenths value as decreased to 0 and ones value same as 3 it becomes as 23.000 Think and Grow: Modeling Real Life Example Gasoline prices are listed to the nearest thousandth of a dollar. The final price is rounded to the nearest hundredth. About how much does a customer pay for 1 gallon of regular gasoline at the station shown? Think: What do you know? What do you need to find? How will you solve? Use place value to round the price of 1 gallon of regular gasoline,$2.799, to the nearest hundredth.

So, a customer will pay about $___$ 2.800____ for 1 gallon of gasoline.

Show and Grow

Use the table.

Question 25.
What is the length of the praying mantis rounded to the nearest hundredth?

Given  praying mantis as 3.254 so the  nearest hundredth becomes 3.26

Praying mantis becomes 3.260

Question 26.
What is the length of the cicada rounded to the nearest tenth?

Given cicada 1.48 so rounded to the nearest tenth becomes 1.50

Question 27.
What is the length of the hissing cockroach rounded to the nearest tenth?

Given Hissing cockroach 2.682 so rounded to the nearest tenth is 2.700

Hissing cockroach becomes 2.700

Question 28.
DIG DEEPER!
You have about $3 in coins. Write one possible combination of coins that represents the least amount of money you could have. Write another combination of coins for the greatest amount of money you could have. Answer:$3 Least amount of money combinations – 1. $1.0,$1.0    2.$1.0,$1.5

3.$0.5,$ 2.0 all combinations becomes less than $3$ 3 greatest amount of money combinations- 1. $1.0,$ 2.5   2.$1.5 ,$2.0

3. $2.0 ,$ 2.0 all combinations becomes more than \$3

### Round Decimals Homework & Practice 1.7

Round the number to the place of the underlined digit.
Question 1.
49.012

the underline digit is 4 its round number 4 becomes 5 so it is 50.000

Question 2.
2.308

the underline digit is 2  its round number 2 becomes as 2.000

Question 3.
9.647

the underline digit is 6 its round number 6 becomes 7 so it is 9.700

Question 4.
7.519

the underline digit is 1 its round number 1 becomes  2 so it is 7.520

Question 5.
Round 8.436 to the nearest hundredth.

8.436 to the nearest hundredth, 3 becomes 4 so it is 8.440

Question 6.
Round 15.159 to the nearest ten.

15.159 to the nearest ten ,1 becomes 2 so it is 15.200

Question 7.
Round 1.602 to the nearest whole number.

1.602 to the nearest whole number is 2.0

Question 8.
Round 3.619 to the nearest tenth.

3.619 to the nearest tenth, so 6 becomes 7 it is 3.700

Question 9.
Round 4.183.
Nearest whole number:
Nearest tenth:
Nearest hundredth:

Round 4.183.
Nearest whole number:4.000
Nearest tenth:4.200
Nearest hundredth:4.200

Question 10.
Round 9.076.
Nearest whole number:
Nearest tenth:
Nearest hundredth:

Round 9.076.
Nearest whole number:9.000
Nearest tenth:9.100
Nearest hundredth:9.080

Name the place value to which each number was rounded.
Question 11.
16.932 to 20

16.932 at Tens value it is rounded  so it becomes 20

Question 12.
0.581 to 0.58

0.581 to 0.58

0.581 at Thousandths value has been rounded so 0.58

Question 13.
7.429 to 7.4

7.429 to 7.4

7.429 at Hundredths value has been rounded so 7.4

Question 14.
Structure
Round ★ to the nearest tenth.

the nearest tenth * in the number line is showing at 5.64

Question 15.
Precision
The area of a campground is exactly halfway between 25.9 acres and 26 acres. What is the area of the campground?

Halfway of 25.9 and 26.0 is 25.90+25.60=51.50/2 = 25.75 acres

So the area of the campground is 25.75 acres.

Question 16.
Open-Ended
Name two different numbers that round to 3.8 when rounded to the nearest tenth.

The two numbers that are round to 3.8 when rounded to the nearest tenth place the value becomes 4.0 and  3.90

Question 17.
Open-Ended
Name two different numbers that round to 7.42 when rounded to the nearest hundredth.

The two numbers that round to 7.42 when rounded to the nearest hundredth place the value becomes 7.50 and 7.40

Use the table.

Question 18.
Modeling Real Life
Your science class designs and tests four model boats to find out how much weight they can hold without sinking. What is the greatest weight rounded to the nearest tenth that a boat can hold?

Given weights held without sinking in kilograms are

0.694,0.605,0.592,0.547 among all the weights the greatest weight rounded to the nearest tenth that a boat can hold is (0.694) i.e  0.7 kilograms

Question 19.
Modeling Real Life
What is the least weight rounded to the nearest hundredth that a boat can hold?

The least weight rounded to the nearest hundredth is (0.547)- o.5 kilograms a boat can hold

Review & Refresh

Find the product.
Question 20.
7 × 40

The product of 7 X 40 = 280

Question 21.
5,000 × 9

The product of 5,000 x 9 = 45,000

Question 22.
8 × 200

The product of 8 x 200=1,600

### Place Value Concepts Performance Task

There are 18 species of penguins. Scientists have estimated the populations of 16 penguin species.
Question 1.
What fraction of penguin species have unknown populations?

Given total is 18 species of penguins out of which Scientists have estimated the populations of 16 penguin species. so unknown is 18-16/18=2/18,

so 2/18=1/9 of penguin species have unknown populations

Question 2.
Several species of penguins and their estimated populations and locations are shown.

a. Are there more emperor penguins or rockhopper penguins? Explain.
b. Which species of penguin has the greatest population? Explain.

d. The Galápagos penguin is an endangered species. There are about 1,000 times as many macaroni penguins as Galápagos penguins. About how many Galápagos penguins are there?

a. Rock hopper penguins are more than Emperor

2,460,000>595,000 as  2,460,000 is greater than 595,000 so Rock hopper penguins are more

B. Macaroni species 18 x 106 of penguin has the greatest population as compared to Emperor 595,000,Adelie 4,000,000+7,00,000+40,000=4,740,000 and

Rockhopper-2,460,000

among all the species Macaroni 18 x 106– species is more.

C. Macaroni + Adelie + Rockhopper +Emperor

18,000,000+4,740,000+ 2,460,000 + 595,000 = 25,795,000

25,785,000  to the nearest hundred thousand is 26,000,000

So there are almost 26,000,000 penguins live in Antarctica.

d. 1,000 times as many macaroni penguins as Galápagos penguins is

18 x 106  x 1 x 1000 = 18 x 10

So there are 18 x 10Galápagos penguins available

### Place Value Concepts Activity

Place Value Plug In
Directions:
1. Players take turns.
2. On your turn, roll six dice. Arrange the dice into a six-digit number that matches one of the descriptions.
3. Write your number on the lines.
4. The first player to fill in all of the numbers wins!

### Place Value Concepts Chapter Practice

1.1 Place Value Patterns

Use a place value chart to answer the question.
Question 1.
What number is 10 times as great as 4,000?

10 times as great as 4,000 is 10 x 4,000= 40,000

Question 2.
What number is $$\frac{1}{10}$$ of 8,000?

$$\frac{1}{10}$$ of 8,000 is 8,000/10 = 800

Question 3.
10,000 is 10 times as great as what number?

10,000 is 10 times as great as 1,000

Question 4.
70 is $$\frac{1}{10}$$ of what number?

70 is $$\frac{1}{10}$$ of 700

Question 5.
Complete the table.

300 is 10 times as great as 30  and 30 x 1/10 is 3

6,000 is 10 times as great as 600 and 600 x 1/10  is 60

90,000 is 10 times as great as 9,000 and 9,000 x 1/10 is 900

2,00,000 is 10 times as great as 20,000 and 20,000 x 1/10=2,000

Question 6.
YOU BE THE TEACHER
Your friend says 500 is 10 times as great as 5,000. Is your friend correct? Explain.

No, My friend is wrong because  500 is not 10 times great as 5,000,

500 < 5,000.

1.2 Place Value with Whole Numbers

Question 7.
Write the number in two other forms.
Standard form: 456,701
Word form:
Expanded form:

Word form: Four hundred fifty six thousand, seven hundred and one
Expanded form:4 x 100000 + 5 x 10000 + 6 x 1000 + 7 x 100 + 1

Question 8.
Write the number in two other forms.
Standard form:
Word form: Eight million, sixty thousand, five hundred seventy-three
Expanded form:

Standard form:8,060,573
Expanded form:8 x 1000000+6 x 10000 + 5 x 100 + 7 x 10 + 3

Question 9.
Compare the values of the 4s in the number 900,441,358.

4s value is at lakh or hundred thousandths place and another 4s place is at ten thousandths place.

Question 10.
Write the values of the 6s in the number 96,672.

The values of the 6s in the number 96,672 are

6s place is at thousand and another 6s is at hundreds place

Compare.
Question 11.

83,802 > 83,082

The value at hundred 8 is more/great to 0 at hundreds place

Question 12.

2,498,576 > 2,477,583

The value at 9 at ten thousands place is more/great than 7 at ten thousands place

1.3 Patterns and Powers of 10

Question 13.
Write 10 × 10 as a power.

10 × 10 as a power is 102

Find each product. Use patterns to help.
Question 14.
4 × 10 = _____
4 × 100 = ______
4 × 1,000 = _____
4 × 10,000 = ______

4 × 10 = 40
4 × 100 = 400
4 × 1,000 = 4,000
4 × 10,000 =40,000

Question 15.
3 × 10 = _____
3 × 100 = ______
3 × 1,000 = _____
3 × 10,000 = ______

3 × 10 = 30
3 × 100 = 300
3 × 1,000 = 3,000
3 × 10,000 = 30,000

Question 16.
7 × 10 = _____
7 × 100 = ______
7 × 1,000 = _____
7 × 10,000 = ______

7 × 10 = 70
7 × 100 = 700
7 × 1,000 = 7,000
7 × 10,000 = 70,000

Find the value of the expression.
Question 17.
105

105=1,00,000

Question 18.
8 × 101

8 × 101= 8 x 10 = 80

Question 19.
7 × 104

7 × 104 = 7 x  10 x 10 x 10 x 10= 70,000

Question 20.
3 × 105

3 × 105 = 3 X 10 X 10 X 10 X 10 X 10=3,00,000

Rewrite the number as a whole number multiplied by a power of 10.
Question 21.
5,000

5,000= 5 X 103

Question 22.
600,000

6,00,000= 6 X 105

Question 23.
90

90= 90 X 101

1.4 Decimals to Thousandths

Write the decimal as a fraction.
Question 24.
0.062

0.062= 62 X 1/1,000

Question 25.
0.008

0.008= 8 X 1/1,000

Question 26.
0.195

0.195= 195 X 1/1,000

Write the fraction as a decimal.
Question 27.
$$\frac{2}{1,000}$$

$$\frac{2}{1,000}$$ = 2 x 1/1,000= 0.002

Question 28.
$$\frac{37}{1,000}$$

$$\frac{37}{1,000}$$ = 37 x 1/1,000= 0.037

Question 29.
$$\frac{409}{1,000}$$

$$\frac{409}{1,000}$$= 409/1,000=0.409

Question 30.
0.0.7 is 10 times as great as what number?

0.07 is 10 times great as 0.007

Question 31.
0.04 is $$\frac{1}{10}$$ of what number?

0.04 is $$\frac{1}{10}$$ of 0.4

1.5 Place Value with Decimals

Write the number in two other forms.
Question 32.
Standard form:
Word form:
Expanded form: 5 × 1 + 3 × $$\frac{1}{10}$$ + 8 × $$\frac{1}{100}$$ + 4 × $$\frac{1}{1,000}$$

Standard form:5+0.3+0.08+0.004=5.384
Word form: five and three tenths, eight hundredths and 4 thousandths

Question 33.
Standard form: 2.059
Word form:
Expanded form:

Word form: two and five hundredths and nine thousandths

Expanded form: 2 x 1 + 5 x 1/100 + 9 x 1/1000

Question 34.
Compare the values of the 5s in the number 1.055.

5s value is at hundredths and another 5s value is at thousandths place

Question 35.
Compare the values of the 8s in the number 6.884.

8s place value is at tenths value and other 8s place value is at hundredths place

1.6 Compare Decimals

Compare.
Question 36.

15.891 > 15.791

the 8 value at tenths place is greater than 7 at tenths place

Question 37.

8.205 < 8.250

the 0 at hundredths is less than 5 at hundredths

Question 38.

Both are same

3.600 = 3.6

Order the decimals from least to greatest.
Question 39.
7.008, 7.09, 7.180

7.008<7.09

7.09 <7.18

so the decimals from least to greatest are 7.008 , 7.09, 7.180

Question 40.
50.426, 50.42, 50

50 < 50.42

50.42 < 50.426

so the decimals from least to greatest are 50, 50.42, 5.0426

Question 41.
Modeling Real Life
Newton weighs a treat at the pet store. He says it weighs less than 0.519 ounce but more than 0.453 ounce. Which treats could he have weighed?

Newton says it weighs less than 0.519 ounce  but more than 0.453 ounce,

so Blue berry waffle 0.512 which is in between 0.453<0.512<0.519

and We have more than 0.453 is 0.459 ounce which is Peanut butter and is less than 0.519 ounce

So Peanut butter 0.453 is in between 0.453<0.459<0.519

so newton would have weighed Peanut butter 0.459 ounce

and it can be even Blueberry  waffle 0.512  ounce

newton’s treats could be Peanut butter ,Blueberry waffle

1.7 Round Decimals

Round the number to the place of the underlined digit.
Question 42.
9.514

if 9 is digit then it is rounded as 9.0

if 5 then  it is rounded as 9.500

if 1 then it is rounded as 9.520

if  4 then it is rounded as 9.520,9.510

Question 43.
1.027

1.027 at 2 it is rounded as 1.03

Question 44.
8.469

8.469, 8 is rounded as 8.500 or 8 or 8.000

Question 45.
32.501

in 32.501

3 is rounded as  30.000

2- 33.000

5- 32.6 or 33

0-32.5

1 -32.500

Question 46.
Round 0.176 to the nearest

0.200

Question 47.
Round 6.538 to the nearest tenth. hundredth.

6.500

Question 48.
Round 7.425.
Nearest whole number:
Nearest tenth:
Nearest hundredth:

Nearest whole number:8.000, 8
Nearest tenth:7.500
Nearest hundredth:7.430

Question 49.
Round 2.108.
Nearest whole number:
Nearest tenth:
Nearest hundredth: