Significant figures help to find and establish the number that is in the form of digits. The significant digits used instead of figures. It is easy to identify significant digits by counting the numbers from the 1st non-zero digit located on the left. Significant figures of any given number are nothing but the significant digits they used to convey the meaning according to its accuracy. For example, 2.238 has four significant digits.

Clearly understand the topics available below.

- Rules to find the number of significant figures
- Rounding off a decimal to the required number of significant figures
- Round off to a special unit.

## Significant Figures Rules

1. All non–zero numbers (1, 2, 3, 4, 5) are always significant.

Example:

- 2154 has four significant figures
- 142.35 has four significant figures

2. All zeros between non-zero numbers are always significant.

Example:

- 305.003 has six significant figures.
- 70.00 has four significant figures.
- 61.04020 has seven significant figures.

3. In a decimal number that lies between 0 and 1, all zeros that are to the right of the decimal point but to the left of a non-zero number are not significant.

Example:

- 0.00365 has only three significant figures.
- 0.006040 has four significant figures.

4. In a whole number if there are zeros to the left of an understood decimal point but to the right of a non-zero digit, the case becomes doubtful.

Example:

- 304000 there is an understood decimal point after the given six digits. There are 3 zeros that present to the left of the understood decimal point but to the right of a non-zero number so the case becomes doubtful.
- It is represented as 3.04 × 10⁵ also it consists of 3 significant figures. Also, it can represent as 3.040 × 10⁵, then the number of significant figures is 4.

5. When a decimal is round off to a given number of decimal places, all the final zeros in a decimal number are significant.

Example:

- If we round off 2.875 to two decimal places, we get 3.90 which has 3 significant figures.

### Rounding Off Decimals to the Required Number of Significant Figures

Rounding off the number correct to three significant figures is explained along with the examples.

(1) 63.314

Given that 63.314. It has 5 significant figures. To round off the given number into 3 significant digits, we need to round it off to 1 place after the decimal.

The digit in hundredth place 1 is less than 5. So, the digit in the tenths place remains 3 and the digits 1 and 4 disappear.

Therefore, 63.314 = 63.3 rounded off to 3 significant figures.

(2) 5.3062

Given that 5.3062. It has 5 significant figures. To round off the given number into 3 significant digits, we need to round it off to 2 places after the decimal.

The digit in thousandth place 6 is greater than 5. So, the digit in the hundredth place becomes 1 and the digits 6 and 2 disappear.

Therefore, 5.3062 = 5.31 rounded off to 3 significant figures.

(3) 50.003

Given that 50.003. It has 5 significant figures. To round off the given number into 3 significant digits, we need to round it off to 1 place after the decimal.

The digit in hundredth place 0 is less than 5. So, the digit in the tenths place remains 0 and the digits 0 and 3 disappear.

Therefore, 50.003 = 50.0 rounded off to 3 significant figures.

(4) 0.0002489

Given that 0.0002489. It has 4 significant figures. To round off the given number into 3 significant digits, we need to round it off to 6 places after the decimal.

The digit 9 is greater than 5. So, the digit 8 changes to 9, and the digit 9 disappear.

Therefore, 0.0002489 = 0.000249 rounded off to 3 significant figures.

(5) 0.0002477

Given that 0.0002477. It has 4 significant figures. To round off the given number into 3 significant digits, we need to round it off to 6 places after the decimal.

The digit 7 is greater than 5. So, the digit 7 changes to 8, and the digit 7 disappear.

Therefore, 0.0002477 = 0.000248 rounded off to 3 significant figures.

(6) 8.404

Given that 8.404. It has 4 significant figures. To round off the given number into 3 significant digits, we need to round it off to 2 places after the decimal.

The digit 4 is less than 5. So, the digit 0 remains the same 0, and the digit 4 disappears.

Therefore, 8.404 = 8.40 rounded off to 3 significant figures.

(7) 4.888

Given that 4.888. It has 4 significant figures. To round off the given number into 3 significant digits, we need to round it off to 2 places after the decimal.

The digit 8 is greater than 5. So, the digit 8 becomes 9, and the digit 8 disappears.

Therefore, 4.888 = 4.89 rounded off to 3 significant figures.

(8) 6.999

Given that 6.999. It has 4 significant figures. To round off the given number into 3 significant digits, we need to round it off to 0 places after the decimal.

The digit 9 is greater than 5. So, the digit 6 becomes 7, and the digits 9 disappears.

Therefore, 6.999 = 7 rounded off to 3 significant figures.

### Round Off the Following Measurements Examples

(i) 1384.977 kg correct to 6 significant figures.

Given that 1384.977 kg. It has 7 significant figures. To round off the given number into 6 significant digits, we need to round it off to 2 places after the decimal.

The digit 7 is greater than 5. So, the digit 7 becomes 8, and the digits 7 disappears.

Therefore, 1384.977 kg = 1384.98 kg rounded off to 6 significant figures.

(ii) 303.203 g correct to 4 significant figures.

Given that 303.203 g. It has 6 significant figures. To round off the given number into 4 significant digits, we need to round it off to 1 place after the decimal.

The digit 0 is less than 5. So, the digit 2 remains 2, and the digits 0 and 3 disappears.

Therefore, 303.203 g = 303.2 kg rounded off to 4 significant figures.

(iii) 2.0829 mg correct to 2 significant figures.

Given that 2.0829 mg. It has 5 significant figures. To round off the given number into 5 significant digits, we need to round it off to 1 place after the decimal.

The digit 8 is greater than 5. So, the digit 0 becomes 1, and the digits 8, 2, and 9 disappears.

Therefore, 2.0829 mg = 2.1 mg rounded off to 2 significant figures.

(iv) 0.004784 km correct to 1 significant figures.

Given that 0.004784 km. It has 4 significant figures. To round off the given number into 5 significant digits, we need to round it off to 3 places after the decimal.

The digit 7 is greater than 5. So, the digit 4 becomes 5, and the digits 7, 8, and 4 disappear.

Therefore, 0.004784 km = 0.005 km rounded off to 1 significant figures.

### Rounding Off to a Specified Unit Examples

(i) Round off $ 65537 to the nearest 10 dollars.

Given that $ 65537. 65537 is in between 65530 and 65540. 65537 is closer to 65540. Therefore, $ 65537 to the nearest 10 dollars is $ 65540.

(ii) Round off $ 208.287 to the nearest 10 cents.

Given that $ 208.287. $ 208.287 is in between 208.20 and 208.30. 208.287 is closer to 208.30. Therefore, $ 208.287 to the nearest 10 cents is $ 208.30.

(iii) Round off 892.58 to the nearest dollar.

Given that $ 892.58. $ 892.58 is in between 892 and 893. 892.58 is closer to 893. Therefore, 892.58 to the nearest dollar is $893.

(iv) Round off 575.085 to the nearest cents.

Given that 575.085. 575.085 is in between 575.080 and 575.90. 575.085 is closer to 575.90. Therefore, 575.085 to the nearest cents is 575.90.

(v) Round off 19.077 cm to the nearest mm.

Given that 19.077 cm. 19.077 cm is in between 19.0 cm and 19.1 cm. 19.077 cm is closer to 19.1 cm. 19.1 cm = 191 mm. Therefore, 19.077 cm to the nearest mm is 191 mm.

(vi) Round off 63.5389 m to the nearest cm.

Given that 63.5389 m. 63.5389 m is closer to 65.54 m. Therefore, 63.5389 m to the nearest cm is 65.54 m.

(vii) 0.00848 kg to nearest g.

Since 1 g = 0.001 kg so to round off 0.00848 kg to the nearest g, we have to round it off to 3 places of decimal. Therefore, 0.00848 kg = 0.008 kg rounded off to the nearest g.

(viii) 18.3373 g to the nearest mg.

Since 1 mg = 0.001 g so to round off 18.3373 g to the nearest mg, we have to round it off to three places of decimal. Therefore, 18.3373 g = 18.337 g rounded off to the nearest mg.