## Significant Figures

In rounding off significant figures or significant digits we will be very useful because it enables us to simplify complex calculation.

**We will about……..**

● 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.

**What are Significant figures? **

If we have to find the speed of car with the help of speedometer, we observe that the speed lies between 92.4 km/hr and 92.5 km/hr. By close observation, we can say approximately that the speed of car is 92.46 km/hr. The last digit 6 is however uncertain.

Thus, significant figures are all certain digits in a measurement plus one uncertain digit. The use of significant figures in measurement and value is a form of rounding.

Thus, in the above example, we say that 92.46 km/hr has four significant figures.

**Rules for finding the number of significant figures: **

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

**For example;**

● 1325 has four significant figures

● 235.14 has four significant figures

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

**For example;**

● 204.003 has six significant figures.

● 50.00 has four significant figures.

● 51.02010 has seven significant figures.

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

**For example;**

● 0.00247 has only three significant figures.

● 0.002030 has four significant figures.

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

In the number 402000, there is a understood decimal point after the given six digits. There are 3 zeros that lie to the left of the understood decimal point but to the right of a non - zero number so the case becomes doubtful.

If it is expressed as 4.02 × 10^{5}, it becomes clear and we can say that 4.02 × 10^{5} has 3 significant figures. It is expressed as 4.020 × 10^{5}, 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.

**For example;**

If we round off 6.785 to two decimal places, we get 6.80 which has 3 significant figures.

**Rounding off decimals to the required number of significant figures: **

*Rounding off the number correct to three significant figures*

(1) **53.214** → It has 5 significant figures.

To round off it to 3 significant digits, we required to round it off to 1 place after the decimal.

Therefore, 53.214 = 53.2 rounded off to 3 significant figures.

[The digit in hundredths place is 1 which is less than 5. So, the digit in the tenths place remains 2 and the digits 1 and 4 disappear.]

(2) **4.3062** → It has 5 significant figures. To round it off to 3 significant figures we round it off to the 2^{nd} place after the decimal point.

So, 4.3062 = 4.31 correct to three significant figures.

(3) **30.002** → It has 5 significant figures. To round it off to 3 significant figures, we required to round it off to 1 decimal place after the decimal point.

30.002 = 30.0 correct to 3 significant figures.

(4) **0.0001378** → It has 4 significant figures. To round it off to 3 significant figures, we require to round it off to 6 decimal places after the decimal point 0.0001378 = 0.000138 correct to 3 significant figures.

(5) **0.0001366** → It has 4 significant figures. To round it off to 3 significant figures, we require to round it off to 6 decimal places after the decimal point.

0.0001366 = 0.000137 correct to 3 significant figures.

(6) **7.304** → 7.30 correct to 3 significant figures.

(7) **4.888** → 4.89 correct to 3 significant figures.

(8) **5.999** → 6 correct to 3 significant figures.

**Examples to round off the following measurements: **

(i) 1273.866 kg correct to 6 significant figures. It has 7 significant figures. To round it off to 6 significant figures, we round it off to 2 decimal place after the decimal point.

Therefore, 1273.866 = 1273.87 correct to 6 significant figures.

(ii) 203.102 g correct to 4 significant figures. It has 6 significant figures. To round it off to 4 significant figures, we round it off to 1^{st} decimal place after the decimal point 203.102 = 203.1 correct to 4 significant figures.

(iii) 1.0718 mg correct to 2 significant figures. It has 5 significant figures. To round it off to 2 significant figures, we round it off to 1^{st} decimal place after the decimal point.

1.0718 = 1.1 correct to 2 significant figures.

(iv) 0.003674 km correct to 1 significant figure. It has 4 significant figures. To round it off to 1 significant figure, we round it off to 3 places after the decimal point.

Therefore, 0.003674 = 0.004 correct to 1 significant figure.

** Examples to rounding off to a specified unit**

(i) *Round off $ 65437 to the nearest 10 dollars.*

$ 65440 to the nearest dollar

(ii) *Round off $ 198.287 to the nearest 10 cents.*

To round off 198.287 to the nearest 10 cents, we have to round it off to 1 place of decimal.

= $ 198.30

(iii) *Round off 782.58 to the nearest dollar.*

To round off 782.58 to the nearest dollar, we have to round it off to the nearest whole number.

Therefore, $ 782.58 = $ 783 rounded to the nearest rupee dollar.

(iv) *Round off 475.095 to the nearest cents.*

To round off 475.095 to the nearest cents, we have to round it off to 2 places of decimal. 475.095 rounded off to the nearest cents is 475.10.

(v) *Round off 18.066 cm to the nearest mm.*

Since, 1 mm = 0.1 cm, so to round it off to the nearest mm, we have to round it off to one decimal places.

18.066 cm = 18.1 cm rounded off to the nearest mm or 181 mm.

(vi) *Round off 53.4278 m to the nearest cm.*

Since, 1 cm = 0.01 m, we round off 53.4278 m to the nearest cm. We have to round it off to two places of decimal.

53.427 m = 53.43 m rounded off to the nearest cm or 5343 cm.

(vii) *0.00737 kg to nearest g.*

Since, 1 g = 0.001 kg so to round off 0.00737 kg to the nearest g, we have to round it off to three places of decimal.

Therefore, 0.00737 kg = 0.007 kg rounded off to the nearest g.

(viii) *17.2262 g to the nearest mg.*

Since, 1 mg = 0.001 g so to round off 17.2262 g to the nearest mg, we have to round it off to three places of decimal.

Therefore, 17.2262 g = 17.226 g rounded off to the nearest mg.

**Related Links:**

**Significant Figures**

**Significant Figures**

**Significant Figures - Worksheets****Worksheet on Significant Figures**

8th Grade Math Practice

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