The number of digits in the measured value which include certain digits plus one uncertain (doubtful) digit are known as **significant figures**. In this article we will learn **Significant Figures Rules** and their examples.

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## Rules for Counting the Significant Figures

**Rule 1:** All non-zero digits are significant.

**Rule 2:** All zeros occurring between the non-zero digits are significant, e.g. **5400698** contains seven significant figures.

**Rule 3:** All zeros to the left of non-zero digit in a number with or without decimal point are not significant, e.g. 0.00**634** contains three significant figures.

**Rule 4:** All zeros to the right of non-zero digits in a number without decimal point are not significant, e.g. **14**000 contains two significant figures.

**Rule 5:** The zeros to the right of non-zero digits (trailing zeros) in a number with a decimal point are significant. e.g. 0.**34000** contains five significant figures.

**Note: **

Forget zeros on left but do not forget zeros on the right. Also please note that in scientific notation 23000 should be written as 23.000 × 10^{3}. Thus 23 thousands is written as **23** × 10^{3} and it contains two significant figures.

Similarly, 230 hundreds is written as **230** × 10^{2 }and it contains three significant digits.

Thus power (or exponent) of 10 is irrelevant in finding the significant figures in scientific notation. However, *all the trailing zeros appearing in the base number in it are significant*. The change of units only changes the order of exponent but not the number of significant figures. e.g. 1.40 m = **1.40** × 10^{2} cm, both have three significant figures.

## Rules for rounding off

**Rule 1:** If the digit to be dropped is less than 5, then the preceding digit is left unchanged.

e.g. 6.32 is rounded off to 6.3

**Rule 2:** If the digit to be dropped is more than 5, then the preceding digit is raised by one.

e.g. 4.86 is rounded off to 4.9

**Rule 3:** If the digit to be dropped is 5 followed by digit other than zero, then the preceding digit is raised by one.

e.g. 6.852 is rounded off to 6.9

**Rule 4:** If the digit to be dropped is 5 or 5 followed by zero, then preceding digit is left unchanged, if it is even.

e.g. 3.250 rounded off to 3.2

**Rule 5:** If the digit to be dropped is 5 or 5 followed by zero, then the preceding digit is raised by one, if it is odd.

e.g. 2.750 is rounded off to 2.8

⇒ In **addition or subtraction**, the final result should retain as many decimal places as are there in the number with the least decimal places.

e.g. 1.2 + 1.74 + 1.348 = 4.288

The final result should be rounded off to 4.3

⇒ In **multiplication or division**, the final result should retain as many significant figures as are there in the original number with the least significant figures.

e.g. 1.2 × 1.74 × 1.348 = 2.814624

The final result should be 2.8

## Significant Figures Practice

Q. Identify the number of significant figures.

- 3.0800
- 250
- 3.200 x 10
^{9} - 0.00418
- 91,600
- 0.0101
- 0.003005
- 0.00800

Answer.

a. 3.0800 – five significant figures

b. 250 – two

c. 3.200 x 10^{9 }– four

d. 0.00418 – three

e. 91,600 – three

f. 0.0101 – three

g. 0.003005- four

h. 0.00800 – three