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.
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. 0.00634 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. 14000 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.
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 × 103. Thus 23 thousands is written as 23 × 103 and it contains two significant figures.
Similarly, 230 hundreds is written as 230 × 102 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 × 102 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.
- 3.200 x 109
a. 3.0800 – five significant figures
b. 250 – two
c. 3.200 x 109 – four
d. 0.00418 – three
e. 91,600 – three
f. 0.0101 – three
g. 0.003005- four
h. 0.00800 – three