1.1 Significant Figures (Part 1)

1.1 Significant Figures (Part 1)

1. Significant figures are the relevant digits in an integer or a decimal number which has been rounded up to a value according to a degree of accuracy.

2. In rounding off positive numbers to a given number of significant figures, the significance of zero is shown as below.

(a) All non-zero digits in a number are significant figures (s. f.).
Example:
(i) 568 (3 s. f.)
(ii) 36.97 (4 s. f.)

(b) All zeroes between non-zero digits are significant.
Example:
(i) 7001 (4 s. f.)
(ii) 3.04 (4 s. f.)
(iii) 22.054 (4 s. f.)

(c) All zeroes that lie on the right of a non- zero digit in a decimal are significant.
Example:
(i) 0.70 (2 s. f.)
(ii) 4.500 (4 s. f.)
(iii) 3.00 (3 s. f.)

(d) Zeroes that lie on the left of a non-zero digit in a decimal are not significant.
Example:
(i) 0.05 (1 s. f.)
(ii) 0.0040 (2 s. f.)
(iii) 0.07040 (4 s. f.)

(e) Zeroes at the end of a whole number are to be considered as non significant unless stated otherwise.
Example
(i) 40 (1 s. f.)
(ii) 3670 (3 s. f.)
(iii) 704200 (4 s. f.)

Example 1:
Round off the following numbers correct to three significant figures.
(a) 246 = 246 (3 s. f.)
(b) 2463 = 2460 (3 s. f.)
(c) 24632 = 24600 (3 s. f.)
(d) 0.00745 = 0.00745 (3 s. f.)
(e) 0.007453 = 0.00745 (3 s. f.)
(f) 0.007455 = 0.00746 (3 s. f.)
(g) 0.007403 = 0.00740 (3 s. f.)

Example 2:
Round off each of the following numbers to the number of significant figures indicated in brackets.
(a) 3548 (2 s. f.)
(b) 0.5089 (3 s. f.)
(c) 33.028 (1 s. f.)
(d) 0.40055 (3 s. f.)
(e) 0.681 (2 s. f.)
(f) 38.97 (3 s. f.)

Solution:

(a) 3500 (2 s. f.)
(b) 0.509 (3 s. f.)
(c) 30 (1 s. f.)
(d) 0.401 (3 s. f.)
(e) 0.68 (2 s. f.)
(f) 39.0 (3 s. f.)