Page 51 - ICSE Math 7

⇒ 999x = 1312.1
1312.1 13121 13,121
⇒ x = 999 = 999 × 10 = 9,990

. . 13,121
So, 1.3134 =
9,990
Approximation

The process of expressing a decimal number up to a specific number of decimal places is known as
approximating or rounding off.

Rules for rounding off
Let’s round off a number correct to 3 decimal places to understand the rules for rounding off.

(a) If the digit at the fourth decimal place, i.e., digit at the thousandth place is less than 5, omit all
the digits fourth decimal place onwards.
(b) If the digit at the fourth decimal place is 5 or more, increase the digit at the third decimal place
by 1 and omit all the digits fourth decimal place onwards.

Example 17: Round off the following numbers correct to three decimal places.
(a) 31.3247 (b) 2.7991
Solution: (a) The number closest to 31.3247 correct to three decimal places is 31.325 as the digit
at the fourth decimal place is 7 > 5.
(b) The number closest to 2.7991 correct to three decimal places is 2.799 as the digit
at the fourth decimal place is 1 < 5.

Significant figures
Significant figures represent the total number of digits present in a number. To find the number of
significant figures in a number, follow the rules given below.
(a) All the non-zero numbers are significant. For example, 1,234 and 2,987 have four significant
figures.

(b) All zeros in between non-zero numbers are significant. For example, 25,012 and 35.009 have five
significant figures.

(c) Zeros preceding the first non-zero number are not counted. For example, 0.013 and 0.0024 have
two significant figures.
(d) If a number is rounded off to a specific number of digits and as a result if the last digit becomes
zero, then that zero is significant otherwise not. For example, 24.196 when rounded off to correct
2 decimal places becomes 24.20 which has four significant figures.
Example 18: Round off the following numbers as indicated.

(a) 9.347 correct to three significant figures.
(b) 0.0244 correct to two significant figures.
(c) 0.008 correct to three significant figures.

Solution: (a) 9.347 correct to three significant figures is 9.35.
(b) 0.0244 correct to two significant figures is 0.024.
(c) 0.008 correct to three significant figures is 0.00800.

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