Approximation to Significant Figures & Decimal Places – JSS2 Mathematics Lesson Note (First Term)

Approximation writes a number in a simpler form close to its value. Significant figures (s.f.) are counted from the first non-zero digit. Decimal places (d.p.) are counted after the decimal point. When rounding, a digit from 0 to 4 becomes 0 and a digit from 5 to 9 adds 1 to the digit before it.

Behavioural objectives

By the end of the lesson, students should be able to:

• round off a number to a given number of significant figures;
• round off a number to a given number of decimal places;
• add zeros when a number has fewer decimal places than required;
• calculate and round the answer to a stated degree of accuracy.

How do you round off a number?

To round off a number, look at the digit after the last place you are keeping.

• If the digit is 0, 1, 2, 3 or 4, it changes to 0.
• If the digit is 5, 6, 7, 8 or 9, it changes to 1, and the 1 is added to the digit before it.

Worked examples

Example 1: rounding to significant figures and decimal places

Round off 492.763 to (a) 2 s.f. (b) 3 s.f. (c) 2 d.p. (d) 4 d.p.

Solution

1. 492.763 = 490 (2 s.f.). The third digit is 2, so it changes to 0.
2. 492.763 = 493 (3 s.f.). The 7 changes to 1 and is added to the 2, which becomes 3.
3. 492.763 = 492.76 (2 d.p.). In decimal places, we count after the point.
4. 492.763 = 492.7630 (4 d.p.). The number does not have 4 decimal places, so we add a zero.

Example 2: calculating and rounding the answer

Calculate the following and round your answer to the given degree of accuracy.

1. 576.175 + 20.82 (2 d.p.)
2. 8.52 × 0.0651 (3 s.f.)

Solution

1. 576.175 + 20.82 = 596.995
   596.995 = 597.00 (2 d.p.)
2. 8.52 × 0.0651 = 0.554652
   0.554652 = 0.555 (3 s.f.)

Evaluation

1. Round off 492.763 to 1 s.f.
2. Round off 492.763 to 1 d.p.
3. Write 492.763 to 5 d.p.
4. Round off 0.554652 to 2 s.f.