Addition and Subtraction of Approximations – JSS1 Mathematics Lesson Note (Second Term)

To add or subtract approximations, first work out the sum or difference using the exact numbers. Then round the answer to the number of significant figures (s.f.) the question asks for. The calculation must be done before the rounding. For example, 674 + 975 = 1649, which is 1650 to 3 s.f.

Behavioural objectives

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

• add numbers and give the answer to a stated number of significant figures;
• subtract numbers and give the answer to a stated number of significant figures;
• write a given number to a stated number of significant figures.

How do you add and subtract numbers to a given number of significant figures?

Example 1

Work out each of the following, then give the answer to the stated number of significant figures.

1. 674 + 975 (3 s.f.)
2. 805 + 912 (4 s.f.)
3. 3076 – 621 (2 s.f.)
4. 728 – 97.979 (4 s.f.)

Solutions

1. 674 + 975 = 1649 (1650 to 3 s.f.). Note that you must add the numbers before converting to the degree of accuracy.
2. 805 + 912 = 1717 (1717 to 4 s.f.)
3. 3076 – 621 = 2455 (2500 to 2 s.f.)
4. 728 – 97.979 = 630.021 (630.0 to 4 s.f.)

Evaluation

Write each of the following to the stated number of significant figures.

1. 42.4739 to 5 s.f.
2. 67.3258 to 3 s.f.
3. 879.9087 to 4 s.f.
4. 304.385 to 5 s.f.