significant figures and decimal places

SIGNIFICANT FIGURES AND DECIMAL PLACES

Decimal places

1. Count along the digits to the required number of decimal places.2. Look at the next digit

• If it is less than 5, leave the digit before it as it is.• If it is 5 or more, you must round up the digit before it.

It is often useful to give an answer to a number of decimal places.

If you are asked to round a number to 2 decimal places you must have exactly 2 digits after the decimal point.

The following rules are used:

Examples

1 Write 5.3472 correct to 2 decimal places.

5.3472 the next digit is 7 so you must round up

5.3472 = 5.35 to 2 d.p.

Examples

2 Write 36.4319 correct to 2 decimal places.

36.4319 the next digit is 1 so the digit before it will not change

36.4319 = 36.43 to 2 d.p.

Examples

3 Write 0.0088 correct to 2 decimal places.

0.0088 the next digit is 8 so you must round up

0.0088 = 0.01 to 2 d.p.

Examples

4 Write 126.2043 correct to 2 decimal places.

126.2043 the next digit is 4 so the digit before it will not change

126.2043 = 126.20 to 2 d.p. note: you must keep the 0 in your answer

Examples

5 Write 27.998 correct to 2 decimal places.

27.998 the next digit is 8 so you must round up

27.998 = 28.00 to 2 d.p.

Examples

6 Write 49.3254 correct to 3 decimal places.

49.3254 the next digit is 4 so the digit before it will not change

49.3254 = 49.325 to 3 d.p.

Examples

7 Write 7.8798 correct to 3 decimal places.

7.8798 the next digit is 8 so you must round up

7.8798 = 7.880 to 3 d.p.

Significant figures

1. Count along the digits to the required number of significant figures. (The most significant figure is the first non-zero figure.)2. Look at the next digit

• If it is less than 5, leave the digit before it as it is.• If it is 5 or more, you must round up the digit before it.

You may also be asked to round to a number of significant figures.

To round a number to a given number of significant figures use the following rules:

Examples

1 Write 53872 correct to 2 significant figures.

53872 the next digit is 8 so you must round up

53872 = 54000 to 2 s.f.

Examples

2 Write 76408 correct to 1 significant figure.

76408 the next digit is 6 so the digit before it will not change

76408 = 80000 to 1 s.f.

Examples

3 Write 6.439 correct to 3 significant figures.

6.439 the next digit is 9 so you must round up

6.439 = 6.44 to 3 s.f.

Examples

4 Write 0.00342 correct to 2 significant figures.

0.00342 the next digit is 2 so the digit before it will not change

0.00342 = 0.0034 to 2 s.f.

Examples

5 Write 0.00899 correct to 2 significant figures.

0.00899 the next digit is 9 so you must round up

0.00899 = 0.0090 to 2 s.f.

Estimating

1. Round each of the numbers to 1 significant figure.2. Do the calculation using your rounded numbers.

It is important that you know how to check if your answer to a calculation is a sensible answer.

To estimate the answer to a calculation use the following steps:

Examples

1 Estimate the answer to 5.78 2.14

5.78 6 2.14 2

5.78 2.14 6 2 12

2 Estimate the answer to 28.217 2.97

28.217 30 2.97 3

28.217 2.97 30 3 10

Examples

3 Estimate the answer to 42.8 4.113.22 5.96

42.8 40 4.114

3.22 3 5.96 6

42.8 4.113.22 5.96

40 43 6

3618

2

Examples

4 Estimate the answer to

389 813.7(40.6)2

389 400 813.7 800 40.6 40

389 813.7(40.6)2

400 80040 40

200

10 20