SIGNIFICANT FIGURES AND DECIMAL PLACES

Decimal places 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: Count along the digits to the required number of decimal places. 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.

5.3472 Examples 1 Write 5.3472 correct to 2 decimal places. the next digit is 7 so you must round up 5.3472 = 5.35 to 2 d.p.

36.4319 Examples 2 Write 36.4319 correct to 2 decimal places. the next digit is 1 so the digit before it will not change 36.4319 = 36.43 to 2 d.p.

0.0088 Examples 3 Write 0.0088 correct to 2 decimal places. the next digit is 8 so you must round up 0.0088 = 0.01 to 2 d.p.

126.2043 Examples 4 Write 126.2043 correct to 2 decimal places. 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

27.998 Examples 5 Write 27.998 correct to 2 decimal places. the next digit is 8 so you must round up 27.998 = 28.00 to 2 d.p.

49.3254 Examples 6 Write 49.3254 correct to 3 decimal places. the next digit is 4 so the digit before it will not change 49.3254 = 49.325 to 3 d.p.

7.8798 Examples 7 Write 7.8798 correct to 3 decimal places. the next digit is 8 so you must round up 7.8798 = 7.880 to 3 d.p.

Significant figures 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: 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.

53872 Examples 1 Write 53872 correct to 2 significant figures. the next digit is 8 so you must round up 53872 = 54000 to 2 s.f.

76408 Examples 2 Write 76408 correct to 1 significant figure. the next digit is 6 so the digit before it will not change 76408 = 80000 to 1 s.f.

6.439 Examples 3 Write 6.439 correct to 3 significant figures. the next digit is 9 so you must round up 6.439 = 6.44 to 3 s.f.

0.00342 Examples 4 Write 0.00342 correct to 2 significant figures. the next digit is 2 so the digit before it will not change 0.00342 = 0.0034 to 2 s.f.

0.00899 Examples 5 Write 0.00899 correct to 2 significant figures. the next digit is 9 so you must round up 0.00899 = 0.0090 to 2 s.f.

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

Examples 1 Estimate the answer to 2 Estimate the answer to

Examples 3 Estimate the answer to

Examples 4 Estimate the answer to 10 20