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Significant figures Significant Figures Every measurement has a degree of uncertainty. The number of reliably known digits in a number is called the number of significant figures. For example the radius of the earth is 695 000 000 m. This number is not exact but has been “rounded off” to the nearest million metres. We say the number has three significant figures. The zeros at the end of this number are “not significant”. In some numbers zeros are significant. For example in a measurement stated as 605mm the zero is significant. The rules for determining the number of significant figures are as follows: • • • • all non-zero digits are significant zeros between non-zero digits are significant zeros at the end of a decimal are significant all other zeros are not significant. Using these rules 65.00 has four significant figures but each of the numbers 65, 6500, and 0.0065 has only two significant figures. Example Number 45630 708 0.453 0.091 0.620 Number of Significant Figures 4 3 3 2 3 When performing calculations the final answer should contain only as many significant figures as the number with the least number of significant figures. Keep at least one more digit during the calculations then round to the required number of significant figures for the final answer. Do not confuse decimal places with significant figures. 0.175, 1.175 and 11.175 all have three decimal places, but have respectively, three, four and five significant figures . Page 1 of 2 Examples 1. Round the following to the numbers to three significant figures. (a) 54.8965 Answer = 54.9 Rounding to one decimal place will give three significant figures. Because the next digit is greater than 4 the 8 must be rounded to a 9. (b) 23 426 Answer = 23 400 Rounding to the nearest hundred will give three significant figures. Replace the next two digits with zeros. (c) 2.501 Answer = 2.50 Rounding to two decimal places will give three significant figures. Remember if a zero is included at the end of a decimal number it is significant. 2. Round the following number to one significant figure. (d) 0.000034056 Answer = 0.00003 The leading zeros are not significant. This number will have one significant figure when rounded to five decimal places. Exercise 1 Round the following numbers to the number of significant figures given in the brackets. (a) (b) (c) (d) (e) (f) (g) Exercise 2 96 302 54.918 0.003702 561 045 8.007 23 654 067 0.030048 (2 significant figures) (4 significant figures) (3 significant figures) (3 significant figures) (1 significant figure) (5 significant figures) (4 significant figures) Perform the following calculation giving your answer to the correct number of significant figures. 12.2 × 8.0 × 0.001 2.5 Answers 1. (a) 96 000 (b) 54.92 (c) 0.00370 (d) 561 000 (e) 8 (f) 23 654 000 (g) 0.03005 2. 0.04 Page 2 of 2