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 .
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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
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