Rules for Significant figures
The concept of significant figures may be used to indicate the degree of accuracy or precision in a
measurement. Significant figures (sf) are those digits that are known with certainty followed by the
first digit which is uncertain.
Suppose you want to find the volume of a lead cube. You could measure the length l of the side of
a lead cube with a vernier caliper (refer Figure).
Suppose this length was 1.76 cm and the volume l cm3 from your calculator reads 5.451776. The
measurement 1.76 cm was to three significant figures so the answer can only be to three significant
figures. So that the volume = 5.45 cm3.
The following rules are applied to calculate the significant figures.
1. All non-zero digits are significant. (22.2 has 3 sf)
2. All zeros between two non-zero digits are significant. (1007 has 4 sf)
3. For numbers less than one, zeros directly after the decimal point are not significant. (0.0024 has
2 sf)
4. A zero to the right of a decimal and following a non-zero digit is significant. (0.0500 has 3 sf)
5. All other zeros are not significant. (500 has 1 sf)
Scientific notation allows you to give zero significance. For example, 10 have 1 sf but 1.00 x 101
has 3sf.
6. When adding and subtracting a series of measurements, the least accurate place value in the
answer can only be stated to the same number of significant figures as the measurement of the
series with the least number of decimal places.
For example, if you add 24.2 g and 0.51 g and 7.134 g, your answer is 31.844 g which has
increased in significant digits. The least accurate place value in the series of measurements is 24.2
g with only one number to the right of the decimal point. So the answer can only be expressed to
3sf. Therefore, the answer is 31.8 g or 3.18 × 101 g.
P B Pandey
Unit 1: Measurement (Significant Digit)
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7. When multiplying and dividing a series of measurements, the number of significant figures in
the answer should be equal to the least number of significant figures in any of the data of the
series.
For example, if you multiply 3.22 cm by 12.34 cm by 1.8 cm to find the volume of a piece of wood
your initial answer is 71.52264 cm3. However, the least significant measurement is 1.8 cm with 2
sf. Therefore, the correct answer is 72 cm3 or 7.2 × 101 cm3.
8. When rounding off a number, if the digit following the required rounding off digit is 4 or less,
you maintain the last reportable digit and if it is six or more you increase the last reportable digit
by one. If it is a five followed by more digits except an immediate zero, increase the last reportable
digit. If there is only a five with no digits following, increase reportable odd digits by one and
maintain reportable even digits.
For example if you are asked to round off the following numbers to two significant numbers
6.42 becomes 6.4
6.46 becomes 6.5
6.451 becomes 6.5
6.498 becomes 6.5
6.55 becomes 6.6
6.45 becomes 6.4
As a general rule, round off in the final step of a series of calculations.
Bibliography:
Kerr, G., & Ruth, P. (2009). Physics and Physical Measurement. In Physics (3rd ed., pp. 8-9).
Melton, Vic.: IBID Press.
P B Pandey
Unit 1: Measurement (Significant Digit)
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