APPENDIX B
Significant Figures
Record measurements to the nearest significant figure you can
read. For example you can read your ruler to the nearest mm (=0.1 cm),
and can make a rough estimate of a fraction of a mm (equivalent to
hundredths of a cm). Therefore any measurements made with the cm scale
on your ruler are only significant to two decimal places. So you should
not include in your Data Table more than two figures to the right of the
decimal point for any measurements made with the ruler. Each time you use
a measuring instrument you should decide to what accuracy you can read
the scale, and then decide how many significant figures you should enter
in your data table. Why should you not enter more figures to the right
of the decimal than the significant figures? Your calculator will carry
sufficient significant numbers, so that no rounding errors will occur.
Below are some examples of measurements with the number of significant
figures given, and the corresponding measurements in scientific or
exponential notation. When numbers are very small or very large, you
should use exponential notation. How many significant figures should you
quote in your final results when you combine measurements which have
different numbers of significant figures?
| Measurement | Significant Figures | Exponential Notation |
| 1.329 N | 4 | 1.329 x 100 N |
| 603.1 N | 4 | 6.031 x 102 N |
| 0.003 N | 1 | 3 x 10-3 N |
| 0.79 N | 2 | 7.9 x 10-1 N |
| 200 N | 1 | 2 x 102 N |
| 7,820,000,001 | 10 | 7.820000001 x 109 N |
Take the example of the following four measurements which you wish to
combine by adding:
| 0.55 | m |
| 2 | m |
| 2.233 | m |
| 0.6578 | m |
| ------- | -- |
| 5.4408 | m |
How many significant figures should you give for the sum of these measurements?
The accuracy of your final result is determined by the least number of
significant figures in your data set. The accuracy of the sum is no
better than that of the least accurate measurement which in the example
above is one significant figure. Therefore the sum of the measurements
above should be quoted as 5.
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![[AppendixC]](appbutC.gif)
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