It can be tempting, when calculating an answer or working with numbers, to just record whatever answer a calculator or computer pumps out. For example: Say we want to multiply 24.8201 by 0.0946. Simply punching these numbers into a calculator we get 0.45598146.
However, writing out every calculated value out to eight, nine, ten places will make your data look sloppy, needlessly complicate calculations, and most importantly – will greatly exaggerate the level of precision with which our measurements are being made.
Counting Significant Figures
- All non-zero integers are significant figures.
123 has three significant figures
987654 has six significant figures
- Zeroes located between non-zero integers are significant figures.
701 has three significant figures
60204 has five significant figures
- All zeroes to the left of the first non-zero digit and to the right of the last are not significant.
3.14 has three significant figures
15900000000000 also has three significant figures
0.0078 has two significant figures
0.00000000000000000000000017 also has two significant figures
Operations With Significant Figures
When performing any operation, whether it be addition, subtraction, multiplication, division, etc – your calculated value can be no more precise than the least precise value in the operation. That is to say, the significant figures of your calculated value should be rounded up to match those of the value with the least number of sig figs. Scientific notation should also be used if appropriate.
24.8201 x 0.0946 = 0.45598146 ⇒ .0456
6563 x 107.28 = 704078.64 ⇒ 704100 -or- 7.041 x 105