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.

## Example

24.8201 x 0.0946 = 0.45598146 ⇒ .0456

6563 x 107.28 = 704078.64 ⇒ 704100 -or- 7.041 x 10^{5}