Significant Figures

Summary

  • Any non-zero number is significant
  • Any zero between 2 non-zero numbers is significant
  • Trailing zeros are only significant if there is a decimal point
  • Leading zeros are not significant

Example

Any non-zero number is significant

Number Sig Figs
215 3
9438 4
Example

Any zero between 2 non-zero numbers is significant

Number Sig Figs
204 3
1006 4
Example

Zeros on the right are significant if there is a decimal

Number Sig Figs
500 1
500. 3
500.00 5
Example

Zeros on the left are never significant

Number Sig Figs
0.075 2
0.00043 2

Arithmetic

Multiplication and Division

Rule

The answer should contain no more significant figures than the least accurately known number.

That is, we pick the number with the fewest sig figs, and that's the number of sig figs we should round to.

Example

Round to the appropriate number of sig figs:

solution
We have:

  • 4.6 -> 2 sig figs
  • 3.52 -> 3 sig figs

We should round the final answer to the least number of significant digits (2 in this case). Thus, we have .

Addition and Subtraction

Rule

The last digit retained is set by the least precise digit

Example

Round to the appropriate number of sig figs:

solution
We have:

  • 2.36 -> 3 sig figs, 2 after the decimal point
  • 12.1 -> 3 sig figs, 1 after the decimal point

We should round the final answer to the least number of significant digits on the right of the decimal place (1 in this case). Thus, we have .