## Significant Figures

### How to Find the Number of Significant Figures

The number of significant figures represents how precisely a number is known. Check out the table.

Number | Significant Figures |
---|---|

32 | 2 |

32.5940 | 6 |

325,940 | 5 |

320,000 | 2 |

320,000.0 | 7 |

0.0000032 | 2 |

0.0320 | 3 |

Clearly, significant figures would be simple if it were not for the zeros! However, do the following to find the number of significant figures.

- The first significant figure is the non-zero digit furthest to the left.
- Continue counting to the right.
- Is there a decimal point?
- Yes: continue counting to the last digit of the number.
- No: continue counting only to the last non-zero digit.

That's it!

### Significant Figures and Computations

When doing calculations, follow these rules to determine the significant figures of your answers.

- For multiplication, division, and taking roots the result will have the same number of significant figures as the input number with the least number of significant figures.
- For addition and subtraction, the last significant figure in the result has the
*place value*of the input number whose last significant figure has the largest place value.

Input | Result |
---|---|

3.0 x 1.0 | 3.0 |

3.0 x 1 | 3 |

3,472 x 12 | 42,000 |

2 x 2.075 | 4 |

See these two rules in action: $$ 3.0 \times 1.0 = 3.0 $$ $$ 3.0 \times 1 = 3 $$ $$ 3,472 \times 12 = 42,000 $$ $$ 2 \times 2.075 = 4 $$