# Notation

## Significant digits

All digits in a number are significant except

- zeros on the left;
- zeros on the right
*if there is no decimal point*.

In counted numbers like *twelve eggs* or numbers defined as equalities such as
$\displaystyle 1 \, \text{km} = 1000 \, \text{m}$,
the number of significant digits is infinite.

When you add or subtract numbers, the answer should have no more *decimal places* than the given value with the fewest. When you do anything else, the answer should have no more *significant digits* than the given value with the fewest.

## Scientific notation

We use scientific notation for small numbers and big numbers. It is also useful for making it very clear how many significant digits a number has. For example, we would assume that 100 has one significant digit. To show that there are three, you have to use 1.00 × 10^{2}.

## Metric prefixes

Make sure you remember all the metric prefixes. Also, remember that you can multiply by 3.6 to convert a speed from m/s to km/h (and divide to go the other way).

Prefix | Factor |
---|---|

G | 10^{9} |

M | 10^{6} |

k | 10^{3} |

h | 10^{2} |

da | 10^{1} |

— | 10^{0} |

d | 10^{−1} |

c | 10^{−2} |

m | 10^{−3} |

μ | 10^{−6} |

n | 10^{−9} |