# exponential notation

In physics, very large and very small numbers are written with the help of powers of the number ten. For large numbers,
10^{n} with *n* a positive integer is a 1 with *n* trailing zeros:

10^{0} |
= | 1 | = | Eins |

10^{1} |
= | 10 | = | ten |

10^{2} |
= | 100 | = | a hundred |

10^{3} |
= | 1000 | = | a thousand |

10^{6} |
= | 1000000 | = | a million |

10^{9} |
= | 1000000000 | = | a billion |

10^{12} |
= | 1000000000000 | = | a trillion |

10^{15} |
= | 1000000000000000 | = | a quadrillion |

Very small fractions - numbers that differ very little from zero - can be written with the help of 10^{-n}, with *n* a positive integer (*n* is, again, the number of zeros):

10^{0} |
= | 1 | = | one |

10^{-1} |
= | 0.1 | = | one tenth |

10^{-2} |
= | 0.01 | = | one hundredth |

10^{-3} |
= | 0.001 | = | one thousandth |

10^{-6} |
= | 0.000001 | = | one millionths |

10^{-9} |
= | 0.000000001 | = | one billionths |

10^{-12} |
= | 0.000000000001 | = | one trillionth |

10^{-15} |
= | 0.000000000000001 | = | one quadrillionth |

Numbers that are not powers of ten can be written by factoring out the appropriate powers of ten. For instance,

1748 = 1.748·1000 =
1,748·10^{3},

0.00041755 = 4.1755·10^{-4}
= 4.1755E-4.

### Variants

- scientific notation
- powers of ten