# Scientific notation

## Method of writing numbers with a large amount of digits / From Wikipedia, the free encyclopedia

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**Scientific notation** is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as **scientific form** or **standard index form**, or **standard form** in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators, it is usually known as "SCI" display mode.

**More information**Decimal notation ...

Decimal notation | Scientific notation |
---|---|

2 | 2×10^{0} |

300 | 3×10^{2} |

4321.768 | 4.321768×10^{3} |

−53000 | −5.3×10^{4} |

6720000000 | 6.72×10^{9} |

0.2 | 2×10^{−1} |

987 | 9.87×10^{2} |

0.00000000751 | 7.51×10^{−9} |

In scientific notation, nonzero numbers are written in the form

*m*× 10

^{n}

or *m* times ten raised to the power of *n*, where *n* is an integer, and the coefficient *m* is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer *n* is called the exponent and the real number *m* is called the *significand* or *mantissa*.^{[1]} The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative then a minus sign precedes *m*, as in ordinary decimal notation. In normalized notation, the exponent is chosen so that the absolute value (modulus) of the significand *m* is at least 1 but less than 10.

Decimal floating point is a computer arithmetic system closely related to scientific notation.