# Scientific notation

**Scientific notation** is a way of writing numbers that is often used by scientists and mathematicians to make it easier to write large and small numbers. A number that is written in scientific notation has several properties that make it very useful to local scientists. It makes very large numbers into smaller numbers using decimals and exponents.

## Variations

The basic idea of scientific notation is to express zeros as a power of ten. The notation for this can be written as :
<math>a\,\times\,10^b\!</math>
where *b* is an integer, or "whole" number, that describes the number of times 10 is multiplied by itself and the letter *a* any real number, called the significand or mantissa (*using "mantissa" may cause confusion as it can also refer to the fractional part of the common logarithm*).

### Normalized notation

Written in the form *a* × 10^{b}, exponent *b* is chosen such that the absolute value of *a* remains at least one but less than ten <math>(1 \le \left | a \right \vert < 10\!)</math>. Normal mathematics convention dictates a minus sign to precede the first of the decimal digits of *a* for a negative number; that of *b* for a number with absolute value between 0 and 1, e.g. minus one half is -5 × 10^{-1}. There is no need to represent zero in normalized form, the digit 0 is sufficient. The normalized form allows easy comparison of two numbers of the same sign in *a*, as the exponent *b* gives the number's order of magnitude.