Scientific Notation

Scientific computations often involve very large or very small numbers. In a small number like 0.000000123, the leading zeros are merely placeholders which mark the position of the decimal point.

In scientific notation, the position of the decimal point is relocated using multiplication by a power of 10.

For example, = 0.000000123 . The resulting number consists of a mantissa (1.23) multiplied by 10 raised to an exponent (-7).

Similarly, large numbers are handled using a positive exponent to relocate the decimal point to the right. For example, the number 12300000000 can be written as .

When using scientific notation, the number of digits which are included in the mantissa indicates the accuracy to which the number is known. The digits in the mantissa are said to be significant, to emphasize that the zeros produced by relocating the decimal point do not affect the accuracy of the number.

To provide a standard way of writing numbers in scientific notation, the mantissa is normalized by adjusting the exponent so that the mantissa is greater than 1 and less than 10.

Example:

In normalized form, the number becomes .

Note that the number 0 can not be put into normalized form.

When scientific notation is used with number bases other than 10, the representation is called floating point.