# floating point number

Floating point numbers or floating point numbers are numbers that are very large or very small, cannot be represented as integers and contain fractional values. The representation of floating point numbers is standardized according to IEEE 754. A floating point number consists of the mantissa and the exponent: Mantissa x 2exp.

Since many numbers cannot be represented as floating point numbers because of their digitness, floating point representation involves rounding up or down. The rounding methods are described in the IEEE standard. In the best known one, the digit with the lowest valence is rounded up or down to a fixed number. For example, when rounded to two values, the number 3.657 becomes 3.6. Extremely large and very small numbers are written in exponential notation. Thus, 100,000 becomes 1E5 or 0.000.001 becomes 1E-6.

This exponential notation with base 10 is also used in many programming languages. In this notation, the number 234.56 becomes 0.23456E3. Here, the letter "E" indicates the exponent and acts as a separation between mantissa and exponent.