  # Floating-Point Arithmetic

## What is Floating-Point Arithmetic?

Floating-point arithmetic is arithmetic performed on floating-point representations by any number of automated devices. Floating-point refers to a number where the number’s decimal point, sometimes called a binary point or radix point, can be placed anywhere relative to the significant digits of the number. This feature makes it seem like the decimal point can “float.” For example, the number 123 can be also be represented as 1.23x102 by moving the decimal place. The floating-point system can be used to represent, using a fixed number of digits, the numbers of different orders of magnitude.

### Why is this Useful?

Floating-point arithmetic allows the representation of fractional values and a larger dynamic range compared to integers. Using floating-point arithmetic has some drawbacks. Speed loss on some processors and problems with accuracy can be problems of using this type of arithmetic. For many applications, the benefits of using floating-point arithmetic outweigh the problems associated with it. Programmers who understand how floating-point arithmetic works will be able to mitigate a lot of these problems. For example, floating-point arithmetic does not follow the standard rules of algebra. Programmers often make mistakes by applying normal algebraic rules, which can cause bugs in many programs.

### Applications of Floating-Point Arithmetic

• Mathematics
• Computer Programming