What is the method of representing approximations of real numbers in computing?

Floating point representation is the method used to approximate real numbers in computing. This representation allows for a wide range of values to be represented, including very large and very small numbers, by using a form that consists of a significand (or mantissa) and an exponent. The floating point format enables computers to carry out calculations involving real numbers efficiently despite the inherent limitations in precision when dealing with decimal numbers.

The significant advantage of floating point representation lies in its ability to support decimal points and the fractional part of numbers, which is crucial for applications that require high levels of precision, such as scientific computations or graphics processing. This method adheres to the IEEE 754 standard, which defines how floating point numbers are stored and calculated in binary systems, ensuring consistency across different computer architectures.