A real data type is a data type used in a computer program to represent an approximation of a real number. Because the real numbers are not countable, computers cannot represent them exactly using a finite amount of information. Most often, a computer will use a rational approximation to a real number.
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Rational numbers
The most general data type for a rational number stores the numerator and denominator as integers.
Fixed point numbers
A "fixed point" data type assumes a specific denominator for all numbers. The denominator here is most often a power of two. For example, in a system whose denominator is 65,536 (216), the hexadecimal number 0x12345678 means 0x12345678/65536 or 305419896/65536 or 4660 + 22136/65536 or about 4660.33777. See fixed-point arithmetic.
Floating point numbers
A "floating point" type is a compromise between the flexibility of a general rational type and the speed of fixed-point arithmetic. It uses some of the bits in the data type to specify a power of two for the denominator. See floating point and IEEE Floating Point Standard.
Decimal numbers
Similar to fixed-point or floating-point numbers, except with a denominator that is a power of 10 instead of a power of 2.