A real data type is a data type

Data type

In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...

 used in a computer program

Computer program

A computer program is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute...

 to represent an approximation of a real number

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

.
Because the real numbers are not countable

Countable set

In mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor...

, computers cannot represent them exactly using a finite amount of information.
Most often, a computer will use a rational

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...

 approximation to a real number.

Rational numbers

The most general data type for a rational number

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...

 stores the numerator and denominator as integers.
See Integer

Integer (computer science)

In computer science, an integer is a datum of integral data type, a data type which represents some finite subset of the mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values....

.

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

Power of two

In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....

. 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

Fixed-point arithmetic

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the radix point...

.

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

Floating point

In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...

 and IEEE Floating Point Standard.