Number - Floating-point (system|notation) - (Float|Double) - Approximate numeric

About

The term floating point refers to the fact that the number's radix point can float, that is, it can be placed anywhere relative to the significant digits of the number.

They are fractional numbers written with a decimal point, like 1.970

The floating-point representation is the most widely representation of real numbers.

Floating point describes a numeral system for representing numbers that would be too large or too small to be represented as number. See also: Arbitrary-precision_arithmetic

The value 4.32682E-21F is an example of a float.

Decimal point Position

The position of the decimal point is given by the exponent.

Floating-point numbers can have:

  • a decimal point anywhere from the first to the last digit
  • any number of digits after the decimal point
  • no decimal point at all.

Example

The number 1.25 has:

The number 5 has:

  • a positive sign
  • a mantissa value of 1.01 (in binary),
  • and an exponent of 2 because the mantissa is multiplied by 4 (2 to the power of the exponent 2); 1.25 * 4 equals 5.

Computer Implementation

Syntax and Properties

Floating-point numbers are made up of four components:

  • Digits (normally only significant digit)
  • The sign, which is positive or negative.
  • The mantissa, which is a single-digit binary number followed by a fractional part.
  • The exponent, which tells where the decimal point is located in the number represented.

Sign

The sign is positive or negative

Mantissa

The mantissa is a single-digit binary number followed by a fractional part.

For example:

In the SQL float or double data type , the precision gives the maximum length of the mantissa.

Exponent

An exponent may optionally be used following the number to increase the range (for example, 1.777 e-20).

It tells where the decimal point is located in the number.

Documentation / Reference


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