Deutsches Museum in the context of Floating-point arithmetic

In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base.Numbers of this form are called floating-point numbers.

For example, the number 2469/200 is a floating-point number in base ten with five digits:$${\displaystyle 2469/200=12.345=\!\underbrace {12345} _{\text{significand}}\!\times \!\underbrace {10} _{\text{base}}\!\!\!\!\!\!\!\overbrace {{}^{-3}} ^{\text{exponent}}}$$However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits.The nearest floating-point number with only five digits is 12.346.And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits.In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common.