Are terminal decimals irrational numbers? - Answers

No, all terminal decimals are rational numbers. For a number to be irrational, its decimal representation must be non-terminal (never end) and never repeat. Here are a few terminal decimals and their fractional equivalents. Note that any number which can be expressed as any ratio of integers is rational. 0.333 = 333/1000 0.4 = 4/10 = 2/5 0.1427 = 1427/10000 In general, any terminating decimal expression has a certain number of digits after the decimal point. We will call those digits D1, D2, D3, D4, ... DN. We will ignore the whole-integer part of the number as this is rational and any rational number combined with another rational number is rational. The non-integer part (fractional-part) of this number can be expressed as the ratio: (D1D2D3...DN)/(10N) The numerator is an integer because all of the Dxs are integers from 0 to 9 inclusive. The denominator is an integer because N is the number of digits after the decimal in the terminal decimal expression, and 10 to a finite, integer power is an integer. Thus, any terminating decimal can be expressed as a ratio of two integers and is thus rational (not irrational).