Is 0.333 repeating an irrational number?
A rational number is any number that can be expressed as a fraction of two integers, say where q is not zero. … Take as an example of a rational number with a repeating decimal expansion, 0.333…. I will not go into this here, but a number whose decimal expansion is not terminating or repeating is an irrational number.
Are repeating decimals such as 0.333 a rational number?
It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of 13 becomes periodic just after the decimal point, repeating the single digit “3” forever, i.e. 0.333….
