Which of the following is a rational decimal? a 3.145279856... b .003003003003 c 1/8 d 0.001000100001000001

A number is rational if it is a quotient a÷b of two integers a and b where b≠0.

or, equivalently,

A rational number is a number that satisfies an equation of the form a=bx, where a and b are integers and b≠0.

So 0.333¯¯¯ is a rational number because it is the result we get when we divide 1 by 3, or equivalently, because it is a solution to 1=3x. However, numbers like π and 2√ are not rational because neither of them satisfies an equation of the form a=bx where a and b are integers. This is actually tricky to show and is an exercise left to high school or college.

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