Can the number be written as a fraction of two whole numbers? That one question decides it. These free printable worksheets sort fractions, terminating and repeating decimals, and π.
If they get stuck
The answer key prints on a separate page.
A fraction is already the answer to its own question, so ⅔ is rational. Decimals carry the trap: 0.75 stops and 0.333… repeats, and both can be written as fractions, so both are rational. Only a decimal that neither stops nor repeats is irrational — which is why no question shows a run of digits trailing into an ellipsis, since that could be the start of a repeat nobody has reached and would have no honest answer.
π is the irrational number a child can name without a root sign, and it earns its place on every sheet for exactly that reason. This is the numbers half of the sort, kept apart from the roots page so the decimal rule — stops or repeats means rational — gets its own attention. Every number here is identified from its form, which is the skill the standard asks for and what makes the key checkable.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Rational or irrational numbers, step by step