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.
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.
Why this sheet works
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.
How this one works
One question from this sheet, worked through a step at a time.
0.251
0.251
0.251
a decimal that stops can be written over a power of ten
0.251isrational
One question decides it: can this be written as a fraction of two whole numbers? Not "does it look tidy", and not "is there a root sign" — those are the two guesses that go wrong.
Look at what kind of number it is: a decimal that stops can be written over a power of ten.
So it CAN be written as a fraction. That makes it rational.
Is each number rational or irrational? Circle one.
10.251Rational/Irrational
2−29Rational/Irrational
36/2Rational/Irrational
40.282828…Rational/Irrational
5√10Rational/Irrational
60.29Rational/Irrational
Rational or irrational · Fractions, decimals and πAnswer key
1. 0.251: rational — a decimal that stops can be written over a power of ten2. −29: rational — every whole number is a fraction over 13. 6/2: rational — it is already written as one whole number over another4. 0.282828…: rational — a decimal that repeats forever can still be written as a fraction5. √10: irrational — 10 is not a perfect square, so its root never ends and never repeats6. 0.29: rational — a decimal that stops can be written over a power of ten
