Grade 8 Repeating Decimals as Fractions
Converting repeating decimals to fractions in grade 8, then classifying numbers as rational or irrational. Sixteen problems, printable with answers.
Convert each repeating decimal to a fraction in simplest form, then classify the last three numbers.
- 1.Write 0.777... as a fraction in simplest form.
- 2.Write 0.222... as a fraction in simplest form.
- 3.Write 0.454545... as a fraction in simplest form.
- 4.Write 0.818181... as a fraction in simplest form.
- 5.Write 0.123123... as a fraction in simplest form.
- 6.Write 0.555... as a fraction in simplest form.
- 7.Write 0.363636... as a fraction in simplest form.
- 8.Write 0.666... as a fraction in simplest form.
- 9.Write 0.111... as a fraction in simplest form.
- 10.Write 0.272727... as a fraction in simplest form.
- 11.Write 0.428571428571... as a fraction in simplest form.
- 12.Write 0.1666... as a fraction in simplest form.
- 13.Write 0.8333... as a fraction in simplest form.
- 14.Is √16 rational or irrational?
- 15.Is √10 rational or irrational?
- 16.Is 0.25 rational or irrational?
What this worksheet covers
This is a 16-problem sheet — one page to work through, one page of answers to check against. Within that, every problem is set in a short real-world situation, so the first decision is which operation the situation calls for; several problems use mixed numbers, which have to be handled without dropping the whole-number part. It is written against Common Core 8.NS.1 — part of The Number System in grade 8.
Skills practiced
The skill underneath these problems is negative rational numbers, complex fractions, repeating decimals. Working the page asks a student to read a situation and choose an operation before computing, work in fractional units and simplify the result, and keep decimal points aligned rather than right-aligning digits out of habit. Watch how the answers are reached, not just whether they land — the method is what carries into grade 9.
How to use this worksheet
Expect this to take twenty minutes or so of genuine attention. At grade 8, work in fractions rewards care over speed — a student who rushes it will get the arithmetic right and the signs wrong. Print a second copy before writing on the first; a sheet worked twice a week apart tells you far more than a sheet worked once.
One mistake to watch for
Bigger denominator means bigger fraction: 1/8 is judged larger than 1/3.
Whole-number ordering is being applied to the denominator, where the relationship is inverted.
Cut the same strip into 3 and into 8 pieces side by side. More pieces from one whole means smaller pieces — the denominator counts how many the whole was split into.
Related worksheets
A step either side
Fractions either side of grade 8, for stepping the difficulty rather than repeating it.
- Grade 7 Complex Fractions and Unit Rates — grade 7, 16 problems
No sign-up and no paywall — download the fractions sheet, print it, and the answers for all sixteen problems are on the page behind it.