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.
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Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
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
Sixteen integers problems fill this mixed review page; problem 6 asks "Write 0.555... as a fraction in simplest form.", and the sheet stays at that level throughout. What makes this set particular: each problem arrives as a few sentences of context rather than a bare expression and several problems use mixed numbers, which have to be handled without dropping the whole-number part. Further down, problem 11 asks "Write 0.428571428571... as a fraction in simplest form.". Common Core 8.NS.1 is the slot this page fills.
Skills practised
At grade 8, integers is about integer exponents, the product, quotient and power rules, negative exponents and scientific notation, and this sheet takes one slice of that. What a student is asked to do here is grade 8 Repeating Decimals as Fractions. To finish it, a student has to read a situation and choose an operation before computing and keep the decimal points aligned. Fifteen different answers appear across the sixteen problems, so a student cannot copy one result down the page.
About the mixed review format
The 16 problems are deliberately assorted — problem 6, "Write 0.555... as a fraction in simplest form." is followed by something of another shape — so the student has to read each one rather than run the last method again. Mixing the four operations on signed numbers forces the student to pick the right sign rule for each problem.
Set A, Set B and Set C
Set A is the original MathSheetLab worksheet; Sets B and C keep its structure and redraw the numbers, with each answer recomputed rather than copied. Where Set A's problem 9 is "Write 0.111... as a fraction in simplest form.", Set B's is "Write 0.555... as a fraction in simplest form.".
How to use this worksheet
Work it without a calculator. Every one of the sixteen integers problems is designed to be done by hand, and reaching for a calculator at grade 8 skips exactly the reasoning being built. If more than a third of the sixteen problems come back wrong, stop and step back a grade in integers rather than assigning Set B.
Other grade 8 integers formats
The same skill in the other formats available at this grade.
- Drill — 8.EE.1 — Integer Exponents: Mixed Operations Practice, 22 problems
- Timed Drill — Grade 8 Multiplying Numbers in Scientific Notation, 16 problems
- Missing Number — Grade 8 Integers Missing Number, 24 problems
- Word Problems — Grade 8 Integers Word Problems, 10 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- Grade 7 Subtracting Rational Numbers — grade 7, 20 problems
Mixed Review sheets in other grade 8 topics
Six PDFs, no sign-up: three versions of this grade 8 integers mixed review and three answer keys, each sixteen problems long.