Grade 8 · Math

8th grade Turn a repeating decimal into a fraction worksheet

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Turn a repeating decimal into a fraction

Grade 8 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Kira finds a repeating decimal on a quiz card. If x = 0.111…, what fraction is x, in simplest form?
Luz reads a repeating decimal off a calculator. If x = 0.3030…, what fraction is x, in simplest form?
Noah spots a repeating decimal in a math book. If x = 0.9090…, what fraction is x, in simplest form?
Pia tests a repeating decimal in a puzzle. If x = 0.7272…, what fraction is x, in simplest form?
Ren reads a repeating decimal with a whole part. An improper fraction is fine. If x = 2.333…, what fraction is x, in simplest form?
Tala finds a repeating decimal with a whole part. An improper fraction is fine. If x = 1.8181…, what fraction is x, in simplest form?
Strip of the digits: 4.[6] [6] [6] ... Zee meets a repeating decimal with a whole part. An improper fraction is fine. If x = 4.666…, what fraction is x, in simplest form?
8.
Ari matches a repeating decimal to a fraction card. Which fraction equals 0.8484…?
- 28/33
- 84/100
- 33/28
- 84/9
9.
Esme matches a repeating decimal to a fraction on a game card. Which fraction equals 0.1414…?
- 99/14
- 14/100
- 14/99
- 14/9
10.
Jun checks which fraction a repeating decimal equals. Which fraction equals 0.5757…?
- 19/33
- 33/19
- 57/9
- 57/100

Turn a repeating decimal into a fraction. Every version has 10 questions, and the answer key prints on the second page.

I can write a repeating decimal like 0.4545… as a fraction in simplest form: 5/11.
I can say why the answer needs a subtraction: x and 100x have the same repeat, so it cancels.
I can handle a whole part (2.333…), digits in front (0.1666…), and a string of nines (0.999… = 1).

Standard: 8.NS.A.1 (decimal expansions: repeating decimals are rational)

repeating decimal: A decimal with a block of digits that repeats forever, like 0.4545….

block: The digits that repeat: in 0.4545… the block is 45.

front digits: Digits between the point and the block: in 0.1666… the front digit is 1.

cancel: Subtract two lines whose repeats match, and the repeat disappears.

simplest form: A fraction whose top and bottom share no factor other than 1.

Your child read a repeating decimal as if it ended, for example 0.45 repeating as 45/100.

Your child used the wrong number of nines on the bottom.

Your child left the front digits out of a decimal like 0.1666….

Ask: does 0.4545… stop after the 45, or does it keep going?

Ask: how many digits repeat? That many nines go under the block.

Ask: which digits come before the repeat, and are they part of the number?

What is the most common mistake with turn a repeating decimal into a fraction?

Your child read a repeating decimal as if it ended, for example 0.45 repeating as 45/100.

How can I help my child with turn a repeating decimal into a fraction?

Ask: does 0.4545… stop after the 45, or does it keep going?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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