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 - Challenge Me

NameDate

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

Kira finds a decimal where one digit comes before the repeat. If x = 0.1666…, what fraction is x, in simplest form?
Milo sees a decimal with a digit in front of the repeating 7. If x = 0.3777…, what fraction is x, in simplest form?
Noah decodes a decimal with two digits before the repeat. If x = 0.58333…, what fraction is x, in simplest form?
Pia has a puzzle card with a decimal made only of nines. If x = 0.999…, what fraction is x, in simplest form?
Ren gets a card with a whole number and a string of nines. If x = 2.999…, what fraction is x, in simplest form?
Zee reads a decimal with a whole part, a 6 and a string of nines. If x = 1.6999…, what fraction is x, in simplest form?
7.
Ari starts to turn a repeating decimal into a fraction. Starting from x = 0.7878…, which line lets the repeats cancel when subtracted?
- x + 100 = 100.7878…
- 100x = 78.78787…
- 1000x = 787.87878…
- 10x = 7.87878…
8.
Esme writes the first line of a conversion. Starting from x = 0.9595…, which line lets the repeats cancel when subtracted?
- x + 100 = 100.9595…
- 100x = 95.95959…
- 10x = 9.59595…
- 1000x = 959.59595…
Kira adds two repeating decimals from a puzzle. In simplest form, what is 0.444… + 0.1212…?
Luz adds two repeating decimals in a game. In simplest form, what is 0.888… + 0.3636…?

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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