Turn a repeating decimal into a fraction

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Kira finds a decimal where one digit comes before the repeat. If x = 0.1666…, what fraction is x, in simplest form?

   1/6
2. 2.

   Luz reads a decimal with a digit before the repeat. If x = 0.8333…, what fraction is x, in simplest form?

   5/6
3. 3.

   Milo sees a decimal with a digit in front of the repeating 7. If x = 0.3777…, what fraction is x, in simplest form?

   17/45
4. 4.

   Noah decodes a decimal with two digits before the repeat. If x = 0.58333…, what fraction is x, in simplest form?

   7/12
5. 5.

   Ren gets a card with a whole number and a string of nines. If x = 2.999…, what fraction is x, in simplest form?

   3
6. 6.

   Tala meets a decimal with a 4 before a string of nines. If x = 0.4999…, what fraction is x, in simplest form?

   1/2
7. 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…
   • 10x = 7.87878…
   • 1000x = 787.87878…
8. 8.

   Bo begins a conversion at the board. Starting from x = 0.4141…, which line lets the repeats cancel when subtracted?

   • 10x = 4.14141…
   • x + 100 = 100.4141…
   • 1000x = 414.14141…
   • 100x = 41.41414…
9. 9.

   Esme writes the first line of a conversion. Starting from x = 0.9595…, which line lets the repeats cancel when subtracted?

   • 1000x = 959.59595…
   • 100x = 95.95959…
   • x + 100 = 100.9595…
   • 10x = 9.59595…
10. 10.

    Luz adds two repeating decimals in a game. In simplest form, what is 0.888… + 0.3636…?

    124/99