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Write repeating decimals as fractions

Grade 8 math · Fieldbook Learning

Name ______________________ Date __________

Let x be the decimal. Multiply by a power of 10 to line up the repeating part, then subtract.

  1. The decimal 0.515151… has the digits 51 repeating forever. Write it as a fraction in lowest terms.
  2. The decimal 0.595959… has the digits 59 repeating forever. Write it as a fraction in lowest terms.
  3. The decimal 0.828282… has the digits 82 repeating forever. Write it as a fraction in lowest terms.
  4. The decimal 0.111111… has the digits 1 repeating forever. Write it as a fraction in lowest terms.
  5. The decimal 0.222222… has the digits 2 repeating forever. Write it as a fraction in lowest terms.
  6. The decimal 0.777777… has the digits 7 repeating forever. Write it as a fraction in lowest terms.
  7. The decimal 0.466666… has a leading 4 followed by the digits 6 repeating forever. Write it as a fraction in lowest terms.
  8. The decimal 0.617171… has a leading 6 followed by the digits 17 repeating forever. Write it as a fraction in lowest terms.
  9. The decimal 0.949494… has the digits 94 repeating forever. Write it as a fraction in lowest terms.
  10. The decimal 0.101010… has the digits 10 repeating forever. Write it as a fraction in lowest terms.
  11. The decimal 0.161616… has the digits 16 repeating forever. Write it as a fraction in lowest terms.
  12. The decimal 0.753535… has a leading 7 followed by the digits 53 repeating forever. Write it as a fraction in lowest terms.
  13. The decimal 0.377777… has a leading 3 followed by the digits 7 repeating forever. Write it as a fraction in lowest terms.
  14. The decimal 0.622222… has a leading 6 followed by the digits 2 repeating forever. Write it as a fraction in lowest terms.
  15. The decimal 0.811111… has a leading 8 followed by the digits 1 repeating forever. Write it as a fraction in lowest terms.
  16. The decimal 0.937373… has a leading 9 followed by the digits 37 repeating forever. Write it as a fraction in lowest terms.
  17. The decimal 0.555555… has the digits 5 repeating forever. Write it as a fraction in lowest terms.
  18. The decimal 0.189898… has a leading 1 followed by the digits 89 repeating forever. Write it as a fraction in lowest terms.
  19. The decimal 0.322222… has a leading 3 followed by the digits 2 repeating forever. Write it as a fraction in lowest terms.
  20. The decimal 0.444444… has the digits 4 repeating forever. Write it as a fraction in lowest terms.
More free practice: fieldbooklearning.com/practice/grade-8/write-repeating-decimals-as-fractions/

Answer key: Write repeating decimals as fractions

  1. 17/33
  2. 59/99
  3. 82/99
  4. 1/9
  5. 2/9
  6. 7/9
  7. 7/15
  8. 611/990
  9. 94/99
  10. 10/99
  11. 16/99
  12. 373/495
  13. 17/45
  14. 28/45
  15. 73/90
  16. 464/495
  17. 5/9
  18. 94/495
  19. 29/90
  20. 4/9