Recurring Decimals as Exact Fractions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Endless decimals, exact fractions

Mathematics · Number Representation & Place Value · ages 14-15
Name ______________________   Date ____________

  1. Write 3/8 as a decimal.

    Answer: ______________

  2. What is 0.777... (the 7 repeating forever) as a fraction in lowest terms?

    • 7/9
    • 7/10
    • 3/4
    • 7/8

  3. What is 0.777 (7 repeating forever) as a fraction in lowest terms?

    • 7/10
    • 7/9
    • 3/4

  4. Amara says 0.999 (9 repeating forever) is exactly equal to 1. Is Amara right?

    Circle one:   True   False

  5. What is 0.4545 (45 repeating) as a fraction in lowest terms?

    • 5/11
    • 4/11
    • 45/100

  6. Tom says 0.16333... has the digits 16 before the repeating part starts. Is Tom right?

    Circle one:   True   False

  7. Which of these fractions gives a terminating decimal?

    • 1/8
    • 1/3
    • 1/6
    • 1/7

  8. Which of these fractions gives a terminating decimal?

    • 2/3
    • 5/11
    • 3/8

  9. What is 0.16333 (only the 3 repeating) as a fraction in lowest terms?

    • 16/99
    • 49/30
    • 49/300

  10. Tom says 0.16333 has the digits 16 before the repeating part starts. Is Tom right?

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Endless decimals, exact fractions W1-mt_Mb-sXIZDWd-s1

  1. 0.375 · 8 = 2 x 2 x 2, with no 3s or other primes, so the decimal terminates: 3/8 = 0.375.
  2. 7/9 · Let x = 0.777..., then 10x = 7.777..., and 10x - x = 7, so 9x = 7 and x = 7/9.
  3. 7/9 · Ten x minus x is 7, so 9x equals 7 and x is 7/9.
  4. True · The subtraction gives 9x equals 9, so x is 1 exactly.
  5. 5/11 · Shift two digits: 100x minus x is 45, so x is 45/99, which is 5/11.
  6. True · Tom is right: the repeat is just the 3, so the non repeating part is 16 and the decimal is 0.16 followed by endless 3s.
  7. 1/8 · 8 = 2^3, with only 2s in its prime factors, so 1/8 terminates at 0.125. The others all recur.
  8. 3/8 · Only 3/8 has a denominator of just 2s, so only it ends.
  9. 49/300 · 1000x minus 100x gives 900x equals 147, which simplifies to 49/300.
  10. True · The 16 sits still and only the 3 cycles, so Tom is right.
Worksheet · LightMySky