Worksheet: Converting Recurring Decimals to Fractions

In this worksheet, we will practice converting a recurring decimal to a fraction or a mixed number.

Q1:

Convert 0.354 to a fraction.

  • A 3 9 1 1 0
  • B 1 1 8 3 3 3
  • C 3 1 9 9 0 0
  • D 2 9 9 0
  • E 5 9 1 6 5

Q2:

Convert 0.547 to a fraction.

  • A 2 7 1 4 9 5
  • B 5 4 7 9 9 0
  • C 5 4 7 1 , 0 0 0
  • D 2 7 1 5 0 0
  • E 2 7 1 5 0 5

Q3:

Convert 0.347 to a fraction.

  • A 3 1 3 9 9 0
  • B 3 1 3 9 0 0
  • C 3 4 7 9 9 0
  • D 3 4 4 9 0 0
  • E 3 4 7 9 0 0

Q4:

Express 0.75 as a rational number in its simplest form.

  • A 7 5 1 0 0
  • B0.7575
  • C 2 5 3 3
  • D 1 7 5

Q5:

Which of the following is true?

  • A 4 . 3 3 > 4 . 3 3
  • B 4 . 3 3 < 4 . 3 3
  • C 4 . 3 3 = 4 . 3 3

Q6:

Convert 0.37 to a fraction.

  • A 3 7 1 0 1
  • B 3 7 1 0 0
  • C 3 7 3 1 0 1
  • D 3 7 9 9
  • E 3 7 3 9 9

Q7:

Answer the following questions for the recurring decimal 0.24, that is, 0.24242424.

Let 𝑥=0.24. Find an expression for 100𝑥.

  • A 1 0 0 𝑥 = 2 4 2 . 4 2
  • B 1 0 0 𝑥 = 0 . 2 4
  • C 1 0 0 𝑥 = 2 4 . 2 4
  • D 1 0 0 𝑥 = 2 . 4 2
  • E 1 0 0 𝑥 = 2 0 . 2 4

Subtract 𝑥 from 100𝑥 to find an expression for 99𝑥.

  • A 9 9 𝑥 = 2 0
  • B 9 9 𝑥 = 4 2
  • C 9 9 𝑥 = 2
  • D 9 9 𝑥 = 2 4 2
  • E 9 9 𝑥 = 2 4

Find 𝑥.

  • A 𝑥 = 2 0 9 9
  • B 𝑥 = 2 2 9
  • C 𝑥 = 1 4 3 3
  • D 𝑥 = 2 9 9
  • E 𝑥 = 8 3 3

Q8:

Answer the following questions for the recurring decimal 0.4, that is, 0.44444.

Let 𝑥=0.4 Find an expression for 10𝑥.

  • A 1 0 𝑥 = 0 . 0 4
  • B 1 0 𝑥 = 4 . 4
  • C 1 0 𝑥 = 4 4 4 . 4
  • D 1 0 𝑥 = 4 4 . 4
  • E 1 0 𝑥 = 0 . 4

Subtract 𝑥 from 10𝑥 to find an expression for 9𝑥.

  • A 9 𝑥 = 4
  • B 9 𝑥 = 4 4 4
  • C 9 𝑥 = 4 0
  • D 9 𝑥 = 4 4
  • E 9 𝑥 = 1 0

Find 𝑥.

  • A 𝑥 = 5 2
  • B 𝑥 = 9 4
  • C 𝑥 = 4 0 9
  • D 𝑥 = 4 9
  • E 𝑥 = 2 5

Q9:

Convert 0.7 to a fraction.

  • A 7 9
  • B 1 1 7
  • C 7 1 0
  • D 7 1 1
  • E 9 7

Q10:

Answer the following questions for the recurring decimal 0.265, that is, 0.2656565.

Let 𝑥=0.265. Find an expression for 10𝑥.

  • A 1 0 𝑥 = 0 . 2 6 5
  • B 1 0 𝑥 = 2 6 . 6 5
  • C 1 0 𝑥 = 2 0 . 6 5
  • D 1 0 𝑥 = 2 . 6 5
  • E 1 0 𝑥 = 2 . 2 6 5

Find an expression for 1,000𝑥.

  • A 1 , 0 0 0 𝑥 = 2 6 5 . 2 6 5
  • B 1 , 0 0 0 𝑥 = 2 , 6 5 6 . 5 6
  • C 1 , 0 0 0 𝑥 = 2 6 . 6 5
  • D 1 , 0 0 0 𝑥 = 2 . 6 5
  • E 1 , 0 0 0 𝑥 = 2 6 5 . 6 5

Subtract 10𝑥 from 1,000𝑥 to find an expression for 990𝑥.

  • A 9 9 0 𝑥 = 2 6 3
  • B 9 9 0 𝑥 = 2 , 6 5 6
  • C 9 9 0 𝑥 = 2 5
  • D 9 9 0 𝑥 = 2 6
  • E 9 9 0 𝑥 = 2

Find 𝑥.

  • A 𝑥 = 2 6 3 9 9 0
  • B 𝑥 = 2 9 9 0
  • C 𝑥 = 4 9 5 9 9 0
  • D 𝑥 = 5 1 9 8
  • E 𝑥 = 1 3 4 9 5

Q11:

Simplify 0.76, giving your answer in the form 𝑎𝑏.

  • A 7 6 2 5
  • B 1 9 2 5
  • C 1 9 1 0 0
  • D 7 6 1 0
  • E 7 6 1 0 0

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