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.

  • A39110
  • B118333
  • C319900
  • D2990
  • E59165

Q2:

Convert 0.547 to a fraction.

  • A271495
  • B547990
  • C5471,000
  • D271500
  • E271505

Q3:

Convert 0.347 to a fraction.

  • A313990
  • B313900
  • C347990
  • D344900
  • E347900

Q4:

Express 0.75 as a rational number in its simplest form.

  • A75100
  • B0.7575
  • C2533
  • D175

Q5:

Which of the following is true?

  • A4.33>4.33
  • B4.33<4.33
  • C4.33=4.33

Q6:

Convert 0.37 to a fraction.

  • A37101
  • B37100
  • C373101
  • D3799
  • E37399

Q7:

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

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

  • A100𝑥=242.42
  • B100𝑥=0.24
  • C100𝑥=24.24
  • D100𝑥=2.42
  • E100𝑥=20.24

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

  • A99𝑥=20
  • B99𝑥=42
  • C99𝑥=2
  • D99𝑥=242
  • E99𝑥=24

Find 𝑥.

  • A𝑥=2099
  • B𝑥=229
  • C𝑥=1433
  • D𝑥=299
  • E𝑥=833

Q8:

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

Let 𝑥=0.4 Find an expression for 10𝑥.

  • A10𝑥=0.04
  • B10𝑥=4.4
  • C10𝑥=444.4
  • D10𝑥=44.4
  • E10𝑥=0.4

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

  • A9𝑥=4
  • B9𝑥=444
  • C9𝑥=40
  • D9𝑥=44
  • E9𝑥=10

Find 𝑥.

  • A𝑥=52
  • B𝑥=94
  • C𝑥=409
  • D𝑥=49
  • E𝑥=25

Q9:

Convert 0.7 to a fraction.

  • A79
  • B117
  • C710
  • D711
  • E97

Q10:

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

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

  • A10𝑥=0.265
  • B10𝑥=26.65
  • C10𝑥=20.65
  • D10𝑥=2.65
  • E10𝑥=2.265

Find an expression for 1,000𝑥.

  • A1,000𝑥=265.265
  • B1,000𝑥=2,656.56
  • C1,000𝑥=26.65
  • D1,000𝑥=2.65
  • E1,000𝑥=265.65

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

  • A990𝑥=263
  • B990𝑥=2,656
  • C990𝑥=25
  • D990𝑥=26
  • E990𝑥=2

Find 𝑥.

  • A𝑥=263990
  • B𝑥=2990
  • C𝑥=495990
  • D𝑥=5198
  • E𝑥=13495

Q11:

Simplify 0.76, giving your answer in the form 𝑎𝑏.

  • A7625
  • B1925
  • C19100
  • D7610
  • E76100

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.