Lesson Worksheet: Converting between Fractions and Recurring Decimals Mathematics

In this worksheet, we will practice converting fractions to recurring decimals and recurring decimals to fractions using a calculator.


Which of the following fractions has a recurring decimal expansion?

  • A12
  • B35
  • C813
  • D34
  • E38


Convert 17 to a decimal.

  • A0.07142
  • B0.142857
  • C0.28571
  • D0.0666
  • E0.08333


Write 83 as a recurring decimal.

  • A2.67
  • B2.7
  • C2.6
  • D2.7
  • E2.6


Write 1156 as a recurring decimal.

  • A11.83
  • B11.̇84
  • C11.8
  • D11.84
  • E11.̇83


Benjamin was told he could have 13 or 0.34 of the total jam inside a jar. Convert 13 to a decimal, and determine which option would give Benjamin more jam.

  • A0.3, 0.34 of the total jam
  • B0.3, 13 of the total jam
  • C0.3, 13 of the total jam
  • D0.32, 0.34 of the total jam
  • E0.3, 0.34 of the total jam


Which of the following is a fraction that can be expressed as a repeating decimal with two different alternating digits?

  • A23
  • B1619
  • C133
  • D134
  • E417


Use a calculator to convert 3.1 into a fraction.

  • A3110
  • B289
  • C19
  • D289
  • E928


Use a calculator to write 1.23 as a fraction.

  • A12299
  • B99122
  • C12299
  • D122990
  • E1,22099


The table shows the wingspans of different birds. Name the bird that has the smallest minimum wingspan and the bird that has the greatest maximum wingspan, and give their wingspans in decimal form.

BirdMinimum Wingspan (ft)Maximum Wingspan (ft)
Whooping crane716714
Bald eagle6712712
Black-footed albatross63107112
  • Abald eagle: 6.583 ft, bald eagle: 7.5 ft
  • Bblack-footed albatross: 6.3 ft, whooping crane: 7.25 ft
  • Cblack-footed albatross: 6.3 ft, black-footed albatross: 7.083 ft
  • Dblack-footed albatross: 6.3 ft, bald eagle: 7.5 ft
  • Ebald eagle: 6.583 ft, black-footed albatross: 7.083 ft


Emma can dig 13499 holes in an hour, and Charlotte can dig 1518 holes in an hour. By converting both fractions into decimals, determine who is faster at digging holes.

  • AThere is not enough information to determine the answer.
  • BCharlotte is faster.
  • CEmma is faster.
  • DThey are equally fast.

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