Worksheet: Converting Fractions to Recurring Decimals

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In this worksheet, we will practice converting a fraction into a decimal, noting that the decimal expansion of a rational number either terminates or eventually repeats.

Q1:

Fill in the blank: 23≈ to the nearest 110.

Q2:

Fill in the blanks: 913≈ to the nearest 1100.

Q3:

Convert 17 to a decimal.

  • A 0 . 0 7 1 4 2
  • B 0 . 1 4 2 8 5 7
  • C 0 . 2 8 5 7 1
  • D 0 . 0 6 6 6
  • E 0 . 0 8 3 3 3

Q4:

Which of the following fractions has a recurring decimal expansion?

  • A 1 2
  • B 3 5
  • C 8 1 3
  • D 3 4
  • E 3 8

Q5:

Convert 13 into its decimal form.

  • A0.3
  • B0.33
  • C 0 . 3
  • D0.4
  • E0.34

Q6:

Convert 23 into its decimal form.

  • A0.67
  • B0.7
  • C 0 . 6 7
  • D0.6
  • E 0 . 6

Q7:

Convert 490 to a decimal.

  • A 0 . 0 4
  • B 0 . 0 4
  • C 0 . 5
  • D 0 . 4
  • E 0 . 1 5

Q8:

Write 29 as a recurring decimal.

  • A 0 . 2
  • B 0 . 2 2
  • C 0 . 3
  • D 0 . 2 2 2

Q9:

Which of the following are a fraction and its decimal value that lie between 14 and 78?

  • A 2 3 2 4 , 0 . 9 5 8 3
  • B 1 1 6 , 0.0625
  • C 5 2 4 , 0 . 2 0 8 3
  • D 1 5 1 6 , 0.9375
  • E 1 3 , 0 . 3

Q10:

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.

Bird Minimum Wingspan (ft) Maximum Wingspan (ft)
Whooping crane 7 1 6 7 1 4
Bald eagle 6 7 1 2 7 1 2
Black-footed albatross 6 3 1 0 7 1 1 2
  • 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

Q11:

Mason has started a long division to convert the fraction 417 into its decimal form. His result so far is 0.2352941176470588. Mason is about to give up, thinking 417 is not a repeating decimal. How many decimals do you think are missing before it starts to repeat?

  • Aone
  • Ban infinite number
  • Ctwo
  • Dthree
  • Ezero

Q12:

Convert 13 to a decimal.

  • A 0 . 1
  • B 0 . 6
  • C 0 . 0 3
  • D 0 . 3
  • E 0 . 0 6

Q13:

Express 56 as a decimal.

  • A 0 . 8 3
  • B0.83
  • C0.84
  • D 0 . 6
  • E0.56

Q14:

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

  • A 2 3
  • B 1 6 1 9
  • C 1 3 3
  • D 1 3 4
  • E 4 1 7

Q15:

Mason 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 Mason more jam.

  • A 0 . 3 , 0.34 of the total jam
  • B0.3, 13 of the total jam
  • C 0 . 3 , 1 3 of the total jam
  • D0.32, 0.34 of the total jam
  • E0.3, 0.34 of the total jam

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