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Worksheet: Converting between Repeating Decimals and Fractions

Q1:

Express 5 6 as a decimal.

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

Q2:

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

Q3:

Which of the following fractions has a recurring decimal expansion?

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

Q4:

Convert 1 3 into its decimal form.

  • A0.34
  • B0.3
  • C0.33
  • D 0 . 3
  • E0.4

Q5:

Convert 2 3 into its decimal form.

  • A0.67
  • B0.6
  • C 0 . 6 7
  • D 0 . 6
  • E0.7

Q6:

Answer the following questions for the recurring decimal 0 . 2 4 , that is, 0 . 2 4 2 4 2 4 2 4 … .

Let π‘₯ = 0 . 2 4 . Find an expression for 1 0 0 π‘₯ .

  • A 1 0 0 π‘₯ = 2 4 2 . 4 2
  • B 1 0 0 π‘₯ = 2 . 4 2
  • C 1 0 0 π‘₯ = 2 0 . 2 4
  • D 1 0 0 π‘₯ = 2 4 . 2 4
  • E 1 0 0 π‘₯ = 0 . 2 4

Subtract π‘₯ from 1 0 0 π‘₯ to find an expression for 9 9 π‘₯ .

  • A 9 9 π‘₯ = 2 4
  • B 9 9 π‘₯ = 2 0
  • C 9 9 π‘₯ = 2 4 2
  • D 9 9 π‘₯ = 2
  • E 9 9 π‘₯ = 4 2

Find π‘₯ .

  • A π‘₯ = 1 4 3 3
  • B π‘₯ = 2 9 9
  • C π‘₯ = 8 3 3
  • D π‘₯ = 2 2 9
  • E π‘₯ = 2 0 9 9

Q7:

Answer the following questions for the recurring decimal 0 . 4 , that is, 0 . 4 4 4 4 4 … .

Let π‘₯ = 0 . 4 Find an expression for 1 0 π‘₯ .

  • A 1 0 π‘₯ = 4 4 . 4
  • B 1 0 π‘₯ = 0 . 4
  • C 1 0 π‘₯ = 4 4 4 . 4
  • D 1 0 π‘₯ = 4 . 4
  • E 1 0 π‘₯ = 0 . 0 4

Subtract π‘₯ from 1 0 π‘₯ to find an expression for 9 π‘₯ .

  • A 9 π‘₯ = 4
  • B 9 π‘₯ = 4 0
  • C 9 π‘₯ = 1 0
  • D 9 π‘₯ = 4 4
  • E 9 π‘₯ = 4 4 4

Find π‘₯ .

  • A π‘₯ = 9 4
  • B π‘₯ = 2 5
  • C π‘₯ = 4 9
  • D π‘₯ = 5 2
  • E π‘₯ = 4 0 9

Q8:

Evaluate giving the answer in its simplest form.

  • A
  • B
  • C
  • D

Q9:

Convert 1 3 to a decimal.

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

Q10:

Convert 4 9 0 to a decimal.

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

Q11:

Convert 0 . 7 to a fraction.

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

Q12:

Write as a recurring decimal.

  • A
  • B
  • C
  • D

Q13:

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 3 4
  • C 4 1 7
  • D 1 3 3
  • E 1 6 1 9

Q14:

Mason was told he could have 1 3 or 0.34 of the total jam inside a jar. Convert 1 3 to a decimal, and determine which option would give Mason more jam.

  • A0.32, 0.34 of the total jam
  • B 0 . 3 , 1 3 of the total jam
  • C0.3, 0.34 of the total jam
  • D 0 . 3 , 0.34 of the total jam
  • E0.3, 1 3 of the total jam

Q15:

Answer the following questions for the recurring decimal 0 . 2 6 5 , that is, 0 . 2 6 5 6 5 6 5 … .

Let π‘₯ = 0 . 2 6 5 . Find an expression for 1 0 π‘₯ .

  • A 1 0 π‘₯ = 2 . 2 6 5
  • B 1 0 π‘₯ = 2 6 . 6 5
  • C 1 0 π‘₯ = 0 . 2 6 5
  • D 1 0 π‘₯ = 2 . 6 5
  • E 1 0 π‘₯ = 2 0 . 6 5

Find an expression for 1 0 0 0 π‘₯ .

  • A 1 0 0 0 π‘₯ = 2 6 5 . 6 5
  • B 1 0 0 0 π‘₯ = 2 6 5 . 2 6 5
  • C 1 0 0 0 π‘₯ = 2 6 . 6 5
  • D 1 0 0 0 π‘₯ = 2 . 6 5
  • E 1 0 0 0 π‘₯ = 2 6 5 6 . 5 6

Subtract 1 0 π‘₯ from 1 0 0 0 π‘₯ to find an expression for 9 9 0 π‘₯ .

  • A 9 9 0 π‘₯ = 2 6
  • B 9 9 0 π‘₯ = 2
  • C 9 9 0 π‘₯ = 2 6 3
  • D 9 9 0 π‘₯ = 2 6 5 6
  • E 9 9 0 π‘₯ = 2 5

Find π‘₯ .

  • A π‘₯ = 2 6 3 9 9 0
  • B π‘₯ = 1 3 4 9 5
  • C π‘₯ = 5 1 9 8
  • D π‘₯ = 2 9 9 0
  • E π‘₯ = 4 9 5 9 9 0