# Worksheet: Converting between Repeating Decimals and Fractions

Q1:

Express as a decimal.

• A
• B0.83
• C0.84
• D
• E0.56

Q2:

Which of the following is true?

• A
• B
• C

Q3:

Which of the following fractions has a recurring decimal expansion?

• A
• B
• C
• D
• E

Q4:

Convert into its decimal form.

• A0.34
• B0.3
• C0.33
• D
• E0.4

Q5:

Convert into its decimal form.

• A0.67
• B0.6
• C
• D
• E0.7

Q6:

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

Let . Find an expression for .

• A
• B
• C
• D
• E

Subtract from to find an expression for .

• A
• B
• C
• D
• E

Find .

• A
• B
• C
• D
• E

Q7:

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

Let Find an expression for .

• A
• B
• C
• D
• E

Subtract from to find an expression for .

• A
• B
• C
• D
• E

Find .

• A
• B
• C
• D
• E

Q8:

Evaluate giving the answer in its simplest form.

• A
• B
• C
• D

Q9:

Convert to a decimal.

• A
• B
• C
• D
• E

Q10:

Convert to a decimal.

• A
• B
• C
• D
• E

Q11:

Convert to a fraction.

• A
• B
• C
• D
• E

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
• B
• C
• D
• E

Q14:

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

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

Q15:

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

Let . Find an expression for .

• A
• B
• C
• D
• E

Find an expression for .

• A
• B
• C
• D
• E

Subtract from to find an expression for .

• A
• B
• C
• D
• E

Find .

• A
• B
• C
• D
• E