# 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.

Q1:

Which of the following fractions has a recurring decimal expansion?

• A
• B
• C
• D
• E

Q2:

Convert to a decimal.

• A
• B
• C
• D
• E

Q3:

Write as a recurring decimal.

• A
• B
• C2.6
• D2.7
• E

Q4:

Write as a recurring decimal.

• A11.83
• B
• C11.8
• D11.84
• E

Q5:

Benjamin 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 Benjamin more jam.

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

Q6:

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

Q7:

Use a calculator to convert into a fraction.

• A
• B
• C
• D
• E

Q8:

Use a calculator to write as a fraction.

• A
• B
• C
• D
• E

Q9:

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 crane
Bald eagle
Black-footed albatross
• Abald eagle: 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: ft
• Dblack-footed albatross: 6.3 ft, bald eagle: 7.5 ft
• Ebald eagle: ft, black-footed albatross: ft

Q10:

Emma can dig holes in an hour, and Charlotte can dig 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.