# Worksheet: Converting Fractions to Recurring Decimals

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: to the nearest .

**Q2: **

Fill in the blanks: to the nearest .

**Q4: **

Which of the following fractions has a recurring decimal expansion?

- A
- B
- C
- D
- E

**Q5: **

Convert into its decimal form.

- A0.3
- B0.33
- C
- D0.4
- E0.34

**Q6: **

Convert into its decimal form.

- A0.67
- B0.7
- C
- D0.6
- E

**Q7: **

Convert to a decimal.

- A
- B
- C
- D
- E

**Q8: **

Write as a recurring decimal.

- A
- B
- C
- D

**Q9: **

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

- A ,
- B , 0.0625
- C ,
- D , 0.9375
- E ,

**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 | ||

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

**Q11: **

Mason has started a long division to convert the fraction into its decimal form. His result so far is 0.2352941176470588. Mason is about to give up, thinking 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

**Q14: **

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

**Q15: **

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.

- 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