Wayground
Writing repeating decimals as fractions - Printable Mathematics Worksheets - Wayground

Writing repeating decimals as fractions

15 questions

8th - 8th Grade

Mathematics

This Grade 8 mathematics worksheet helps students convert decimal representations into fractions, with emphasis on repeating decimals. Across 15 multiple-choice questions, students work with pure repeating decimals, mixed decimals that include nonrepeating digits before the repeating pattern, terminating decimals, negative values, and values greater than one. The varied item set requires students to identify the repeating block, select an appropriate place-value relationship, and recognize a fraction that represents the decimal. The worksheet is useful for guided practice, independent review, homework, or a formative check after introducing repeating-decimal notation. Teachers can use the answer choices to discuss common denominator patterns such as 9, 99, and 999, as well as the need to simplify results and preserve the sign of a negative decimal. This free printable worksheet includes a complete answer key, making it practical for Grade 8 math instruction and review.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Writing repeating decimals as fractions

Total questions: 15

Name
Class
Date
1.

Convert the following decimal into a fraction. 

0.36‾0.\overline{36}  

a)

4/9

b)

4/11

c)

4/13

d)

3/13

2.

Convert the following decimal into a fraction.

 

0.083‾0.08\overline{3}  

a)

1/10

b)

1/11

c)

1/12

d)

1/13

3.
a)
7/50
b)
14/9
c)
7/45
d)
14/99
4.
a)
2/3
b)
-2/3
c)
3/5
d)
-3/5
5.

Convert the following decimal into a fraction. 

0.83‾0.8\overline{3}  

a)

5/6

b)

7/8


c)

9/11

d)

12/14

6.

Convert the following decimal into a fraction.

0.16‾0.1\overline{6}

a)

1/7

b)

2/11


c)

2/13

d)

1/6

7.

Convert the following decimal into a fraction.

0.45‾0.\overline{45}

a)

5/9

b)

6/11

c)

4/9

d)

5/11

8.

Convert the following decimal into a fraction.

1.583‾1.58\overline{3}

a)

19/12

b)

17/12

c)

16/11

d)

17/11

9.
Convert 3.56 to a fraction.
a)
3.56/100
b)
353/99
c)
89/25
d)
28/5
10.
Convert -0.467467467... to a fraction
a)
-4674/10000
b)
-467/999
c)
-467/1000
d)
-467/99
11.
Convert 4.363636... to a fraction.
a)
48/11
b)
4/11
c)
4.36/99
d)
34/25
12.
Convert 0.264 to a fraction.
a)
88/333
b)
66/25
c)
2/9
d)
33/125
13.
Convert 0.769769769... to a fraction.
a)
769/999
b)
769/1000
c)
769/100
d)
769/99
14.
Convert 0.266666... to a fraction.
a)
26/99
b)
8/3
c)
4/15
d)
2.6/9
15.
Convert 0.5282828... to a fraction.
a)
523/999
b)
5.28/99
c)
4/75
d)
523/990
Answer Key

Writing repeating decimals as fractions

Total questions: 15

1.
b)

4/11

2.
c)

1/12

3.
d) 14/99
4.
b) -2/3
5.
a)

5/6

6.
d)

1/6

7.
d)

5/11

8.
a)

19/12

9.
c) 89/25
10.
b) -467/999
11.
a) 48/11
12.
b) 66/25
13.
a) 769/999
14.
c) 4/15
15.
d) 523/990

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the “Writing repeating decimals as fractions” worksheet cover?

This Grade 8 worksheet uses 15 multiple-choice questions to practise converting pure repeating decimals, mixed repeating decimals, terminating decimals, negative decimals, and decimals greater than one into fractions. Students must identify the repeating pattern, use its place value to form an equivalent fraction, and select the matching simplified result.

How can I use this worksheet to teach students to write repeating decimals as fractions?

First model the algebraic method with a decimal whose repeating block has one, two, or three digits: let the decimal equal x, multiply by the appropriate power of 10, subtract, and solve for x. Then use the worksheet’s multiple-choice items to compare pure repeating forms with mixed forms such as a nonrepeating portion followed by a repeating block. Ask students to explain why the number of repeating digits determines whether the subtraction uses 9, 99, or 999.

What mistakes should I watch for when students complete this repeating-decimals worksheet?

Watch for students treating a mixed repeating decimal as though every digit repeats, using a denominator based on the total number of visible digits, or forgetting to preserve a negative sign. Students may also choose an unsimplified or incorrectly scaled fraction, especially for decimals greater than one. The multiple-choice format makes these errors visible when distractors differ by a place-value factor or by the length of the repeating block.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can use the 15 multiple-choice items for paper practice or online assessment. It includes a complete answer key for checking student responses. For printable submissions, you can scan student work with the Wayground for Teachers app to help grade the worksheet efficiently.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the repeating-decimal notation and multiple-choice options are easier to track. You can also apply a dyslexia-friendly font or translate the worksheet into another language when that supports access to the fraction-conversion task.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion