Math Practice Problems - Repeating Decimals

MathScore EduFighter is one of the best math games on the Internet today. You can start playing for free!

Repeating Decimals - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

Want unlimited math worksheets? Learn more about our online math practice software.
See some of our other supported math practice problems.

Complexity=3, Mode=noNonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Complexity=1, Mode=NonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Complexity=2, Mode=NonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Complexity=3, Mode=NonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Answers

Complexity=2, Mode=noNonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Problem

Correct Answer

Your Answer

7.54

Solution
x = 7.54.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10²x = 100x = 754. 54
10^{non-repeating length}x = 10⁰x = 1x = 7.54
100x - 1x = 99x = 754.54 - 7.54 = 747

x =

747

Problem

Correct Answer

Your Answer

10.68

Solution
x = 10.68.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10²x = 100x = 1068. 68
10^{non-repeating length}x = 10⁰x = 1x = 10.68
100x - 1x = 99x = 1068.68 - 10.68 = 1058

x =

1058

Complexity=3, Mode=noNonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Problem

Correct Answer

Your Answer

1.605

Solution
x = 1.605.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10³x = 1000x = 1605. 605
10^{non-repeating length}x = 10⁰x = 1x = 1.605
1000x - 1x = 999x = 1605.605 - 1.605 = 1604

x =

1604

999

605

999

Problem

Correct Answer

Your Answer

5.110

Solution
x = 5.110.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10³x = 1000x = 5110. 110
10^{non-repeating length}x = 10⁰x = 1x = 5.110
1000x - 1x = 999x = 5110.110 - 5.110 = 5105

x =

5105

999

110

999

Complexity=1, Mode=NonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Problem

Correct Answer

Your Answer

2.28

Solution
x = 2.28.
Length of non-repeating decimal part = 1.
Length of repeating decimal part = 1.
10^{repeating + non-repeating length}x = 10²x = 100x = 228. 8
10^{non-repeating length}x = 10¹x = 10x = 22.8
100x - 10x = 90x = 228.8 - 22.8 = 206

x =

206

103

Problem

Correct Answer

Your Answer

5.84

Solution
x = 5.84.
Length of non-repeating decimal part = 1.
Length of repeating decimal part = 1.
10^{repeating + non-repeating length}x = 10²x = 100x = 584. 4
10^{non-repeating length}x = 10¹x = 10x = 58.4
100x - 10x = 90x = 584.4 - 58.4 = 526

x =

526

263

Complexity=2, Mode=NonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Problem

Correct Answer

Your Answer

3.8315

Solution
x = 3.8315.
Length of non-repeating decimal part = 2.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10⁴x = 10000x = 38315. 15
10^{non-repeating length}x = 10²x = 100x = 383.15
10000x - 100x = 9900x = 38315.15 - 383.15 = 37932

x =

37932

9900

3161

825

686

825

Problem

Correct Answer

Your Answer

7.9422

Solution
x = 7.9422.
Length of non-repeating decimal part = 2.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10⁴x = 10000x = 79422. 22
10^{non-repeating length}x = 10²x = 100x = 794.22
10000x - 100x = 9900x = 79422.22 - 794.22 = 78628

x =

78628

9900

1787

225

212

225

Complexity=3, Mode=NonRptDec

Convert the following decimals into simplified mixed fractions. If the whole number in the fraction is 0, just leave it blank.

Problem

Correct Answer

Your Answer

9.844111

Solution
x = 9.844111.
Length of non-repeating decimal part = 3.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10⁶x = 1000000x = 9844111. 111
10^{non-repeating length}x = 10³x = 1000x = 9844.111
1000000x - 1000x = 999000x = 9844111.111 - 9844.111 = 9834267

x =

9834267

999000

88597

9000

7597

9000

Problem

Correct Answer

Your Answer

6.819354

Solution
x = 6.819354.
Length of non-repeating decimal part = 3.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10⁶x = 1000000x = 6819354. 354
10^{non-repeating length}x = 10³x = 1000x = 6819.354
1000000x - 1000x = 999000x = 6819354.354 - 6819.354 = 6812535

x =

6812535

999000

454169

66600

6	54569 66600

Learn more about our online math practice software.

"MathScore works."
- John Cradler, Educational Technology Expert