Math Practice Problems - Repeating Decimals

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.

Learn more about our online math practice software.
See some of our other supported math practice problems.

Complexity=2, Mode=noNonRptDec

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

6.23

4.35

Complexity=3, Mode=noNonRptDec

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

4.838

0.881

Complexity=1, Mode=NonRptDec

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

4.28

6.19

Complexity=2, Mode=NonRptDec

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

1.8652

2.1076

Complexity=3, Mode=NonRptDec

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

8.589891

10.833405

Answers

Complexity=2, Mode=noNonRptDec

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

Problem

Correct Answer

Your Answer

6.23

Solution
x = 6.23.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10²x = 100x = 623. 23
10^{non-repeating length}x = 10⁰x = 1x = 6.23
100x - 1x = 99x = 623.23 - 6.23 = 617

x =

617

Problem

Correct Answer

Your Answer

4.35

Solution
x = 4.35.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10²x = 100x = 435. 35
10^{non-repeating length}x = 10⁰x = 1x = 4.35
100x - 1x = 99x = 435.35 - 4.35 = 431

x =

431

Complexity=3, Mode=noNonRptDec

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

Problem

Correct Answer

Your Answer

4.838

Solution
x = 4.838.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10³x = 1000x = 4838. 838
10^{non-repeating length}x = 10⁰x = 1x = 4.838
1000x - 1x = 999x = 4838.838 - 4.838 = 4834

x =

4834

999

838

999

Problem

Correct Answer

Your Answer

0.881

Solution
x = 0.881.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10³x = 1000x = 881. 881
10^{non-repeating length}x = 10⁰x = 1x = 0.881
1000x - 1x = 999x = 881.881 - 0.881 = 881

x =

881

999

881

999

Complexity=1, Mode=NonRptDec

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

Problem

Correct Answer

Your Answer

4.28

Solution
x = 4.28.
Length of non-repeating decimal part = 1.
Length of repeating decimal part = 1.
10^{repeating + non-repeating length}x = 10²x = 100x = 428. 8
10^{non-repeating length}x = 10¹x = 10x = 42.8
100x - 10x = 90x = 428.8 - 42.8 = 386

x =

386

193

Problem

Correct Answer

Your Answer

6.19

Solution
x = 6.19.
Length of non-repeating decimal part = 1.
Length of repeating decimal part = 1.
10^{repeating + non-repeating length}x = 10²x = 100x = 619. 9
10^{non-repeating length}x = 10¹x = 10x = 61.9
100x - 10x = 90x = 619.9 - 61.9 = 558

x =

558

Complexity=2, Mode=NonRptDec

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

Problem

Correct Answer

Your Answer

1.8652

Solution
x = 1.8652.
Length of non-repeating decimal part = 2.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10⁴x = 10000x = 18652. 52
10^{non-repeating length}x = 10²x = 100x = 186.52
10000x - 100x = 9900x = 18652.52 - 186.52 = 18466

x =

18466

9900

9233

4950

4283

4950

Problem

Correct Answer

Your Answer

2.1076

Solution
x = 2.1076.
Length of non-repeating decimal part = 2.
Length of repeating decimal part = 2.
10^{repeating + non-repeating length}x = 10⁴x = 10000x = 21076. 76
10^{non-repeating length}x = 10²x = 100x = 210.76
10000x - 100x = 9900x = 21076.76 - 210.76 = 20866

x =

20866

9900

10433

4950

533

4950

Complexity=3, Mode=NonRptDec

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

Problem

Correct Answer

Your Answer

8.589891

Solution
x = 8.589891.
Length of non-repeating decimal part = 3.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10⁶x = 1000000x = 8589891. 891
10^{non-repeating length}x = 10³x = 1000x = 8589.891
1000000x - 1000x = 999000x = 8589891.891 - 8589.891 = 8581302

x =

8581302

999000

158913

18500

8	10913 18500

Problem

Correct Answer

Your Answer

10.833405

Solution
x = 10.833405.
Length of non-repeating decimal part = 3.
Length of repeating decimal part = 3.
10^{repeating + non-repeating length}x = 10⁶x = 1000000x = 10833405. 405
10^{non-repeating length}x = 10³x = 1000x = 10833.405
1000000x - 1000x = 999000x = 10833405.405 - 10833.405 = 10822572

x =

10822572

999000

100209

9250

7709

9250

Learn more about our online math practice software.

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