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## 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.

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### 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.

1.
7.54
2.
10.68

### 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.

1.
1.605
2.
5.110

### 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.

1.
2.28
2.
5.84

### 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.

1.
3.8315
2.
7.9422

### 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.

1.
9.844111
2.
6.819354

### 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.

17.54
Solution
x = 7.54.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 2.
10repeating + non-repeating lengthx = 102x = 100x = 754. 54
10non-repeating lengthx = 10 0x = 1x = 7.54
100x - 1x = 99x = 754.54 - 7.54 = 747

x =
 74799
=
 8311
=
 7 611
210.68
Solution
x = 10.68.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 2.
10repeating + non-repeating lengthx = 102x = 100x = 1068. 68
10non-repeating lengthx = 10 0x = 1x = 10.68
100x - 1x = 99x = 1068.68 - 10.68 = 1058

x =
 105899
=
 10 6899

### 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.

11.605
Solution
x = 1.605.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 3.
10repeating + non-repeating lengthx = 103x = 1000x = 1605. 605
10non-repeating lengthx = 10 0x = 1x = 1.605
1000x - 1x = 999x = 1605.605 - 1.605 = 1604

x =
 1604999
=
 1 605999
25.110
Solution
x = 5.110.
Length of non-repeating decimal part = 0.
Length of repeating decimal part = 3.
10repeating + non-repeating lengthx = 103x = 1000x = 5110. 110
10non-repeating lengthx = 10 0x = 1x = 5.110
1000x - 1x = 999x = 5110.110 - 5.110 = 5105

x =
 5105999
=
 5 110999

### 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.

12.28
Solution
x = 2.28.
Length of non-repeating decimal part = 1.
Length of repeating decimal part = 1.
10repeating + non-repeating lengthx = 102x = 100x = 228. 8
10non-repeating lengthx = 10 1x = 10x = 22.8
100x - 10x = 90x = 228.8 - 22.8 = 206

x =
 20690
=
 10345
=
 2 1345
25.84
Solution
x = 5.84.
Length of non-repeating decimal part = 1.
Length of repeating decimal part = 1.
10repeating + non-repeating lengthx = 102x = 100x = 584. 4
10non-repeating lengthx = 10 1x = 10x = 58.4
100x - 10x = 90x = 584.4 - 58.4 = 526

x =
 52690
=
 26345
=
 5 3845

### 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.

13.8315
Solution
x = 3.8315.
Length of non-repeating decimal part = 2.
Length of repeating decimal part = 2.
10repeating + non-repeating lengthx = 104x = 10000x = 38315. 15
10non-repeating lengthx = 10 2x = 100x = 383.15
10000x - 100x = 9900x = 38315.15 - 383.15 = 37932

x =
 379329900
=
 3161825
=
 3 686825
27.9422
Solution
x = 7.9422.
Length of non-repeating decimal part = 2.
Length of repeating decimal part = 2.
10repeating + non-repeating lengthx = 104x = 10000x = 79422. 22
10non-repeating lengthx = 10 2x = 100x = 794.22
10000x - 100x = 9900x = 79422.22 - 794.22 = 78628

x =
 786289900
=
 1787225
=
 7 212225

### 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.

19.844111
Solution
x = 9.844111.
Length of non-repeating decimal part = 3.
Length of repeating decimal part = 3.
10repeating + non-repeating lengthx = 106x = 1000000x = 9844111. 111
10non-repeating lengthx = 10 3x = 1000x = 9844.111
1000000x - 1000x = 999000x = 9844111.111 - 9844.111 = 9834267

x =
 9834267999000
=
 885979000
=
 9 75979000
26.819354
Solution
x = 6.819354.
Length of non-repeating decimal part = 3.
Length of repeating decimal part = 3.
10repeating + non-repeating lengthx = 106x = 1000000x = 6819354. 354
10non-repeating lengthx = 10 3x = 1000x = 6819.354
1000000x - 1000x = 999000x = 6819354.354 - 6819.354 = 6812535

x =
 6812535999000
=
 45416966600
=
 6 5456966600