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Converting Rational Numbers - Worksheet 10 - 7th Grade

Hard

Convert terminating fractions and signed decimals exactly; express repeating decimals as fractions.

hard: Combine signed quantities or work backwards from a result.

23 problems · 15-20 minutes · Skills: rational numbers, fractions, decimals, percents

About This Worksheet

This hard-level worksheet contains 23 problems designed for 7th Grade students practicing converting rational numbers. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Read signed numbers and fractions; recall multiplication and division facts.

  • Convert terminating fractions and signed decimals exactly; express repeating decimals as fractions.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Write 13/10 as an exact decimal.
Solution Steps:
  1. Divide the numerator by the denominator.
  2. The quotient is 1.3.
Answer: 1.3
Tip: Check your result using the method in the example before moving to the next question.
1
Write 0.111… as a fraction. The digit 1 repeats forever.
2
Write 0.5 as a fraction in simplest form.
3
Write -45/25 as an exact decimal.
4
Write 0.444… as a fraction. The digit 4 repeats forever.
5
Write -3/5 as an exact decimal.
6
Write 1.125 as a fraction in simplest form.
7
Write 0.888… as a fraction. The digit 8 repeats forever.
8
Write 2.2 as a fraction in simplest form.
9
Write -9/5 as an exact decimal.
10
Write 0.222… as a fraction. The digit 2 repeats forever.
11
Write -11/4 as an exact decimal.
12
Write 0.25 as a fraction in simplest form.
13
Write 0.666… as a fraction. The digit 6 repeats forever.
14
Write -0.5 as a fraction in simplest form.
15
Write -190/100 as an exact decimal.
16
Write 0.777… as a fraction. The digit 7 repeats forever.
17
Write 6/20 as an exact decimal.
18
Write -1.59 as a fraction in simplest form.
19
Write 0.555… as a fraction. The digit 5 repeats forever.
20
Write 2.55 as a fraction in simplest form.
21
Write -8/5 as an exact decimal.
22
Write 0.333… as a fraction. The digit 3 repeats forever.
23
Write -5/4 as an exact decimal.

Answer Key

1. 1/92. 1/23. -1.84. 4/95. -0.66. 9/87. 8/98. 11/59. -1.810. 2/911. -2.7512. 1/413. 2/314. -1/215. -1.916. 7/917. 0.318. -159/10019. 5/920. 51/2021. -1.622. 1/323. -1.25

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Frequently Asked Questions

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What skills does this rational numbers worksheet cover?

This worksheet focuses on rational numbers, fractions, decimals, percents. It is designed for 7th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 23 problems. It typically takes 15-20 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.