Repeating decimal to fraction

Here you will learn about converting a repeating decimal to a fraction including how to define a repeating decimal.

Students will first learn about converting repeating decimals (often called recurring decimals) to fractions as part of the number system in katex is not definedth grade.

What is converting a repeating decimal to fraction?

Converting a repeating decimal to fraction is representing the repeating decimals as a fraction without changing its value.

A repeating decimal (recurring decimal) is a decimal number that has a digit (or group of digits) right of the decimal point that repeats forever. The part that repeats can also be shown by placing a line over the first to the last digit of the repeating pattern. Repeating decimals are also known as non-terminating decimals.

For example,

are all repeating decimals.

To convert a repeating decimal to a fraction, you can form an equation. E.g.

Keep track by labeling equations katex is not defined etc.

You need to be able to multiply both sides of this equation confidently by different powers of katex is not defined E.g.

What is converting a repeating decimal to fraction?

Common Core State Standards

How does this relate to katex is not definedth grade math?

• Grade 8 – The Number System (8.NS.A.1)
  Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

How to convert a repeating decimal to fraction

In order to convert from a repeating decimal to a fraction, you need to:

1. Equate the repeating decimal to a variable, katex is not defined to create katex is not defined
2. Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined
3. Subtract katex is not defined from katex is not defined
4. Divide the value by the coefficient of katex is not defined
5. Simplify the fraction.
6. State the answer.

Repeating decimal to fraction examples

Example 1: converting with a simple repeating decimal (one repeated digit)

Convert katex is not defined to a fraction.

1. Equate the repeating decimal to a variable, katex is not defined to create katex is not defined

2Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined

As katex is not defined has one repeating digit, multiply by katex is not defined Remember, because you are multiplying the whole of katex is not defined by katex is not defined, you also need to multiply the variable katex is not defined by katex is not defined

3Subtract katex is not defined from katex is not defined

Subtract the first equation from the second equation.

4Divide the value by the coefficient of katex is not defined

As katex is not defined is equal to katex is not defined and katex is not defined it can be stated that katex is not defined and katex is not defined are equal to one another.

5Simplify the fraction.

This fraction cannot be simplified as the only factor that katex is not defined and katex is not defined share is katex is not defined

6State your answer.

Example 2: converting with a repeating decimal with simplifying (two repeated digits)

Convert katex is not defined to a fraction.

Example 3: converting with a repeating decimal (one repeated digit)

Convert katex is not defined to a fraction.

Example 4: converting with a repeating decimal (two repeated digits)

Convert katex is not defined to a fraction.

Example 5: converting with a repeating decimal greater than 1 (one repeated digit)

Convert katex is not defined to a fraction.

Example 6: converting with a more complex repeating decimal (two repeated digits)

Convert katex is not defined to a fraction.

Teaching tips for converting repeating decimals to fractions

• Students should have a firm grasp on what recurring or repeating decimals are before beginning to convert them. Make sure students have a clear definition to refer back to.

• Encourage students to identify the repeating pattern in the decimals as the repeating digits. Make sure to emphasize that the recurring part of the decimal repeats indefinitely.

• Use of a converting repeating decimals to fractions worksheet will provide students with plenty of opportunities to practice.

• Post step-by-step instructions within the classroom or have students write steps down in a math journal to refer back to when needed.

Easy mistakes to make

• Multiplying by an incorrect power of katex is not defined
  You must make sure you are multiplying by the correct power of katex is not defined so the repeating part of the decimal can be eliminated. For example,
  Multiplying katex is not defined by katex is not defined does not help us eliminate the repeating decimal by subtraction. In this example you need to multiply by katex is not defined because you can now eliminate the repeating aspect of the decimal by subtraction.
  
  • Incorrect:
    katex is not defined
    katex is not defined does not eliminate the repeating decimal..
    
  • Correct:
    katex is not defined
    katex is not defined does eliminate the repeating decimal.

• Leaving the fraction with a decimal in the numerator
  Fractions should not include a decimal. For example, katex is not defined
  In this example, multiply the numerator and denominator by katex is not defined to be left with katex is not defined

• Not simplifying the fraction
  Always check to see if you have simplified the fraction into its simplest form.
  The easiest way to do this is by using a divisibility check to see if the numerator and denominator are divisible by another number besides katex is not defined

Related converting fractions decimals and percentages lessons

• Percent to decimal
• Decimal to percent
• Percent to fraction
• Fraction to percent
• Decimal to fraction
• Fraction to decimal

The next lessons are

• Ratio
• Percent
• Compound measures
• Proportion

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