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# Lesson 10: Converting Repeating Decimals to Fractions - how to convert repeating decimal to fraction NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 8?7
Lesson 10: Converting Repeating Decimals to Fractions
Classwork
Example 1
There is a fraction with an infinite decimal expansion of 0. 81. Find the fraction.
Exercises 1-2
1. There is a fraction with an infinite decimal expansion of 0. 123. Let = 0. 123.
a. Explain why looking at 1000 helps us find the fractional representation of .
Lesson 10: Converting Repeating Decimals to Fractions
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 8?7
b. What is as a fraction?
2. There is a fraction with a decimal expansion of 0. 4. Find the fraction, and check your answer using a calculator.
Lesson 10: Converting Repeating Decimals to Fractions
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NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 8?7
Example 2
Could it be that 2.138 is also a fraction?
Lesson 10: Converting Repeating Decimals to Fractions
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How do you turn decimals into a fraction? Convert Decimals to Fractions. Step 1: Write down the decimal divided by 1, like this: decimal 1. Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Step 3: Simplify (or reduce) the fraction.

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