Repeating Decimals to Fractions

The video tutorial explains how to convert repeating decimals into fractions. It provides three examples, each demonstrating the step-by-step process of matching repeating decimals to their equivalent fractions. The instructor uses algebraic methods, including setting up equations and simplifying fractions, to illustrate the conversion process. The tutorial emphasizes understanding the pattern and logic behind the conversion, ensuring learners can apply the method independently.

What is the first step in converting a repeating decimal to a fraction?

• Subtract the repeating part

• Let X equal the repeating decimal

• Divide by the number of repeating digits

• Multiply the decimal by 100

How do you eliminate the repeating part of the decimal in the first conversion?

• Add the repeating decimal to itself

• Use a calculator to find the fraction

• Multiply by a power of 10 and subtract

• Divide by the number of repeating digits

What is the fraction equivalent of 0.72 repeating?

• 7/11

• 9/11

• 8/11

• 7/9

In the second conversion, what is the purpose of multiplying by 10 and then by 100?

• To move the decimal point to the left

• To isolate the repeating digit

• To simplify the fraction

• To check the accuracy of the conversion

What is the fraction equivalent of 0.73 repeating?

• 11/15

• 7/10

• 3/4

• 5/6

What is the final step in converting a repeating decimal to a fraction?

• Subtract the original decimal

• Multiply by 100

• Divide by the difference

• Simplify the fraction

What is the fraction equivalent of 0.78 repeating?

• 25/33

• 26/33

• 27/33

• 28/33