Practice Objectives
• Demonstrate an understanding of the addition property of equality
• Demonstrate an understanding of the multiplication property of equality
• Demonstrate the ability to convert a repeating decimal into a fraction

## Practice Converting a Repeating Decimal into a Fraction

Instructions:

Answer 7/10 questions correctly to pass.

Convert each repeating decimal into a fraction.

Report your answer as a simplified fraction or a whole number (when possible).

Problem:

Correct! Not Correct! Converting a Repeating Decimal into a Fraction:

Scenario 1:

When the series of repeating digits begins immediately after the decimal point.

1. Write the repeating part of the number in the numerator of a fraction
2. Write the denominator of the fraction as the same number of 9's as we have digits in the numerator
3. Simplify the fraction

Scenario 2:

When the series of repeating digits does not begin immediately after the decimal point.

1. Set the repeating decimal equal to a variable
• We will refer to this as equation #1
2. Multiply both sides of the equation by 10n where n is the number of digits in the repeating pattern
• We will refer to this as equation #2
3. Subtract away equation #1 from equation #2
• We do this by subtracting the left side of equation #1 away from the left side of equation #2 and the right side of equation #1 from the right side of equation #2
4. Solve the equation, this will give us the fractional equivalent for our repeating decimal
5. Simplify the fraction

Step-by-Step:

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