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Write the repeating decimal as a fraction.
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Q. Write the repeating decimal as a fraction.
- Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern in the decimal is , which repeats indefinitely.
- Assign Variable: Let equal the repeating decimal, so we can write an equation to represent it.Let
- Multiply by Power of : Multiply by a power of that moves the decimal point to the right so that it aligns with the start of the repeating pattern.If we multiply by (since the repeating pattern has two digits), we get:
- Subtract Original Number: Subtract the original number from the result of the multiplication to eliminate the repeating pattern.
- Solve for x: Solve for x by dividing both sides of the equation by .
- Simplify Fraction: Simplify the fraction if possible.Both the numerator and the denominator are divisible by .
