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Write the repeating decimal as a fraction.
Full solution
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 .
- Assign Variable: Let equal the repeating decimal. Let
- Multiply by Power of : Multiply by a power of that moves the decimal point to the right so that the repeating pattern aligns with the original decimal.Since the repeating pattern is three digits long, we multiply by (which is ) to move the decimal point three places to the right.
- Subtract Equations: Subtract the original equation from the new equation to eliminate the repeating decimals.
- Solve for x: Solve for x by dividing both sides of the equation by .
- Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it.The GCD of and is .
