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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 decimal: Let's identify the repeating part of the decimal. The digits are repeating.
- Represent as : Let's represent the repeating decimal as :
- Shift decimal point: To convert the repeating decimal to a fraction, we multiply by (since there are three digits in the repeating sequence) to shift the decimal point three places to the right:
- Subtract original x: Now, we subtract the original x from to get rid of the repeating decimals:
- Solve for x: This subtraction gives us:
- Find GCD: Now, we solve for by dividing both sides of the equation by :
- Simplify fraction: We can simplify the fraction by finding the greatest common divisor (GCD) of and . The GCD of and is .
- Final result: Divide both the numerator and the denominator by the GCD to simplify the fraction:
- Final result: Divide both the numerator and the denominator by the GCD to simplify the fraction: After simplification, we get:
