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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: Let's identify the repeating pattern in the decimal. The digits repeat indefinitely.
- Represent as : Let's represent the repeating decimal as :
- Multiply by : To convert this repeating decimal into a fraction, we can multiply by , since the repeating pattern has three digits. This will 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:
- Perform subtraction: Performing the subtraction, we get:
- Solve for x: Now, we solve for by dividing both sides of the equation by :
- Find GCD: We can simplify the fraction by finding the greatest common divisor (GCD) of and . The GCD of and is .
- Divide by GCD: Divide both the numerator and the denominator by the GCD to simplify the fraction:
- Simplify fraction: After simplification, we get:
