Solution - Fraction to decimal (repeating)
Step-by-step explanation
1. Parse fraction to decimal repeating input
Operation detected: fraction to decimal repeating conversion.
Normalize numerator and denominator from the input.
Rewrite the fraction as a long-division setup.
Plan: generate digits while tracking remainders to detect repetition.
Parse the fraction and set up long division before generating decimal digits.
2. Execute long-division cycle transcript
At each cycle: multiply remainder by 10, divide by denominator, record digit and new remainder.
This cycle contributes one new decimal digit.
This cycle contributes one new decimal digit.
This cycle contributes one new decimal digit.
This cycle contributes one new decimal digit.
Remainder reached zero, so decimal generation stops.
The remainder reaches zero, so the decimal terminates with no repeating block.
3. Conclude decimal representation
Conclusion: the fraction converts to a terminating decimal.
Study tip: terminating decimals can be written without parentheses.
Write the terminating decimal directly: .
Why learn this
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Repeating decimals are common in algebra and statistics. Detecting cycles helps with exact arithmetic and checking answers.