Solution - Fraction to decimal (repeating)
0.(3)
Step-by-step explanation
1. Set up division
Interpret the fraction as division: = .
2. Track remainders and cycle
During long division, repeated remainders indicate a repeating cycle. Early remainders: , repeating part: .
3. Write decimal result
Compose the decimal using non-repeating and repeating parts. Non-repeating: , repeating: , final: .
Why learn this
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Repeating decimals are common in algebra and statistics. Detecting cycles helps with exact arithmetic and checking answers.