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Solution - Fraction to decimal (repeating)

1. (6)

1.(6)

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Step-by-step explanation

1. Parse fraction to decimal repeating input

$\frac{20}{12}$

Operation detected: fraction to decimal repeating conversion.

$\frac{20}{12}$

Normalize numerator and denominator from the input.

$\frac{20}{12}$

Rewrite the fraction as a long-division setup.

$20 \div 12$

Plan: generate digits while tracking remainders to detect repetition.

$20 \div 12$

Parse the fraction and set up long division before generating decimal digits.

2. Execute long-division cycle transcript

$\frac{20}{12}$

At each cycle: multiply remainder by 10, divide by denominator, record digit and new remainder.

$\frac{20}{12}$

$\frac{80}{12} = d i g i t 6, r e m a \in d e r 8$

This cycle contributes one new decimal digit.

$8$

A remainder repeated, so digits from that point form the repeating cycle.

$1. (6)$

A repeated remainder appears, so the repeating block is $6$ .

3. Conclude decimal representation

$20 / 12 = 1. (6)$

$1. (6)$

Conclusion: the fraction converts to a repeating decimal.

$1. (6)$

Study tip: keep parentheses around repeating digits to preserve exact value.

$1. (6)$

Write the repeating decimal with parentheses: $1. (6)$ .

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Repeating decimals are common in algebra and statistics. Detecting cycles helps with exact arithmetic and checking answers.

Terms and topics

Fraction to decimal (repeating)

Solution - Fraction to decimal (repeating)

Step-by-step explanation

1. Parse fraction to decimal repeating input

2. Execute long-division cycle transcript

3. Conclude decimal representation

Why learn this

Terms and topics

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