Solution - Fraction to decimal (repeating)

$$\frac{95}{97}$$

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

$$\frac{95}{97}$$

This cycle contributes one new decimal digit.

$$77$$

This cycle contributes one new decimal digit.

$$91$$

This cycle contributes one new decimal digit.

$$37$$

This cycle contributes one new decimal digit.

$$79$$

This cycle contributes one new decimal digit.

$$14$$

This cycle contributes one new decimal digit.

$$43$$

This cycle contributes one new decimal digit.

$$42$$

This cycle contributes one new decimal digit.

$$32$$

This cycle contributes one new decimal digit.

$$29$$

This cycle contributes one new decimal digit.

$$96$$

This cycle contributes one new decimal digit.

$$87$$

This cycle contributes one new decimal digit.

$$94$$

This cycle contributes one new decimal digit.

$$67$$

This cycle contributes one new decimal digit.

$$88$$

Cycle transcript shortened for readability; continue using the same pattern.

$$14$$

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

$$0.\left(979381443298969072164948453608247422680412371134020618556701030927835051546391752577319587628865\right)$$

A repeated remainder appears, so the repeating block is $$979381443298969072164948453608247422680412371134020618556701030927835051546391752577319587628865$$.

$$0.\left(979381443298969072164948453608247422680412371134020618556701030927835051546391752577319587628865\right)$$

Conclusion: the fraction converts to a repeating decimal.

$$0.\left(979381443298969072164948453608247422680412371134020618556701030927835051546391752577319587628865\right)$$

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

$$0.\left(979381443298969072164948453608247422680412371134020618556701030927835051546391752577319587628865\right)$$

Write the repeating decimal with parentheses: $$0.\left(979381443298969072164948453608247422680412371134020618556701030927835051546391752577319587628865\right)$$.