Solution - Fraction to decimal (repeating)

$$\frac{5}{12}$$

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

$$\frac{5}{12}$$

This cycle contributes one new decimal digit.

$$2$$

This cycle contributes one new decimal digit.

$$8$$

This cycle contributes one new decimal digit.

$$8$$

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

$$0.41\left(6\right)$$

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

$$0.41\left(6\right)$$

Conclusion: the fraction converts to a repeating decimal.

$$0.41\left(6\right)$$

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

$$0.41\left(6\right)$$

Write the repeating decimal with parentheses: $$0.41\left(6\right)$$.