# How do you convert a fraction to a decimal?

Apr 11, 2016

$\left(\text{numerator")/("denominator}\right)$

e.g. $\frac{1}{10} = 0.1$

Apr 11, 2016

By long division.

#### Explanation:

Ultimately you can find a decimal expansion for any fraction of the form $\frac{a}{b}$ for integers $a$ and $b$ by long division.

For example, consider $\frac{186}{7}$:

Eventually the remainders in long division will repeat. In this example, the remainder starts to repeat with the value $4$ occurring for the second time.

That means that the quotient will start to repeat too and we find:

$\frac{186}{7} = 26.57142857142857142857 \ldots$

which can be written:

$\frac{186}{7} = 26. \overline{571428}$

The bar over the sequence $571428$ indicates the repeating section.