# How do you simplify and make the fraction 16/88 into a decimal?

Oct 1, 2015

To simplify, factor the numerator and denominator to find the greatest common factor $8$ and divide both by that to find:

$\frac{16}{88} = \frac{2}{11}$

Then find $\frac{2}{11} = 0. \dot{1} \dot{8}$

#### Explanation:

$16 = 2 \cdot 8$ and $88 = 11 \cdot 8$

So:

$\frac{16}{88} = \frac{2 \cdot 8}{11 \cdot 8} = \frac{2}{11} \cdot \frac{8}{8} = \frac{2}{11}$

To convert $\frac{2}{11}$ to a decimal we can long divide and recognise the repetition of the remainder...

Notice that after a couple of digits we're back to the number $2$ we first started with. So $\frac{2}{11} = 0.18181818 \ldots = 0. \dot{1} \dot{8}$

Alternatively, just notice that $9 \times 11 = 99$, so

$\frac{2}{11} = \frac{2}{11} \cdot \frac{9}{9} = \frac{18}{99} = 0. \dot{1} \dot{8}$