# Using long division, write the rational number -9/24 as a terminating decimal?

Apr 30, 2017

$- \frac{9}{24} = - 0.375$

#### Explanation:

Let us divide $9$ by $24$ using long division.

$\textcolor{w h i t e}{\times \times x} 0 . \textcolor{w h i t e}{1} 3 \textcolor{w h i t e}{x} 7 \textcolor{w h i t e}{x} 5$
$\textcolor{w h i t e}{\times} 24 | \overline{9 \textcolor{w h i t e}{x} .0 \textcolor{w h i t e}{x} 0} \textcolor{w h i t e}{x} 0$
color(white)(xxxxx)ul(7color(white)("x)2)color(red)(darr
$\textcolor{w h i t e}{\times \times x} 1 \textcolor{w h i t e}{x} 8 \textcolor{w h i t e}{x} \text{0}$
$\textcolor{w h i t e}{\times \times x} \underline{1 \textcolor{w h i t e}{x} 6 \textcolor{w h i t e}{x} 8}$
$\textcolor{w h i t e}{\times \times \times x} 1 \textcolor{w h i t e}{x} 2 \textcolor{w h i t e}{x} \text{0}$
color(white)(xxxxxxx)ul(1color(white)(x)2color(white)(x)0
$\textcolor{w h i t e}{\times \times \times \times x} \textcolor{w h i t e}{x} -$

and hence

$- \frac{9}{24} = - 0.375$