# What is 0.89 divided by 5.60?

May 16, 2017

$0.89 \div 5.60 = \frac{0.89}{5.6} = 0.159 \text{ }$ (to 3 decimal places.)

#### Explanation:

It is not comfortable to divide BY a decimal, so we multiply by powers of $10$ to change what the question looks like.

$0.89 \div 5.60 = \frac{0.89}{5.6}$

$\frac{0.89}{5.6} \times \frac{10}{10} = \frac{8.9}{56} \text{ } \rightarrow \left(\frac{10}{10} = 1\right)$so the value stays the same.

Now you can divide as usual because the denominator is a whole number, not a decimal fraction.

$\textcolor{w h i t e}{\ldots \ldots . . x \ldots \ldots \ldots} \underline{0.1589}$
color(white)(..............)56)8.9000
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots . .} \underline{56}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots . .} 330$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots . .} \underline{280}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} 500$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \underline{448}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} 520$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \underline{504}$

The answer is a recurring decimal. From this answer we can round off to 3 decimal places to get $0.159$