# How do you divide rational numbers in decimal form?

Mar 23, 2018

By example: This is one method of many.

#### Explanation:

Just picking values at random, suppose we had: $\frac{2.35}{2.65}$
$\textcolor{b l u e}{\text{Making the numbers more straight forward}}$

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

$\textcolor{g r e e n}{\left[\frac{2.35}{2.65} \textcolor{red}{\times 1}\right] \textcolor{w h i t e}{\text{ddd") -> color(white)("ddd}} \left[\frac{2.35}{2.65} \textcolor{red}{\times \frac{100}{100}}\right]}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddd")->color(white)("ddddddd}} \frac{235}{265} = \frac{47}{53}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Conducting the division}}$

What follows is one method of many.

Note that $47$ is the same as $470 \times \frac{1}{10}$

I will use this adjustment approach to make division itself more straight forward. We will need to apply the appropriate adjustment at the end.

So for $47 \div 53$ we have $470 \div 53 \textcolor{m a \ge n t a}{\times \frac{1}{10}}$

$\textcolor{w h i t e}{\text{ddddddd}} 470 \textcolor{m a \ge n t a}{\times \frac{1}{10}}$
$\textcolor{m a \ge n t a}{8} \left(53\right) \to \underline{424 \leftarrow \text{ Subtract}}$
color(white)("dddddddd")46 larr" less than 53 so we adjust again"
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$\textcolor{w h i t e}{\text{ddddddd}} 460 \textcolor{m a \ge n t a}{\times \frac{1}{10}}$
$\textcolor{m a \ge n t a}{8} \left(53\right) \to \underline{424 \leftarrow \text{ Subtract}}$
color(white)("dddddddd") 36larr" less than 53 so we adjust again"
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
$\textcolor{w h i t e}{\text{ddddddd}} 360 \textcolor{m a \ge n t a}{\times \frac{1}{10}}$
$\textcolor{m a \ge n t a}{6} \left(53\right) \to \underline{318 \leftarrow \text{ Subtract}}$
color(white)("dddddddd")42larr" less than 53 so we adjust again"
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
$\textcolor{m a \ge n t a}{\text{AND SO THE CYCLE CONTINUES:}}$

So far we have:

$\textcolor{m a \ge n t a}{886 \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} = 0.886}$

The full printout from my calculator is: 0.88679245283