# How do you simplify 9.594 div 0.06?

Apr 9, 2017

A way to get round the decimal place in the initial division expression.

$159.9$

#### Explanation:

Note that $9.594$ is the same as $9594 \times \frac{1}{1000}$

Note that $0.06$ is the same as $6 \times \frac{1}{100}$

So $9.594 \div 0.006$ is the same as $\left[9594 \div 6\right] \times \left[\frac{1}{1000} \div \frac{1}{100}\right]$

$\left(9594 \div 6\right) \times \frac{1}{10}$

I will do the division first then multiply by the $\frac{1}{10}$ at the very end

$\text{ } 9594$
$\textcolor{m a \ge n t a}{1000} \times 6 \to \underline{6000} \leftarrow \text{ subtract}$
$\text{ } 3594$
$\textcolor{m a \ge n t a}{\textcolor{w h i t e}{1} 500} \times 6 \to \underline{3000} \leftarrow \text{ subtract}$
$\text{ } 594$
$\textcolor{m a \ge n t a}{\textcolor{w h i t e}{10} 90} \times 6 \to \underline{\textcolor{w h i t e}{0} 540} \leftarrow \text{ subtract}$
$\text{ } \textcolor{w h i t e}{0} 54$
$\textcolor{m a \ge n t a}{\textcolor{w h i t e}{100} 9} \times 6 \to \text{ "ul(54) larr" subtract}$
$\text{ } 0$

As we have 0 we may now stop the division

$9594 \div 6 = \textcolor{m a \ge n t a}{1599}$

Now we multiply by the $\frac{1}{10}$ giving:

$159.9$
~~~~~~~~~~~~~~~~~~~~~~~~~~~

If the division had not finished with a 0 at that point then we would have gone into decimal values.

Aug 11, 2017

$= 159.6$

#### Explanation:

The rule with dividing BY a decimal is simple ... DON'T!!

You can change any decimal into a whole number by multiplying by a power of $10$

Write the division as a fraction:

$\frac{9.594}{0.06}$

Multiply the numerator and the denominator by the same number

$\frac{9.594}{\textcolor{b l u e}{0.06}} \textcolor{red}{\times \frac{100}{100}} \text{ } \leftarrow \left[\textcolor{red}{\frac{100}{100} = 1}\right]$

This changes the denominator into a whole number:

$= \frac{959.4}{\textcolor{b l u e}{6}} \text{ } \leftarrow$ divide as usual

$6 | \underline{9 {\text{ "^3 5" "^5 9." }}^{5} 4}$
$\textcolor{w h i t e}{\times} 1 \textcolor{w h i t e}{x . x} 5 \textcolor{w h i t e}{\times x} 9. \textcolor{w h i t e}{x .} 6 \text{ } \leftarrow$ details below

$= 159.6$

$9 \div 6 = 1 \text{ carry } 3$
$35 \div 6 = 5 \text{ carry } 5$
$59 \div 6 = 9 \text{ carry } 5$
$54 \div 6 = 9$ , no remainder