# How do you convert 4/5 into a decimal and percent?

May 13, 2016

color(blue)(4/5 -> 80% -> 80/100)

$\textcolor{b l u e}{\frac{4}{5} \equiv \frac{8}{10} \equiv 0.8}$

#### Explanation:

Decimal values are made up of:

$\ldots + 100 ' s + 10 ' s + 1 ' s + \text{ decimal point "+1/10color(white)("")^(ths)+1/100color(white)("")^(ths)+1/1000color(white)("")^(ths)+..." and so on.}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Considering "4/5" as a decimal}}$

The denominator is 5 so if we can convert this to 10 we have our first decimal place of counting in tenths.

Multiply by 1 but in the form of $1 = \frac{2}{2}$ giving:

$\frac{4}{5} \text{ "-=" "4/5xx1" "-=4/5xx2/2" " =" "(4xx2)/(5xx2)" " =" } \frac{8}{10}$

So $\textcolor{b l u e}{\frac{4}{5} \equiv \frac{8}{10} \equiv 0.8}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Considering "4/5" as a percentage}}$

Percentage can be written in 2 ways.

Suppose we hade 60 percent. Then this can be written as

60%" which is the same as "60/100

So percentage is counting in 1/100color(white)("")^(ths)

Multiply by 1 in the form of $1 = \frac{2}{2} \text{ and then by } 1 = \frac{10}{10}$

$\frac{4}{5} \times \frac{2}{2} \times \frac{10}{10} \text{ " -=" "8/10xx10/10" "-=" } \frac{80}{100}$

So color(blue)(4/5 -> 80% -> 80/100)