# What is 2.4 as a percentage?

Mar 31, 2016

2,4xx100%=240%

Mar 31, 2016

240%. With a very detailed explanation about how percentage works.

#### Explanation:

Note that 2.4 is $2 + \frac{4}{10}$

So as an improper fraction this is $\frac{24}{10}$

$\textcolor{b l u e}{\text{Using short cut method:}}$

Converting to a percentage ->24/10xx 100% = 24xx10%=240%
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Viewed another way:

The whole number 2 can be written as $\frac{10}{10} + \frac{10}{10}$

So the whole thing is:$\frac{10}{10} + \frac{10}{10} + \frac{4}{10}$

So this gives you 2 lots of 100% plus (4/10xx100)%
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$\textcolor{b l u e}{\text{From first principles}}$

Percentage is just another way of writing fraction. The only difference is the bottom number (denominator) is fixed at 100.

So you write $\frac{x}{100}$. This is the equivalent of x%

So how do we convert our $\textcolor{g r e e n}{\frac{24}{10}}$ into percentage fractional format. We use the principle of ratios.

We need to change the denominator from 10 into 100.

So if we multiply by 1 but in the form of $\textcolor{red}{1 = \frac{10}{10}}$ we have

color(green)(24/10)xxcolor(red)(10/10)" "=" "color(green)((24color(red)(xx10))/(10color(red)(xx10)) color(blue)(" "=" " 240/100= 24%)

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