What is 2.4 as a percentage?

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Answer 1 · 2016-03-31T14:27:08

$2,4xx100%=240%$

Answer 2 · 2016-03-31T15:46:01

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

Note that 2.4 is $2+4/10$

So as an improper fraction this is $24/10$

$color(blue)("Using short cut method:")$

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

The whole number 2 can be written as $10/10+10/10$

So the whole thing is: $10/10+10/10+4/10$

So this gives you 2 lots of $100%$ plus $(4/10xx100)%$
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$color(blue)("From first principles")$

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

So you write $x/100$ . This is the equivalent of $x%$

So how do we convert our $color(green)(24/10)$ 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 $color(red)(1=10/10)$ 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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