Question

What is 2.4 as a percentage?

Answer 1

`2,4xx100%=240%`

Answer 2

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

Explanation:

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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