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Why do we multiply by 100 while calculating percentage ?

    example : 2/100 * 100 =2%
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It is because 2% is easier to visualize as compared to 0.02. For example, if I am talking about a small gain of money, 0.1% is a lot easier to 'visualize' as compared to 0.001. – picakhu Jul 11 '12 at 12:32
% is a notation symbol that means "divided by 100". – Djaian Jul 11 '12 at 13:05

% represents out of $100$. If you have $a$ things out of $n$,then what would you have if there were $100$ things in total, that is given by percent.

Now, Suppose you have $a$ things out of total of $b$ things ,then,

$\implies$ if there were total number of things =$1,$ then you would have = $\frac{a}{b}$ things out of $1$ thing

$\implies$ if total number of things$=100\implies $ you would have $=\frac{a}{b}\times 100$ out of those $100$ things and this is what calculating percent is.

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first 2 lines are clear to me but the example is still not clear. – user286035 Jul 11 '12 at 14:07

Think of a percent as being like a unit, designed especially for describing ratios between 0 and 1, which come up naturally when we talk about parts of a whole. In analogy, we don't measure small objects in meters, because meters are cumbersome. But 1 meter is the same a 100 centimeters, so we multiply by 100 when converting. It's just a change of units.

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What does it mean for some quantity to be "x%", example, "60%"?
- it means that we are expressing something as a fraction of 100, that is "x%" means "x divided by 100", or "60%" means "60 divided by 100".
- if anyone expresses different fractions as a fraction of a different number, you will have to do some arithmetic to know which is larger or smaller, but if we all agree we will express it as a fraction with base 100, it is much easier to compare, example compare 1/3 to 3/10, which is larger or smaller. it is slightly easier to compare 33.33% with 30% and conclude that 33.33% is larger, but it is slightly harder to realize that by looking at fractions to a different base.

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