# Figuring out the percentage of A in relation to B

I have two numbers

13.49 and 7.8

I want to know how to figure out how much 7.8 is of 13.49 in percentage

e.g. 7.8 is 80% of 13.49

What is the best way to do this?

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The percentage is $\frac {7.8}{13.49}\cdot 100 \%\approx 57.82 \%$ Note that multiplying by $100 \%$ is multiplying by $1$.

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7.8 is not 80% of 13.49.

Given a number $A$ and a number $B$. $A$ is

$(100)(\frac{A}{B})$%

of $B$.

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It was an example, if I knew what I was doing I probably wouldn't be asking this question – mk_89 Aug 11 '12 at 21:00
@mk_89: You could have used a variable, as in "$7.8$ is $p\%$ of $13.49$". That way you'd have made clear what you mean without making a wrong statement. – celtschk Aug 11 '12 at 21:20

The word "percent" is derived from the Latin per centum, which means roughly "by the hundred". The upshot is that "$X$ percent" means "$X$ out of one hundred", or numerically, $\frac X {100}$.

In general, if we say something like "$Y$ is (some fraction) of $Z$", what we mean is that $Y$ is (equal to) that fraction times $Z$. Consider some examples: What is $\frac23$ of $9$? What is $\frac23$ times $9$?

In the context of percentages, it's the same idea, only our fraction will have denominator $100$. For your example, we have that $7.8$ is $X$ percent of $13.49$, where $X$ is some number that we're trying to figure out. Remember, that translates mathematically to $$7.8=\frac{X}{100}\cdot 13.49,$$ so multiplying both sides by $100$ gives us $$780=13.49X,$$ and dividing by $13.49$ gives us $$X=\frac{780}{13.49}\approx 57.82.$$ Therefore, "$7.8$ is $X$ percent of $13.49$" translates to "$7.8$ is approximately $57.82$ percent of $13.49$", or (if we want it to be exact and don't want decimals in our fractions) to "7.8 is $\frac{78000}{1349}$ percent of $13.49$".

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