$\begingroup$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?
$\endgroup$3 Answers
$\begingroup$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 $13.49$".
$\endgroup$$\begingroup$The percentage is $\frac {7.8}{13.49}\cdot 100 \%\approx 57.82 \%$ Note that multiplying by $100 \%$ is multiplying by $1$.
$\endgroup$$\begingroup$7.8 is not 80% of 13.49.
Given a number $A$ and a number $B$. $A$ is
$(100)(\frac{A}{B})$%
of $B$.
$\endgroup$2
