Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question

3 Answers 3

up vote 1 down vote accepted

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

share|improve this answer

7.8 is not 80% of 13.49.

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

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

of $B$.

share|improve this answer
    
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
1  
@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 $13.49$".

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.