Is there any way to convert fraction to percentage without converting to decimal?

Question

I know that you can convert fraction to percentage without converting to decimal.

Ex:

2/5 = 2/5 * 20/20 = 40%

How about fractions with denominator that cannot be converted to 100

Ex: 2/13

Is there any way / formula to solve this without converting the fraction to decimal?

Answer 1

No. Note that $40\%$ simply means $\dfrac{40}{100}$. So, can you write $\dfrac2{13}$ as $\dfrac k{100}$ for some integer $k$? No, because$$\frac2{13}=\frac k{100}\iff200=13k.$$But $200$ is not a multiple of $13$.

Answer 2

To convert a fraction to a percentage, simply change the denominator to $100.$ To do this, multiply by $1=100/100=100\%,$ which does not change anything.

Thus, for example, we have that $$2/13=2/13×100\%=200/13\%=15\frac{5}{13}\%.$$