1. ## Percentages

I haven't done much math since high school, so please be patient with me.

100 * 0.8 = 80

80 * X = 100

X is equal to 1.25, which was pretty easy to find after trial and error, but the trial and error process takes a lot longer with something like this:

5,680 * 0.802 = 4555.36

4555.36 * X = 5,680

X is equal to ~1.2468827930174563591022444, but that took forever to find through trial and error. How can I easily find X?

2. ## Re: Percentages

80x = 100 therefore x = 100/80

3. ## Re: Percentages

You can take the reciprocal of the number you're replacing. For your example above note that $X = \dfrac{1}{0.8}$

edit: This is exactly the same as Pickslides' answer. You can multiply my answer by 100/100 to get his

For your second example it will be $X = \dfrac{1}{0.802}$. Normally we'd just use a calculator to solve for X but you can do it using fractions.

$\dfrac{1}{0.802} \times \dfrac{1000}{1000} = \dfrac{1000}{802}$. This will cancel by at least 2.

Thanks guys!