# Inverse of percentage?

What is the best way to cacluate the inverse of a percentage? For example:

100 * .85 = 85
85 * x = 100
x = 100 / 85
x = 1.17647


Also,

279 * .85 = 237.15
237.15 * x = 279
x = 279 / 237.15
x = 1.17647


For any percentile y (i.e. .85), how do I cacluate its inverse (i.e. 1.17647)? Is the best way to just choose arbitrary numbers (operands) as I've done above? Or is there a more elegant solution?

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## 1 Answer

Simply calculate its multiplicative inverse by definition: for a non-zero real number $y$, $$y^{-1} = \frac 1y.$$

E.g., set your initial value to 1:

1 * . 85 = .85
.85 * x = 1
x = 1 / .85
x = 1.17647

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Yeah, I guess I was just overthinking (or perhaps underthinking) it. But thanks, your answer makes sense. – Kirk Woll Jul 4 '11 at 4:23