# How to figure percentage change?

How would I figure out the percent a number change has?

Let's say I have this number: 88 and now it's 240. How would I find out the percent raise it went up by?

Thanks.

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$(240-88)/88\approx 173\%$ –  Guess who it is. Jul 21 '11 at 17:47
@J.M: I guess you forgot to multiply by $100$ –  user9413 Jul 21 '11 at 17:48
1.73 and 173% are the same thing, only in different "units". –  Guess who it is. Jul 21 '11 at 17:49

The percent change from one value (the "initial value") to another value (the "final value") is defined as

$\displaystyle \frac{(\mathrm{final \; value})\; - \; (\mathrm{initial \; value})}{\mathrm{initial \; value}} \; \times \;$ 100%

In your case, the computation is

$\displaystyle\frac{240 - 88}{88} \; \times$ 100%

$= \displaystyle \frac{152}{88} \; \times$ 100%

$= 1.72727... \; \times$ 100%

$= 172.727...$%

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To elaborate on J. M.'s comment, note that you are actually looking for the solution $m$ of the equation $$\bigg(88 + \frac{m}{{100}}88 \bigg) = 240.$$ The solution is $$m = \bigg(\frac{{240 - 88}}{{88}}\bigg)100 = \bigg(\frac{{240}}{{88}} - 1\bigg)100 \approx 172.7.$$

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$\text{percentage value} = \frac{240-88}{88} \times 100$

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