# What is the percent change of 1 to 12?

May 11, 2018

(a) 12 is 1200% of 1.
(b) The increase from 1 to 12 is 1100%.
(That is, 12 is 1100% more than 1.)

#### Explanation:

(a) On a scale where the number $1$ is marked as 100%, we would like to know the percent value that $12$ is matched with.

In math words:

"1 is to 100% as 12 is to what?"

1/(100%) = 12/(square)

Solving for the box, we get

square = (12 xx 100%) / 1" " = 1200%

(b) If we are interested in the increase (or the change from 1 to 12, we do the same thing, but we compare "1 is 100%" to the difference between 12 and 1.

1/(100%) = (12-1)/(square)

Solving for the box:

square = (11 xx 100%)/1 " "=1100%

This may seem rather large, but we remember that 12 itself is already 12 times larger than 1, and 1 is like our whole (our 100%). So it makes sense that a number that's 12 times larger than what we're calling 100% would itself be considered 1200%.