# Change factor

If something gets larger than it was originally, is the change factor greater or less than 1?

## Change factor

Using percentage is helpful when we talk about a ratio between things. But when we deal with changes expressed in percentages, there's a handy trick to know, it is called change factor. Change means that there is more or less of something, and factor, the factor you are going to multiply by. Here is a pile of money - let's say, a thousand kroner - you have borrowed it from the bank at 5% interest. How much do you have to pay back?

1,000 kroner plus 5% of 1,000 kroner, that is 1,000 + 0,05 * 1,000 - since 5% is five-hundredths or 0,05. A simpler way to calculate it is like this, 1,000 * 1,05. 1,000 * 1 is the thousand you borrowed, and the five-hundredths is the interest. 1,05 is the change factor, a factor that you multiply by to know how much there is after a change. These are Leon's jeans.

They are 120 centimeters long, but they will shrink by 2% after a wash. So how long will they be then? Right now, the jeans are 100% of their original size, if they shrink by 2% you take 100 - 2: 98. The change factor is therefore 0,98, which is 98-hundredths. 120 * 0,98 is 117,6, well they got a little shorter.

In other words, the change factor is the number that you multiply by the original amount to get the amount after the change. When describing an increase, the change factor is one plus the percentage of the increase. When describing a decrease, it is one minus the percentage of the decrease. The original amount times the change factor equals the amount after the change, sometimes this is called a growth factor. It means the same thing, but it sounds like amounts can only increase if it's called this, so we say change factor.