Absolute difference

Transcription

So suppose in the news you hear tuition is expected to increase 7% next year. If tuition this year was $1,200 per quarter, what will be next year? So there is couple of ways we can think about this. One way would be to say that if we're going to add an additional 7% on top of the tuition the next year. Next year will be our original 100% plus an extra 0.07%, or in other words, 107% of this year. So in other words our tuition this year was $1200, let's find 107% of that $1200. And, of course, usually we don't actually multiply it by the percent, we go ahead and rewrite it as a decimal. We go ahead and multiply, we come up with next year's tuition will be $1,284 per oops, per quarter. Now, another way we could have done this would be to say that 7% of 1,200. In other words, we could have started by just figuring out what the increase was going to be, so we could have said $1,200 times 7% is $84. In other words, the tuition is going to increase by $84 and then the tuition this year plus the increase gives us the expected tuition for next year, and that been another way to approach the same problem. And here is another problem the value of a car dropped from 7400 to a hundred dollars to $6800 over the last year. What percent decrease is this? So let's figure out, first off, how much the actual value decreased. If we take the new price minus the old price, we see that the price dropped by $600, so a $600 decrease. Now, usually when we talk about changes, it's easiest to talk about the absolute value of the change, which in this case would be $600. And we call this an absolute change, this is the actual change in absolute value, the actual change from one year to the next so it is $600 decrease. But we're really interested in the percent change and so we need to take this out of the starting amount. Now, this is really important when we talk about changes, relative changes, we need the, the absolute change. The absolute change divided by the starting quantity. So our change was 600 but that needs to be relative to our starting quantity. In this case we dropped from 6, 7,400, so it makes sense to count 7,400. As what we call the base of our percent? Now, base ends up being really important, and we'll see later. But for now we'll just say 600 out of 7400, if we divided that we would get 0.081, which is an 8.1% decrease. And again, this is what we call a relative change. And absolute changes and relative changes are two different ways to describe how somethings changed, and both have their value. often times though, the relative change is more useful to see sort of help big of a change it is because it describes that change relative to the starting at point.