Applying percent error: pedometer

0:00- [Instructor] A pedometer records steps that are 9% greater than the actual number of steps. A student actually walks 8,000 steps. How many steps does the pedometer show? Pause the video and try to answer that. All right, so in questions like this, it's really important to think about, okay, what is the estimate, or the recording, versus what is the actual.

0:23The actual we see here is 8,000. And what we wanna figure out is how many steps does the pedometer show? And they tell us the pedometer records steps that are 9% greater than the actual. So the pedometer is going to overestimate the number of steps. It's going to be 9% more than this actual value, right over here.

0:47So the number of steps that the pedometer shows is going to be 8,000, that's the actual, plus nine, that looks like a percent sign, plus 9% times 8,000. Or another way to think about it, this is also the same thing as 8,000 plus 0.09 times 8,000. You could also think about it as the same thing as 1.09 times 8,000.

1:18These are all the same thing, but let's just calculate what this is. If I had nine times eight, that is going to be 72. But if I did nine times 8,000, that is 72,000. But I don't have nine times 8,000, I have nine hundredths. So I need to divide this by 100. Or another way to think about it, I have two places to the right of the decimal, so I need two places to the right of the decimal here.

1:46So I'm gonna overestimate by 720 steps. They're not asking us how much did we overestimate by. They're asking us the total number of steps the pedometer showed. So it'd be 8,000 plus 720, so 8,720 steps. And we're done.