Applying percent error: skateboard
About this video
A measuring tape showed a skateboard 2.1 cm longer than its actual length, a 3% overestimate. Using percent error = error ÷ actual, the video solves actual × 3% = 2.1, so actual = 2.1 ÷ 0.03 = 70 cm. The tape would have shown 72.1 cm.
You'll be able to
- write percent error as error divided by actual.
- solve for the actual value when I know the error and the percent error.
- divide by a decimal like 0.03 using patterns.
Key words
- Percent error
- The measured error divided by the actual value, written as a percent.
- Measured error
- How far off the measurement was, in units, here 2.1 cm.
- Overestimate
- A measurement that is larger than the actual value.
Transcript
- [Instructor] A measuring tape showed that a skateboard was 2.1 centimeters longer than its actual length. This was an overestimate of 3%. What was the actual length of the skateboard? Pause the video. Have a go at that. All right, so the important thing to realize is if we have a percent error, percent error, this is going to be equal to the actual error.
So the actual number as opposed to, well, percentages, you could view as a number, but the actual measured error, actual, maybe I'll do this. I'll say, I'll call that measured error. Measured error or actual error, or sometimes just error for short, over the actual measurement or the actual length.
Now, we know the percent error here, that is 3%. And of course this would be a decimal, you could say times 100% to say, oh, that's how I'm converting 2 percentages. So we could say 3% is going to be equal to our measured error, and that is 2.1 centimeters. So 2.1 centimeters divided by the actual.
So we really just need to solve for actual here. So we could multiply both sides by the actual. So let's do that. So actual, I could just use a for here, but I'll just keep writing it out, times actual, those cancel out. So the actual times 3% is equal to 2.1 centimeters.
Fair enough. Now, we can divide both sides by 3%. And so you'd get actual is equal to 2.1. Actually, let me just write this down. I'm using the word actual too much. Actual times 3% is equal to 2.1 centimeters. And now we can divide both sides by 3%. Whoops. We can divide both sides by 3%, and we get 3% divided by 3%.
You get actual is equal to 2.1 centimeters divided by 3%. That's also the same thing as 2.1 centimeters divided by 0.03. That's the same thing as 3%. And so this is going to be equal to, let's see, 2.1 divided by 3 would be 0.7. 2.1 divided by 0.3 would be 7. 2.1 divided by 0.03 would be 70.
So this is equal to 70 centimeters, the actual length of the skateboard. And I just calculated that. We could have done that with a little bit of long division with decimals if we like. You can review that on Khan Academy if you forgot how to do that. And that's all they're asking, the actual length of the skateboard.
Now, there's another interesting question we could answer. If they said, what was the length that the measuring tape showed? Well, they said that the measuring tape was 2.1 centimeters longer than the actual length. So if they asked us what the measuring tape length was, it would be 2.1 plus the 70 centimeters, so 72.1.
If they said it was 2.1 less, and if this was an underestimate, then we would be subtracting from that.
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