Percentage error

Okay kiddo, so let's imagine that you have a toy car and you want to measure how long it is. You measure it with a ruler and you find out that it's 10 centimeters long. But then, you ask your friend to measure it too, and they say that it's 11 centimeters long.

Now, you might think that your friend made a mistake or that their ruler is wrong. But it's possible that both of you made a mistake, or that your rulers are a little bit different. So, we use something called percentage error to see how much our measurements differ from what we expect.

Percentage error is just a fancy way of saying how much our measurement differs from the true value, expressed as a percentage. To calculate the percentage error, we need to know three things: the true value, the measured value, and the formula for percentage error.

The true value is what we expect the measurement to be. In this case, it might be the actual length of the toy car, if we could measure it perfectly. The measured value is what we actually measured with our rulers. The formula for percentage error is:

Percentage error = (Measured value - True value) / True value x 100%

So, let's use an example to see how this works. Say that the true length of the toy car is actually 12 centimeters, but you measured it as 10 centimeters, and your friend measured it as 11 centimeters. To calculate the percentage error for your measurement, we plug in the numbers:

Percentage error = (10 - 12) / 12 x 100%
Percentage error = -2 / 12 x 100%
Percentage error = -0.1667 x 100%
Percentage error = -16.67%

Uh oh, that's a negative percentage error! That means that our measurement was too small compared to the true value. But for your friend's measurement, we get:

Percentage error = (11 - 12) / 12 x 100%
Percentage error = -1 / 12 x 100%
Percentage error = -0.0833 x 100%
Percentage error = -8.33%

So your friend's measurement was also too small, but not as much as yours.

In summary, percentage error is just a way to see how much our measurements differ from what we expect, expressed as a percentage. We use the formula:

Percentage error = (Measured value - True value) / True value x 100%

And we calculate it for each measurement that we take.