Watch the video for definitions and also examples the percent error and also difference:

## What is Percent Error?

Percent errors tells you how large your errors are when you measure something in one experiment. Smaller sized values typical that you space close to the embraced or actual value. Because that example, a 1% error means that girlfriend got very close to the accepted value, while 45% method that friend were fairly a long way off from the true value. Measurement errors are largely unavoidable: tools can it is in imprecise, hands have the right to shake, or your tools just could not have actually the capability to measure accurately. Percent error will let friend know just how badly these inescapable errors impacted your results.

You are watching: How to find the accepted value

## Formula

The formula is:**PE = (|accepted worth – speculative value| \ welcomed value) x 100%. **

**Example question:** The accepted distance to the moon is 238,855 miles.* You measure up the distance as 249,200 miles. What is the percent error?**Solution:**Step 1: Insert her data right into the formula:PE = (|accepted worth – speculative value| \ embraced value) x 100% =((|238,855 miles – 249,200|) \ 238,855 miles) x 100% =Step 2: Solve:(10345 \ 238,855 miles) x 100% =0.0433 * 100% =**4.33%.**

*That’s the mean distance, yet let’s assume it’s the distance on the job you’re taking the measurement!

**Note**: in some sciences, the absolute value sign is periodically (but no always) omitted. You may want to refer to your textbook to view if the author is omitting the absolute worth sign. If you aren’t sure, the many common type is **with** the absolute worth sign.

## Alternate Wording

Accepted value is sometimes called the “true” worth or “theoretical” value, so you could see the formula created in slightly different ways:

PE = (|true value – speculative value| \ true value) x 100%. PE = (|theoretical worth – experimental value| \ theoretical value) x 100%.All 3 versions of the formula median the precise same thing — it’s just different wording.

## Alternative an interpretation of Percent Error using relative Error

The percent error is sometimes reported together being 100% times the loved one error. Be mindful though, due to the fact that there are actually **two species of family member error**: one for precision and also one because that accuracy (not sure of the difference in between the two? See: Accuracy and Precision). The meaning “100% time the loved one error” is only true if you are using the “accuracy” version of loved one error:

The an interpretation does *not *work if you’re using the RE for precision:

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## What is Percent Difference?

Percent distinction is nearly the same as percent error, only rather of one “true” value and also one “experimental” value, you compare two experimental values. The formula is:

**CITE THIS AS:**

**Stephanie Glen**. "Percent Error / Percent Difference: Definition, Examples" native

**gaianation.net**: primary school Statistics because that the rest of us! https://www.gaianation.net/percent-error-difference/

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