# Accuracy & Error in Measurements

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

When making measurements, it is important to be as accurate as possible. In this lesson, learn about what accuracy is and how we measure and quantify exactly how much error there is in a measurement.

## Why does Accuracy Matter?

A few weeks ago, I decided to buy a new rug for my bedroom. I wanted a rug that covered as much of the room as possible, so I measured the length and width of the room with a ruler. I went to the store and picked out a beautiful rug, then brought it home and unrolled it in my room. To my surprise, it didn't fit! The rug was too big for the room! What happened? It's likely that my measurements of the size of the room weren't very accurate, which led to a lot of wasted time and money.

Accuracy is defined as how close a measurement is to the true or accepted value. Being able to make accurate measurements is crucial not only for making sure you can buy the right size rug, but also in many other fields, such as construction, science, and engineering.

## How to Calculate Percent Error

It is often helpful to know exactly HOW accurate your measurements are. One way that you can do this is by calculating how much error there is in the measurements. The word error just means a mistake or deviation from what is expected, but there is a way that we can quantify exactly how much error there is in a measurement. This is called percent error, and it is a ratio of the difference between the true value of your measurement and the true value. This ratio is then multiplied by 100 to make it a percent.

Notice that the numerator in this expression is enclosed by two absolute value symbols (they look like this: | ). This means that what is inside these symbols should always be made positive.

Now, let's go back to the problem of my too-large rug. When I measured the size of my room, I got that it was 9 ft wide. However, the actual width of my room was 7.5 ft. What was the percent error in my measurement?

I really didn't do a very good job of making accurate measurements, did I? My measurement was 20% bigger than the actual size of the room. I guess that's why my new rug didn't fit!

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