Betsy has a Ph.D. in biomedical engineering from the University of Memphis, M.S. from the University of Virginia, and B.S. from Mississippi State University. She has over 10 years of experience developing STEM curriculum and teaching physics, engineering, and biology.
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!
What would happen if your measurement was SMALLER than the true value instead of larger? Let's look at an example of that too. Suppose that in a science experiment, you measure the acceleration of a falling ball to be 8.7 m/s2. You know that the true value of the acceleration due to gravity on Earth is 9.8 m/s2.
Did you notice that the percent error was still positive? In this calculation, you should always use the absolute value of the quantity in the numerator. Whether the measurement is bigger than the true value or the true value is bigger than the measurements, the percent error should still be positive.
Accuracy is defined as how close a measurement is to the true or accepted value. It is important to make accurate measurements, and often, you may need to know exactly HOW accurate your measurements are. The amount of error in a measurement can be quantified by calculating the percent error between the measurement and the true or accepted value.
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