# The Effects of Measurement & Rounding Errors

Instructor: James Anderson

James Anderson is a PhD Candidate in Agricultural Sciences specializing in Plant Breeding. He has taught several classes during this time, including Plant Genetics, Plant Breeding, Field Plot Techniques, Precision Agriculture, and Soil Fertlility Evaluation.

Just how accurate are we in the things we do? When we measure something or round an answer in a math problem, we are essentially saying that's close enough. But, how close is close enough? Let's explore the effects of measurement and rounding errors.

## Accuracy in Measurement

Measurement in math and science comes down to accuracy and precision. We use the concept of accuracy in everyday life. Being able to choose how accurate we want to be in our measurements is important because it affects the result by introducing error. Accuracy is all about getting the correct measurement and thus is dependent on the instrument and scale of measurement that we use. Precision deals with whether the measurement can be reproduced. So, how accurate do we want to be? Well, that depends on what we are doing.

Suppose you are buying grass seed for your yard. The package lists seeding rates in pounds per square foot of lawn, so how many pounds do you need to buy? To figure out how much seed to buy, you must first measure your lawn. But, how accurate do you need to be for what you are doing?

Seeding rates are calculated at the rate of pounds of seed per 1,000 square feet. Does it make sense, then, to measure your yard in inches? If you think about it, that doesn't make much sense because you are buying seed based on an amount per 1,000 square feet. You use a tape measure to measure in feet instead of a ruler to measure in inches. Then you can figure out how much seed you need based on the number of square feet in the lawn. Accuracy to the nearest square inch is not necessary.

What about when you deal with much smaller numbers, though? For instance, scientists constantly look at different properties of soybean seeds. They want to know how much oil, protein, and carbohydrates are in the seeds, so they need to figure out how to measure these things. One of the ways to measure oil content is to weigh the dried seeds and then remove the oil through various methods. The difference in weight between the dry seed with oil and the dry seed without oil will tell you how much oil was in the seed. The average weight of a soybean is under one gram.

In this case, you want to have accurate scales so you can to determine how much oil leaves the seed. The degree of accuracy desired in your measurement is different than in calculating the amount of grass seed because the soybean is very small to start out with (around one gram) and the amount of oil in it is even smaller than that.

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