Accuracy usually involves errors that can be corrected: human error, instrument error, and method error. Precision, however, is a description of how exact a measurement can be. It is dependent on the measurement device used. Study the ruler below. Do you notice anything regarding how precise the ruler is?
Take a look at the divisions on the top half of the ruler for centimeters. Every centimeter from 0 to 20 has two divisions, from 0 to 10 you have 20 divisions between each centimeter, but only 10 divisions from 10 to 20. The measurements that can be made between 0 and 10 are more precise than those from 10 to 20 because there are more divisions. Similarly, measurements from 2 to 4 inches are more precise than the ones from 0 to 2 and from 4 to 8 inches are the least number of divisions. In other words, the more divisions a measurement device has, the more precise your measurements can be.
You can show the precision of the measuring instrument using digits. When measuring, provide the number of digits you can tell exactly on the device plus one estimated digit beyond. For example, on the ruler above, you can record centimeter measurements to the thousandth of a centimeter provided you are measuring between 0 and 10 and to the hundredths of a centimeter provided you are measuring between 10 and 20.
Question
What is the precision of the ruler from 2 to 4 inches?
Since the divisions are each \(\small\mathsf{ \frac{1}{64} }\) of an inch, you can estimate out to the closest \(\small\mathsf{ \frac{1}{128} }\) of an inch.
Question
Which measurement is more precise? 1.03 cm or 1.033 cm
The number that goes to the thousandths place is more precise than the number that goes to the hundredths place.
