Precision Versus Accuracy

Both precision and accuracy are characteristics of measured values. How precise and accurate are the measurements of the three students? The degree of exactness of a measurement is called its precision. Student 3’s measurements are the most precise, within ± 0.1 cm. The measurements of the other two students are less precise because they have a larger uncertainty.

Precision depends on the instrument and technique used to make the measurement. Generally, the device that has the finest division on its scale produces the most precise measurement. The precision of a measurement is one-half the smallest division of the instrument. For example, the graduated cylinder in Figure 1-11a has divisions of 1 mL. You can measure an object to within 0.5 mL with this device. However, the smallest division on the beaker in Figure 1-11b is 50 mL. How precise were your measurements in the MiniLab?

The significant digits in an answer show its precision. A measure of 67.100 g is precise to the nearest thousandth of a gram. Recall from Section 1.1 the rules for performing operations with measurements given to different levels of precision. If you add 1.2 mL of acid to a beaker containing $2.4 \times 10^2$ mL of water, you cannot say you now have $2.412 \times 10^2$ mL of fluid, because the volume of water was not measured to the nearest tenth of a milliliter, but to 100 times that.

 

Accuracy describes how well the results of a measurement agree with the “real” value; that is, the accepted value as measured by competent experimenters. If the length of the spring that the three students measured had been 14.8 cm, then student 2 would have been most accurate and student 3 least accurate. How accurate do you think your measurements in the Mini Lab on page 8 were? What might have led someone to make inaccurate measurements? How could you check the accuracy of measurements?

A common method for checking the accuracy of an instrument is called the two-point calibration. First, does the instrument read zero when it should? Second, does it give the correct reading when it is measuring an accepted standard, as shown in Figure 1-12? Regular checks for accuracy are performed on critical measuring instruments, such as the radiation output of the machines used to treat cancer.