1. Lesson 2

1.5. Explore

Mathematics 30-3 Module 6

Module 6: Measurement

 

Explore

 

Through the Discover activity, you should have found that all measurements are approximate and dependent on the precision of the measuring tool. Look at the following diagram.

 

This illustration shows the length of a nail to be closer to 4.6 cm than 4.5 cm or 4.7 cm.

 

uncertainty: the margin of error of a measurement, if not stated, is half the precision of the measuring device

 

Source: MathWorks 12 Student Book/Teacher Guide. (Vancouver: Pacific Educational Press, 2011.)

The length of the nail shown is approximately 4.6 cm, meaning it is closer to 4.6 cm than to either 4.5 cm or 4.7 cm. For this reason, it can be said that the length is 4.6 cm, to the nearest tenth of a centimetre. Note that the precision of a measurement is limited by the measuring device. In this case, the precision of the measurement tool is 0.1 cm; therefore, there is some uncertainty in this measurement.

 

A measured value can be written as follows:

 

 

measured value ± measurement uncertainty

 

Although the precision of the measuring device is 0.1 cm, assume the uncertainty is one-half the precision, or 0.05 cm. Therefore, the measurement can be written as (4.6 ± 0.05) cm.

 

Try This 2

 

Use the diagram to answer the following questions.

 

This illustration is a tennis ball being measured by a 15-cm ruler showing 6.7 cm.

tennis ball: iStockphoto/Thinkstock

  1. Measure the diameter of the tennis ball shown using the 15-cm ruler.
  2. The precision of the ruler is 0.1 cm. State the diameter and the uncertainty.
  3. Using the uncertainty, what would be the minimum limit of the measurement?
  4. Using the uncertainty, what is the maximum limit of the measurement?

course folder Save your responses in your course folder.

Subtract the uncertainty from the measured diameter.