Station 1: Length Measurement

Station 1: Length Measurement

Learning objectives: 2, 5

You will find a small object and two measuring instruments: a ruler and a set of digital calipers.

Part A: Getting to know the ruler

  1. Look at the ruler. What is the smallest division marked on it?
  2. Look at the spacing between those divisions. Can you estimate where a measurement falls between two divisions, or does the spacing not allow that? How finely do you think you can read this instrument?
  3. Based on your answers to questions 1 and 2, what is the smallest uncertainty you could honestly claim when reporting a measurement with this ruler? Write down your reasoning.

The smallest division on an analog instrument is called the least count. The smallest uncertainty you can honestly claim when using an instrument is called the Instrument Limit of Error, or ILE. For analog instruments like a ruler, the ILE is equal to the least count or some fraction of it — your judgment about how finely you can read the scale determines which.

Part B: Getting to know the digital calipers

  1. Turn on the digital calipers and look at the display. How many decimal places does it show? What is the value of the last digit displayed?
  2. Watch the display as you hold the calipers still. Does the last digit stay stable or does it fluctuate between values?
  3. If the display is stable, the true value lies somewhere between half a last digit below and half a last digit above what is displayed. For example, if the display reads 24.35 mm, the true value lies between 24.345 mm and 24.355 mm. Based on this, what is the ILE of the calipers when the display is stable?
  4. If the last digit fluctuates, what does that tell you about the instrument’s uncertainty? How would you determine the ILE in that case?
  5. Compare the ILE of the ruler to the ILE of the calipers. Which instrument is more precise?

For digital instruments, the ILE is typically half the value of the last digit when the display is stable. If the last digit fluctuates, the ILE reflects the range of that fluctuation rather than just half the last digit.

Part C: Making measurements

  1. Measure the same dimension of the object with the ruler. Record your measurement in the form (measurement ±ILE) with appropriate units.
  2. Now measure the same dimension with the digital calipers. Record your measurement in the form (measurement ±ILE) with appropriate units.
  3. Compare your two measurements. Do they agree? Which instrument gives you more confidence in your result, and why?
  4. If you wanted to calculate the area or volume of this object, which instrument would you choose and why? What would choosing the less precise instrument cost you in terms of confidence in your result?