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Significant Figures

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A Significant Win

A Significant Win

 

Credit: JOE MADONNA
Source: http://www.flickr.com/photos/84123820@N00/2758143250
License: CC BY-NC 3.0

You may recognize this famous gold medalist. He’s Michael Phelps, the world-champion swimmer. The times of world-class athletes like Michael Phelps may be measured to the hundredths of a second. That’s important because the times are often very close. A new world record may be set by just a split-second difference in time.

Why It Matters

  • The need for accuracy in timing athletic events makes significant figures important. Significant figures are the correct number of digits for reporting a measurement or calculation. Just the thought of significant figures may make you cringe, but using them really isn’t difficult. You just need to apply a few simple rules.
  • Credit: Phil Roeder
    Source: http://www.flickr.com/photos/tabor-roeder/5826742009/
    License: CC BY-NC 3.0

    We must rely on high-speed cameras to capture race times to the hundredth of a second [Figure2]

     

  • How accurately must swimming times be measured, and how many significant figures are required? To answer this question, watch the video below. It shows Michael Phelps setting a new world record in an exciting 100-meter race. Notice how little time separates his time in this race from the previous world record. 

http://www.youtube.com/watch?v=2vK8iJgISXY

Can You Apply It?

Learn more about significant figures at the links below. Then answer the questions that follow.

  1. True or false: The number of significant figures is the minimum number of figures required to report a value without loss of accuracy.
  2. Which figures are significant?
    1. all non-zero figures
    2. any zeros between significant figures
    3. trailing zeros to the right of a decimal point
    4. all of the above
  3. Which figures are not significant?
    1. trailing zeros to the left of a decimal point
    2. leading zeros to the right of a decimal point
    3. leading zeros to the left of a decimal point
    4. two of the above
  4. How many significant figures are there in each of the following numbers?
    1. 1000
    2. 1000.0
    3. 10.005
    4. 0.005
  5. Why is it important to use significant figures when recording a measurement, such as an athlete’s time in a race?
  6. When using a digital measuring device, how many figures are significant?
  7. When using an analog (non-digital) measuring device, how many figures are significant?
  8. What significant figures would you record for the measurement of liquid in the graduated cylinder shown below? Why? (Assume that the cylinder is marked in milliliters.)

Credit: U.S. Navy photo by Mass Communication Specialist 1st Class Sarah Murphy
Source: http://en.wikipedia.org/wiki/File:US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_(Fuel)_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg
License: CC BY-NC 3.0

  1. In the swimming competition in the video above, what was Michael Phelps’ time? What was the previous world record? How much time did he shave off the previous world record?
  2. In this swimming competition, swimmer’s times were measured digitally. How many significant figures are there in Michael Phelps’ winning time? Why?

Image Attributions

  1. [1]^ Credit: JOE MADONNA; Source: http://www.flickr.com/photos/84123820@N00/2758143250; License: CC BY-NC 3.0
  2. [2]^ Credit: Phil Roeder; Source: http://www.flickr.com/photos/tabor-roeder/5826742009/; License: CC BY-NC 3.0
  3. [3]^ Credit: U.S. Navy photo by Mass Communication Specialist 1st Class Sarah Murphy; Source: http://en.wikipedia.org/wiki/File:US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_(Fuel)_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg; License: CC BY-NC 3.0

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