### A Significant Win

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.
- 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.

- http://www.ducksters.com/kidsmath/significant_digits_or_figures.php
- http://web.campbell.edu/faculty/fetterman/Significant%20Figures.htm

- True or false: The number of significant figures is the minimum number of figures required to report a value without loss of accuracy.
- Which figures are significant?
- all non-zero figures
- any zeros between significant figures
- trailing zeros to the right of a decimal point
- all of the above

- Which figures are not significant?
- trailing zeros to the left of a decimal point
- leading zeros to the right of a decimal point
- leading zeros to the left of a decimal point
- two of the above

- How many significant figures are there in each of the following numbers?
- 1000
- 1000.0
- 10.005
- 0.005

- Why is it important to use significant figures when recording a measurement, such as an athlete’s time in a race?
- When using a digital measuring device, how many figures are significant?
- When using an analog (non-digital) measuring device, how many figures are significant?
- 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.)

- 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?
- In this swimming competition, swimmer’s times were measured digitally. How many significant figures are there in Michael Phelps’ winning time? Why?