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Per Capita Example Questions

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1. According to CTIA.org, there were 327.6 million cell phones in the U.S. in 2014. The U.S. population was approximately 317.9 million at that time. How many cell phones per capita were there in the U.S. in 2014 and what does this value tell us?

2. According to KFF.org, there are approximately 15,737 physicians in the state of Indiana. If Indiana's population is 6 million, how many physicians per capita are there in our state?

3. Explain in your own words how to convert a small number to and from scientific notation.

4. The mass of a dust particle is .000000753 grams, express this in scientific notation.

Use this table for Problems # 5 thru # 9.
Motor Vehicle Deaths Data 2009 Census: https://www.census.gov/compendia/statab/cats/transportation/motor_vehicle_accidents_and_fatalities.html
State MV Deaths Population
Indiana 693 6 million
Illinois 911 12.4 million
Ohio 1021 11.35 million
Michigan 871 9.9 million
Alaska 64 0.63 million

5. Find the ratio of Hoosiers to Ohioans (by population) and interpret its meaning.

6. Find the Motor Vehicle Deaths per capita for the states in the table. Hint: These will be small decimal numbers, write them in the blank column in the chart above.

7. Write the deaths per capita in Scientific Notation in the table above.

8. Take the Motor Vehicle Death rate per capita for Indiana and multiply it by 100,000. Explain the meaning of this value in a sentence.

9. Write a few sentences to explain your findings. Which state has the worst rate, the best? Hint: It may be helpful to scale the rates in order to make a more meaningful statement.

10. A hair measures 7.5 x 10-4 inches, express this in standard notation.

11. Find the following using Scientific Notation:
a. 1.48 x 103 divided by 1.2 x 109

b. 2.5 x 10-5 times 5.3 x 1010
Use this table for Problems # 12 thru # 14.
Population density
State Population Area Sq miles Pop Density
Indiana 6 million 36,185
Illinois 12.4 million 56,343
Ohio 11.35 million 41,328
Michigan 9.9 million 58,513
Alaska 0.63 million 587,878

12. Find the population density of the states in the above table (population/area).

13. Which state has the largest number of people per square mile?

14. Which state has the smallest number of people per square mile?

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Solution Summary

The Word file contains the solutions. The Excel file contains re-usable formulas for questions 6, 7, 8, 12, 13 and 14.

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1
327.6 million = 327 600 000
317.9 million = 317 900 000
327 600 000 / 317 900 000 = 1.03
There were 1.03 cell phones per capita in the U.S. in 2014. This tells us that there was slightly more than one cell phone per person.

2
6 million = 6 000 000
15 737 / 6 000 000 = 0.003
There are 0.003 physicians per capita.

3
Step 1) Move the decimal point to the right until it is after the first non-zero number.
Step 2) Count the number of spaces the decimal point was moved in Step 1.
Step 3) Write the answer obtained in Step 1 followed ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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