Scientific Notation Problems
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Section 3: Scientific Notation
1. How many one hundred dollar bills would you need to have ten thousand dollars? Explain.
2. How many 1,000 are there in 10 billion? Explain.
3. Explain in your own words:
a. How to convert a standard number to scientific notation.
b. How to convert a number from scientific notation to a standard number.
4. Write 4,500,000 in scientific notation.
5. Write 120,000 in scientific notation.
6. Write 68 billion in scientific notation.
7. Write 59 million in scientific notation.
8. Write 8.34 x 104 in standard notation.
9. Write 9.4 x 107
a. In standard notation
b. Write out the name of this number.
10. Write 3.476 x 1011
a. In standard notation
b. Write out the name of this number.
11. According to Wikipedia, On December 12, 2013, debt held by the public was approximately $12.312 trillion. Express this figure in scientific notation.
12. The earth is 9.3 x 107 miles to the sun.
a. Write this distance as a standard number.
b. What is the name of this number?
13. There are about 1.01 million K-12 students in Indiana. Indiana spends about $11,700 per pupil.
a. Write each number in scientific notation.
b. Use scientific notation to calculate Indiana's education budget for K-12 pupils.
c. Write a sentence using your answer from part b.
14. A dairy cow can produce 5,400 quarts of milk per year. There are 9.2 million dairy cows in the US.
a. Write each number in scientific notation.
b. Use scientific notation to calculate the total in quarts that all US dairy cows produce.
c. Write a sentence using your answer from part b.
15. According to Wikipedia, the population of China is about 1,362,080,000 and the population of the US is about 317,427,000.
a. Express each population in scientific notation.
b. China's population is how many times bigger than the US population?
16. There are 6.54 million people in Indiana. The area of Indiana is 36,185 square miles.
a. Write each number in scientific notation.
b. Use scientific notation to calculate Indiana's people per square miles.
c. Write a sentence using your answer from part b.
17. The wavelength of light is given by the velocity divided by the frequency. The velocity of blue light is 300,000,000 m/sec, and its frequency is 650,000,000,000,000 cycles per second. What is the wavelength of blue light? Use scientific notation to make your calculation and express your answer.
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Solution Summary
Step-by-step solutions are given to the example problems of scientific notation.
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1
10,000/100 = 100
You need 100 one hundred dollar bills since ten thousand divided by one hundred is 100.
2
(10 * 10^9) / 1,000 = 10 * 10^6 = 10,000,000
There are 10 million 1,000 in 10 billion since 10 billion divided by 1,000 is 10,000,000
3a
1) Move the decimal point to create a number from 1 to less than 10.
2) Count the number of spaces the decimal point was moved. This will be the exponent. 3) If the decimal point was moved to the left in step 1, the exponent is positive. If the decimal point was moved to the right in step 1, the exponent is negative.
4) Write the number from step 1 multiplied by 10 to the exponent of the number from steps 2 and 3 (note if the number is positive or ...
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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