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Lesson 14: Word Problems in Scientific Notation

1. A corporation has 4.8 x 103 employees. The average annual salary for each of its employees is $4.5 x 104. Approximately how much does the corporation pay its employees each year?

2. If 446 billion telephone calls were placed by 135 million United States telephone subscribers, what was the average number of calls per subscriber? (Write your answer in scientific notation)

3. A light year is the distance light travels in a year. On light year is about 5.88 x 1012 miles. The sun is about 1.6 x 10-5 light years from earth. About how many miles is the sun from the earth?

4. The density of silver is 1.05 x 10-2. The density of calcium is 1.5 x 10-3. How many times greater is the density of silver than of calcium?

5. The distance from Earth to the imaginary planet Med is 1.7 x 107 miles. If a spaceship is capable of traveling 1,420 miles per hour, how many days will it take the spaceship to reach the planet Med? Round your answer to the nearest day.

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6. A computer can perform 4.66 x 108 calculations per second. How many calculations can this computer perform in one minute?

7. About 1.37 x 107 people in South Africa speak English. English is the primary language for about 3.7 x 106 of these people. The rest speak it as a secondary language. About how many speak English as a secondary language?

8. The longest bone in the human body averages about 5.05 x 10-1 meters in length. The shortest bone averages 2.8 x 10-3 meters. About how many times greater is the length of the longest bone and the shortest bone?

9. The sun burns about 4.4 x 106 tomes of hydrogen per second. How much hydrogen does the Sun burn in one year? (One year is about 3.16 x 107 seconds)

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10. A rocket can travel 2,000 feet in 3.6 x 10-2 second. How many feet can the rocket travel in one hour? Express your answer in scientific notation.

11. The body of a 150 lb person contains 2.3 x 10-4 lb of copper. How much copper is contained in the bodies of 1200 such people?

12. The speed of light is approximately 3 x 108 m/s. How far does light travel in 6.0 x 101 seconds?

13. The size of the Indian Ocean is 2.7 x 107 square miles. The Arctic Ocean is 1/5 the size of the Indian Ocean. How big is the Arctic Ocean?

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14. The speed of light is 3 x 108 m/s. If the sun is 1.5 x 1011 meters from Earth, how many second does it take light to reach the Earth?

15. A liter is equal to 1 x 106 mm3. There are roughly 5 x 106 red blood cells in 1 mm3 of human blood. How many red blood cells are there in a liter of human blood?

16. Lake Superior has roughly 25 times the volume of Lake Erie. If the volume of Lake Superior is approximately 1.22 x 104 km3, what is the approximate volume of Lake Erie?

17. A car is traveling at a rate of 50 feet in 2 x 10-2 seconds. If the car continues at the same rate, how far will it travel in one hour? Express your answer in scientific notation.

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Supplemental Practice

1. A computer can do 1000 operations in 4.5 x 10-6 seconds. How many operations can be done by this computer in one hour? Express your answer in scientific notation.

2. The geographic area of California is 163,696 sq. mi, and the geographic area of the US is 3,794,101 sq. mi. Let’s round off these figures to 1.637 × 105 and 3.794 × 106. In terms of area, roughly estimate how many Californias would make up one US. Then compute the answer to the nearest ones.

3. The average distance from Earth to the moon is about 3.84 × 105 km, and the distance from Earth to Mars is approximately 9.24 × 107 km in year 2014. On this simplistic level, how much further is when traveling from Earth to Mars than from Earth to the moon?