Name _________________________________________________ Class _______________ Date _______________
Practice
4-4
Operating with Numbers Expressed in Scientific Notation
4-4
Operating with Numbers Expressed in Scientific Notation
1. Add 3.6 × 107 + 5.1 × 107 and write your answer in scientific notation.
2. Subtract 8.4 × 108 – 3.2 × 108 and write your answer in scientific notation.
3. Simplify the expression (7 × 10–6)(7 × 10–6). Write the answer in scientific
notation.
4. A certain star is 4.3 × 102 light years from the Earth. One light year is about
5.9 × 1012 miles. How far from the earth (in miles) is the star?
-8
5. Divide 7.2 # 10- 2 . Express your answer in scientific notation.
3 # 10
6. In one year, the total amount of garbage generated in a certain country
was 6.958 × 1010 pounds. In the same year, the country’s population was
4.57 × 106 people. Determine the pounds of garbage produced per person
in that country in one year.
7. Writing Subtract 2.4 × 105 – 5 × 104. Describe the process of rewriting the
numbers in this problem with the same power of 10.
8. a) Reasoning Subtract 3.95 × 10–2 – 3.36 × 10–2 and write your answer in
scientific notation.
b) Can you write the result using different exponents? Explain.
9. Error Analysis Your friend says that the product of 4.8 × 108 and 2 × 10–3 is
9.6 × 10–5.
a) What is the correct product?
b) What mistake did your friend likely make?
❍ A. Your friend subtracted the exponents instead of adding.
❍ B. Your friend added the numbers instead of multiplying.
❍ C. Your friend incorrectly calculated the exponent of the product.
❍ D. Your friend multiplied the exponents instead of adding.
10. Grocery Shopping A research study reports than an average person purchases
180 granola bars per year. If there are 280 million people in the country, how
many granola bars are purchased by the whole country in one year?
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Practice 4-4
1
Homework K
11. Open-Ended Total consumption of fruit juice in a particular country in 2006
was about 2.28 billion gallons. The population of that country in 2006 was
300 million.
a) What was the average number of gallons of fruit juice consumed per
person in the country in 2006?
b) Using the per person amount from this problem, about how many gallons
would your class consume?
12. Estimation You are given the following expression and asked to find the sum.
3.4 × 104 + 2.58 × 105
a) Round each decimal to the nearest integer. Use these rounded numbers to
estimate the sum.
❍ A. 3 × 104
❍ C. 3 × 105
❍ B. 6 × 105
❍ D. 6 × 104
b) Find the sum. Write your answer in scientific notation.
13. On a certain planet, Continent X has area 6.23 × 106 square miles and
Continent Y has area 6.36 × 106 square miles. Which continent is larger?
By how many square miles is its area greater?
❍ A. The area of Continent X is
of Continent Y.
square miles greater than the area
❍ B. The area of Continent Y is
of Continent X.
square miles greater than the area
14. Think About the Process
a) Describe the procedure for multiplying two numbers in scientific notation.
❍ A. Multiply the first factors, then add the exponents of the powers of 10.
❍ B. Multiply the first factors, then subtract the exponents of the powers
of 10.
❍ C. Add the first factors, then multiply the exponents of the powers of 10.
❍ D. Add the first factors, then add the exponents of the powers of 10.
b) Find the product of (8.1 × 10–5)(6 × 10–5).
15. Think About the Process
5
a) Find the quotient of the first factors of 2.2 # 10-3 . What do you notice?
4.4 # 10
❍ A. The quotient of the first factors is greater than 1 but less than 10.
❍ B. The quotient of the first factors is greater than 10.
❍ C. The quotient of the first factors is less than 1.
5
b) Find 2.2 # 10-3 .
4.4 # 10
c) How does this affect the exponent of the quotient?
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Practice 4-4
2
Homework K
ANSWER
KEY
Practice 4-4: Operating with Numbers Expressed in
Scientific Notation
1. 8.7 × 107
2. 5.2 × 108
3. 4.9 × 10–11
4. 2.537 × 1015
5. 2.4 × 10–6
6. 1.52 × 104
7. 1.9 × 105
8. a) 5.9 × 10–3
b) Answers will vary
9. a) 9.6 × 105
b) C
10. 5.040 × 1010
11. a) 7.6 gallons
b) Answers will vary
12. a) C
b) 2.92 × 105
13. B, 1.3 × 105
14. a) A
b) 4.86 × 10–9
15. a) C
b) 5 × 107
c) Answers will vary
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Practice 4-4
3
Answer Key K