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Practice
4-2
Using Scientific Notation to Describe Very Large Quantities
4-2
Using Scientific Notation to Describe Very Large Quantities
1.Express the number 80,000 in scientific notation.
2.Express the number 60,000 in scientific notation.
3.Express the number 8.5 × 105 in standard form.
4.The diameter of a certain star is about 9.3 × 106 km. Express this diameter in
standard form.
5.Which number is greater?
❍❍ A.6 × 106
❍❍ B.7 × 109
6.A rectangle has length 8 × 104 mm and width 4 × 104 mm. The rectangle’s
length is how many times its width?
7.a)Writing Express the number 5.2 × 106 in standard form.
b) Describe two advantages that scientific notation has over standard form.
Describe two advantages of standard form. Give examples for each.
8.a)Reasoning Which number is less, 6.9 × 106 or 630,000?
b) When you compare two numbers in scientific notation, which do you
compare first, the first factors or the exponents? Explain.
9. Error Analysis Owen incorrectly claims that because 20,000 = 20 × 1,000, he
can express 20,000 in scientific notation as 20 × 103.
a) What was Owen’s error?
❍❍ A. The product he found is correct, but 20 × 103 is not in scientific
notation since 20 is not less than 10.
❍❍ B. The product he found is correct, but 20 × 103 is not in scientific
notation since 20 is not less than 1.
❍❍ C. He found the power of 10 incorrectly since 1,000 ≠ 103.
❍❍ D. He found the product incorrectly since 20,000 ≠ 20 × 1,000.
b) Express 20,000 in scientific notation correctly.
10. Population An historian predicts that by 2050, about 1.56 × 107 people will
live in a certain country. Express this prediction in standard form.
11. a) Multiple Representations Express the mass 6,200,000 kilograms using
scientific notation in two ways, first with kilograms and then with grams.
b) List some other scientific-notation forms for this mass using other metric
prefixes.
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Practice 4-2
1
Homework G
12. Express the number 4.3076 × 108 in standard form.
13. At the end of 2002, the population of Cities A and B were 670,000 and
6.8 × 105, respectively.
a) Which city had the greater population at the end of 2002?
b) In 2003, the populations became equal while the total population stayed
the same. What was each city’s population at the end of 2003?
14. Challenge A scientist is growing bacteria in three colonies, A, B, and C. At
the moment, there are 3.5 × 106 bacteria in Colony A, 2.6 × 106 bacteria in
Colony B, and 9.3 × 106 bacteria in all.
a) Express each of these numbers in standard form.
b) Use those results to find the number of bacteria in Colony C by evaluating
the expression 9.3 × 106 – (3.5 × 106 + 2.6 × 106).
15. Challenge The populations of Cities A and B are 2.6 × 105 and 1,560,000,
respectively. The population of City C is two times the population of City B.
The population of City C is how many times the population of City A?
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Practice 4-2
2
Homework G
ANSWER
KEY
Practice 4-2: U
sing Scientific Notation to Describe Very
Large Quantities
1.8 × 104
2.6 × 104
3.850,000
4.9,300,000 km
5.B
6.2
7.a)5,200,000
b)
Answers will vary
8.a)630,000
b)
Answers will vary
9.a)A
b)
2 × 104
10. 15,600,000
11. a) 6.2 × 106 kg
6.2 × 109 g
b)
Answers will vary
12. 430,760,000
13. a) City B
b)
675,000
14. a) 3.5 × 106 = 3,500,000
2.6 × 106 = 2,600,000
9.3 × 106 = 9,300,000
b)
3,200,000
15. 12
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Practice 4-2
3
Answer Key G