Explanation Given info: (a). The given numbers are 250 million and 5 billion . Compare the two numbers. 250 million 5 billion = 250 × 10 6 5 × 10 9 = 50 × 10 6 10 9 (I) From equation (I), Here, a m is 10 6 , a n is 10 9 , m is 6 and n is 9 . Apply the exponent rule. a m a n = a m − n Substitute 10 6 for a m , 10 9 for a n , 6 for m and 9 for n . 10 6 10 9 = 10 6 − 9 = 10 − 3 = 0.001 Substitute 0.001 for 10 6 10 9 in equation (I). 250 million 5 billion = 50 × 0.001 = 5 × 10 − 2 Thus, the number 250 million is 5 × 10 − 2 times as large as 5 billion . (b). The given numbers are 9.3 × 10 2 and 3.1 × 10 − 2 . Compare the two numbers. 9.3 × 10 2 3.1 × 10 − 2 = 3 × 10 2 10 − 2 (II) Here, a m is 10 2 , a n is 10 − 2 , m is 2 and n is − 2 . Apply the exponent rule. a m a n = a m − n Substitute 10 2 for a m , 10 − 2 for a n , 2 for m and − 2 for n . 10 2 10 − 2 = 10 2 − ( − 2 ) = 10 4 = 10000 Substitute 10000 for 10 2 10 − 2 in equation (II)...

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

6th Edition

ISBN: 9780321914620

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Chapter 3.B, Problem 22E

To determine

To determine: The comparison factor by which the number differ to each other.

(a) $250 million$ , $5 billion$

(b) $9.3 \times 10^{2}$ , $3.1 \times 10^{- 2}$

(c) $10^{- 8}$ , $2 \times 10^{- 13}$

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Chapter 3.B, Problem 21E

Chapter 3.B, Problem 23E

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Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

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The comparison factor by which the number differ to each other. (a) 250 million , 5 billion (b) 9.3 × 10 2 , 3.1 × 10 − 2 (c) 10 − 8 , 2 × 10 − 13

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To determine: The comparison factor by which the number differ to each other. (a) 250 million , 5 billion (b) 9.3×102 , 3.1×10−2 (c) 10−8 , 2×10−13

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Chapter 3 Solutions

To determine: The comparison factor by which the number differ to each other.

(a) $250 million$ , $5 billion$

(b) $9.3 \times 10^{2}$ , $3.1 \times 10^{- 2}$

(c) $10^{- 8}$ , $2 \times 10^{- 13}$