College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.2 - Page 34: 115


$\textbf{a. } \$2.7 \times 10^{12}$ $\textbf{b. } 3.09 \times 10^{8}$ $\textbf{c. } \$8738$

Work Step by Step

$\textbf{a.}$ We must represent $\$2.7$ trillion in scientific notation. $1$ trillion in standard form is $1,000,000,000,000$. $1$ trillion in scientific notation is $1.0 \times 10^{12}$. To represent $\$2.7$ trillion in scientific notation, we can replace $1.0$ with $\$2.7$ to get $\$2.7 \times 10^{12}$. $\textbf{b.}$ We must represent $309$ million in scientific notation. $1$ million in standard form is $1.0 \times 10^{6}$. $309$ in scientific notation is $3.09 \times 10^{2}$. To represent $309$ million in scientific notation, we must replace $1.0$ with $3.09$ and add the exponents $6$ and $2$. This results in a final value of $3.09 \times 10^{8}$. $\textbf{c.}$ We must divide the value found in part $\textbf{a}$ by the value found in part $\textbf{b}$ and represent the solution in decimal notation rounded to the nearest dollar. Therefore, we must divide $\$2.7 \times 10^{12}$ by $3.09 \times 10 ^{8}$. Before we do that, however, we should use the decimal form of the values. To convert from standard form to decimal form, we must shift the decimal point based on the exponent. Since the exponents in both values are positive, we shift the decimal points to the right. The number of places we shift the decimal point is equal to the value of the exponent. This results in $\frac{\$2,700,000,000,000}{309,000,000}$. Rounded to the nearest dollar, this results in $\$8738$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.