Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.7 - Scientific Notation - Exercise Set - Page 91: 76



Work Step by Step

The final form of the expression should be: $a\times10^{n}$. The steps to convert from decimal to scientific notation include: 1. Determine $a$, the numerical factor. Move the decimal point in the given numberto obtain a number whose absolute value is between 1 and 10, including 1. 2. Determine $n$, the exponent on $10^{n}$. The absolute value of $n$ is the number of places the decimal point was moved. The exponent $n$ is positive if the decimal point was moved to the left, negative if the decimal point was moved to the right, and 0 if the decimal point was not moved. For example: Convert $0.000226$ in scientific notation. The numerical factor $a$ would have to be $2.26$ because moving the decimal point further to the right will give a value that’s greater than 10. In obtaining $2.26$, the decimal point was moved $4$ places to the right. Following the statement above, $n$ would be negative. Thus, writing this in the form $ a \times 10^{n}$ = $2.26\times10^{-4}$.
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