Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-2 Scientific Notation - Practice and Problem-Solving Exercises: 43

Answer

$3.18\times10^{-3}$

Work Step by Step

We start with the given expression: $6(5.3\times10^{-4})$ We rewrite the expression using the associative property: $6\times5.3\times10^{-4}$ We multiply the first two terms: $31.8\times10^{-4}$ Since 31.8 is not between 1 and 10, the number is not in scientific notation. To convert a number not in scientific notation with a power of $10$ to scientific notation, we must move the decimal to the left or to the right, counting the number of places, until the number is between $1$ and $10$, and multiply by a power of $10$. If the number is less than $1$, and we moved the decimal to the right, we subtract the number of places we moved the decimal point to the existing power of $10$. If the number is greater than $1$, and we moved the decimal to the left, we add the number of places we moved the decimal point to the existing power of $10$. We move the decimal point $1$ place to the left, so we add $1$ to the power of $10$: $3.18\times10^{-3}$
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