Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Skills Handbook - Scientific Notation and Significant Digits - Exercises - Page 980: 22


$$1.9\times 10^{-8}$$

Work Step by Step

In scientific notation, the number of significant digits is the number of digits in the leading number between $1$ and $10$. The final answer should have the same number of significant digits as the least number of significant digits in any of the numbers involved in the multiplication: $3.972\times 10^{-5}$ has $4$ significant digits $4.7\times 10^{-4}$ has $2$ significant digits Therefore, the final answer should be rounded to have $2$ significant digits. Rearrange factors and multiply: $$(3.972\times 10^{-5})(4.7\times 10^{-4})=(3.972\times 4.7)(10^{-5}\times 10^{-4})$$ $$=1.9\times 10^{-8}.$$
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