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: 20


$$5.8\times 10^{-5}$$

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 division: $3.95\times 10^{4}$ has $3$ significant digits $6.8\times 10^{8}$ has $3$ significant digits. Therefore, the final answer should be rounded to have $2$ significant digits. Rearrange factors and divide: $$\frac{3.95\times 10^{4}}{6.8\times 10^{8}}=\bigg(\frac{3.95}{6.8}\bigg)\bigg(\frac{10^{4}}{10^{8}}\bigg)=5.8\times 10^{-5}.$$
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