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: 17

Answer

$$8.95\times 10^{-12}$$

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: $1.78\times 10^{-7}$ has $3$ significant digits $5.03\times 10^{-5}$ has $3$ significant digits Therefore, the final answer should be rounded to have $3$ significant digits. Rearrange factors and multiply: $$(1.78\times 10^{-7})(5.03\times 10^{-5})=(1.78\times 5.03)(10^{-7}\times 10^{-5})$$ $$=8.95\times 10^{-12}.$$
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