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: 18


$$4\times 10^{18}$$

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: $7.2\times 10^{11}$ has $2$ significant digits $5\times 10^{6}$ has $1$ significant digit. Therefore, the final answer should be rounded to have $1$ significant digit. Rearrange factors and multiply: $$(7.2\times 10^{11})(5\times 10^{6})=(7.2\times 5)(10^{11}\times 10^{6})$$ $$=4\times 10^{18}.$$
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