Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.6 Exponents and Scientific Notation - Exercise Set 5.6 - Page 321: 116

Answer

The mass of 80,000 hydrogen atoms in scientific notation is \[1.336\times {{10}^{-19}}\]gram.

Work Step by Step

It is provided that the mass of one hydrogen atom is \[1.67\times {{10}^{-24}}\text{ gram}\]and it is already in scientific notation. Write 80,000 Hydrogen atoms in scientific notation as follows: \[80,000=8.0\times {{10}^{4}}\] Now, Mass of 80,000 Hydrogen atom is: \[\begin{align} & 8.0\times {{10}^{4}}\times 1.67\times {{10}^{-24}}=\left( 8.0\times 1.67 \right)\times \left( {{10}^{4-24}} \right) \\ & =13.36\times {{10}^{-20}} \\ & =1.336\times {{10}^{-19}}\text{ gram} \end{align}\] Hence, the mass of 80,000 hydrogen atoms in scientific notation is \[1.336\times {{10}^{-19}}\]gram.
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