Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises - Page 24: 101

Answer

$4.03125 \times 10^{27}$ molecules

Work Step by Step

We have a room that is 5m by 10m by 3m. Each cubic meter contains 1000L of gas. And every 22.4L of gas contains $6.02 \times 10^{23}$ molecules. We need to calculate how many molecules are in this room. So first we calculate how many cubic feet this room is. which is Length x Width x Height. $5\times10\times3 = 150$ cubic meters. Next let's calculate how many liters there are in this room. $150 \times 1000 = 150000$ Now we need to divide 150000L by 22.4. $150000 \div 22.4 = 6696.429$ And finally we need to multiply 6696.429 by $6.02 \times 10^{23}$. To simplify this process, let's first convert 6696.429 into scientific notation and then multiply. $6696.429 = 6.696429 \times 10^3$ $(6.696429 \times 10^3) (6.02 \times 10^{23})$ $6.02 * 6.696429 = 40.3125$ and $10^{3+23} = 10^{26}$ So we have an answer of $40.3125 \times 10^{26}$ but that's not in proper scientific notation. We need to move the decimal point over to the left one space and that will add +1 to the exponent on the power of 10. giving us our final answer of: $4.03125 \times 10^{27}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.