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: 118

Answer

One year or 365 days are equals to \[8.760\times {{10}^{3}}\] hours, \[5.256\times {{10}^{5}}\]minutes or\[3.1536\times {{10}^{7}}\]seconds.

Work Step by Step

To convert 365 days in hours, minutes and seconds calculate these values one by one. \[\begin{align} & 1\text{ year}=365\text{ days} \\ & 1\text{ day}=24\text{ hours} \end{align}\] Now, 1-year number of hours is: \[\begin{align} & 1\text{ year}=24\times 365 \\ & =8760\text{ hours} \\ & =8.760\times {{10}^{3}}\text{ hours} \end{align}\] \[\begin{align} & 1\text{ hour}=60\text{ minutes} \\ & 1\text{ minute}=60\text{ seconds} \end{align}\] So, number of minutes in one year is: \[\begin{align} & 1\text{ year}=60\times \left( 8.760\times {{10}^{3}} \right) \\ & =525.6\times {{10}^{3}} \\ & =5.256\times {{10}^{5}} \\ & =5.256\times {{10}^{5}}\text{ minutes} \end{align}\] Number of seconds in one hour is: \[\begin{align} & 1\text{ hour}=60\times 60 \\ & =3600\text{ seconds} \\ & =3.60\times {{10}^{3}}\text{ seconds} \end{align}\] Number of seconds in 1 year is: \[\begin{align} & \text{Number of }\text{seconds in 1 year}=\left( 8.760\times {{10}^{3}} \right)\times \left( 3.60\times {{10}^{3}} \right) \\ & =\left( 8.760\times 3.60 \right)\times \left( {{10}^{3+3}} \right) \\ & =31.536\times {{10}^{6}} \\ & =3.1536\times {{10}^{7}} \end{align}\] Hence, one year or 365 days are equals to \[8.760\times {{10}^{3}}\] hours, \[5.256\times {{10}^{5}}\]minutes or\[3.1536\times {{10}^{7}}\]seconds.
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