College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.2: 122

Answer

$365$ days (one year) is equal to: $8.76\times10^{3}$ hours, $5.256\times10^{6}$ minutes, and $3.1536\times10^{7}$ seconds.

Work Step by Step

Convert 365 days (one year) to hours, to minutes, and, finally, to seconds, to determine how many seconds there are in a year. Express the answer in scientific notation. Hours: $$365\times24$$ To convert a number into scientific notation, move the decimal point so that you have a result whose absolute value is between one and ten, including one. Multiply the result by ten with an exponent equal to the number of places you moved the decimal point. If the decimal was moved to the left, the exponent will be positive. If the decimal was moved to the right, the exponent will be negative. If the decimal was not moved, the exponent will be zero. $=(3.65\times10^{2})(2.4\times10^{1})$ Group like terms and simplify. $=(3.65\times2.4)(10^{2}\times10^{1})$ $=8.76\times10^{(2+1)}$ $=8.76\times10^{3}$ hours Minutes:$$8.76\times10^{3}\times60$$ $=(8.76\times10^{3})(6\times10^{1})$ Group like terms and simplify. $=(8.76\times6)(10^{3}\times10^{1})$ $=52.56\times10^{(3+1)}$ $=(5.256\times10^{1})\times10^{4}$ $=5.256\times10^{(1+4)}$ $=5.256\times10^{5}$ Seconds:$$5.256\times10^{5}\times60$$ $=(5.256\times10^{5})(6\times10^{1})$ Group like terms and simplify. $=(5.256\times6)(10^{5}\times10^{1})$ $=31.536\times10^{(5+1)}$ $=(3.1536\times10^{1})\times10^{6}$ $=3.1536\times10^{(1+6)}$ $=3.1536\times10^{7}$
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