## College Algebra (6th Edition)

$365$ days (one year) is equal to: $8.76\times10^{3}$ hours, $5.256\times10^{6}$ minutes, and $3.1536\times10^{7}$ seconds.
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. $=(5.256\times6)(10^{5}\times10^{1})$ $=31.536\times10^{(5+1)}$ $=(3.1536\times10^{1})\times10^{6}$ $=3.1536\times10^{(1+6)}$ $=3.1536\times10^{7}$