## College Algebra (6th Edition)

$1.1\times10^{7}$
$$\frac{66,000\times0.001}{0.003\times0.002}$$ 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. $$=\frac{(6.6\times10^{4})(1\times10^{-3})}{(3\times10^{-3})(2\times10^{-3})}$$ Regroup like terms then simplify. $$=(\frac{6.6\times1}{3\times2})(\frac{10^{4}\times10^{-3}}{10^{-3}\times10^{-3}})$$ When multiplying exponential expressions with the same non-zero base, add the exponents. $$=(\frac{6.6}{6})(\frac{10^{(4+(-3))}}{10^{(-3+(-3))}})$$ $$=(\frac{6.6}{6})(\frac{10^{(1)}}{10^{-6}})$$ When dividing exponential expressions with the same non-zero base, subtract the exponent of the denominator from the exponent of the numerator. $$=1.1\times10^{(1-(-6))}$$ $$=1.1\times10^{(1+6)}$$ $$=1.1\times10^{7}$$