Algebra 1: Common Core (15th Edition)

If the given numbers are in scientific notation, then $a$ and $b$ are numbers between 1 and 10 (less than 10). (They have one nonzero digit before the decimal point). If their product is greater than ten, then $ab$ has two or more digits before the decimal point, so $ab\times 10^{m+n}$ is NOT in scientific notation. Example 1: $(3.0\times 10^{2})(5.0\times 10^{3})=15.0\times 10^{5}$ (Each factor is in scientific notation; the product is not. It needs to be manipulated...) $15.0\times 10^{5}=1.5\times 10^{1}\times 10^{5}=1.5\times 10^{6}$ Example 2 $(3.0\times 10^{2})(2.0\times 10^{3})=6.0\times 10^{5}$, which is in scientific notation. So, the product CAN be in scientific notation. Answer: sometimes.