## Elementary Algebra

$0.02$
RECALL: (i) Scientific notation has the form $a(10^n)$, where $1 \le a \lt 10$ and where $n$ is an integer. (ii) $\frac{a^{m}}{a^{n}}=a^{m-n}$ Write each number in scientific notation to obtain: $=\dfrac{8.2(10^{-6})}{4.1(10^{-4})}$ Divide $8.2$ and $4.1$ together and the powers of 10 together to obtain: $=\dfrac{8.2}{4.1} \cdot \dfrac{10^{-6}}{10^{-4}} \\=2 \cdot 10^{-6-(-4)} \\=2(10^{-6+4}) \\=2(10^{-2}) \\=0.02$