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Section 2.2 Scientific Notation
A number in the form \(a \times 10^n\) with \(1 \leq |a| \lt 10\) is said to be in scientific notation. For example,
\begin{equation*}
4.25 \times 10^{7} = 42500000, \quad -9\times 10^{-4} = -0.0009
\end{equation*}
are both in scientific notation. We can use properties of exponents to conveniently multiple and divide.
Example 2.7. Multiplying in Scientific Notation.
\begin{align*}
\left(4.25\times 10^7\right) \times \left(-9\times 10^{-4}\right)
\amp=\quad -4.25\times 9.1\times 10^7\times 10^{-4}\\
\amp=\quad -38.675 \times 10^{7-4}\\
\amp=\quad -38.675 \times 10^{3}\\
\amp=\quad -3.8675 \times 10^{1}\times 10^{3}\\
\amp=\quad -3.8675 \times 10^{4}
\end{align*}
Example 2.8. Dividing in Scientific Notation.
\begin{align*}
\frac{4.25\times 10^7}{-9.1\times 10^{-4}}
\amp\approx\quad -0.467 \times 10^{7-(-4)}\\
\amp\approx\quad -0.467 \times 10^{11}\\
\amp\approx\quad -4.67 \times 10^{-1}\times 10^{11}\\
\amp\approx\quad -4.67 \times 10^{10}
\end{align*}
