Question

What is the product of $8.2\times {10}^9$ and$4.5\times {10}^{-5}$ in scientific notation?

Answer 1

Find the product of $8.2\times {10}^9$ and$4.5\times {10}^{-5}$.

The power rule is, $a^m\times a^n=a^{m+n}$.

Use the power rule on the given numbers and simplify.

$\begin{array}{rcl}8.2\times {10}^9\times 4.5\times {10}^{-5}& =& \left(8.2\times 4.5\right)\times \left({10}^9\times {10}^{-5}\right)\\ & =& \left(8.2\times 4.5\right)\times {10}^{9-5}\\ & =& 36.9\times {10}^4\end{array}$

Hence, product of $\mathbf{8}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}$ and$\mathbf{}\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{\times }\mathbf{}{\mathbf{10}}^{\mathbf{-}\mathbf{5}}$ is $\mathbf{36}\mathbf{.}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}$.