# How do you simplify (6.1times10^5)(2.4times10^4)?

Dec 28, 2016

$1.467 \times {10}^{10} \leftarrow \text{ Scientific notation}$

#### Explanation:

$\textcolor{b r o w n}{\text{Breaking this down into a lot of detail so that you can see what is}}$ $\textcolor{b r o w n}{\text{happening.}}$

$6.1$ is the same as $\frac{61}{10} \to 61 \times \frac{1}{10}$

$2.4$ is the same as $\frac{24}{10} \to 24 \times \frac{1}{10}$

So $\left(6.1 \times {10}^{5}\right) \left(2.4 \times {10}^{4}\right) = 6.1 \times {10}^{5} \times 2.4 \times {10}^{4}$

$= 61 \times {10}^{5} / 10 \times 24 \times {10}^{4} / 10$

$= 61 \times 24 \times {10}^{5} / 10 \times {10}^{4} / 10$

$= 61 \times 24 \times {10}^{4} \times {10}^{3}$

$= 61 \times 24 \times {10}^{7}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{w h i t e}{14} 24$
$\underline{\textcolor{w h i t e}{14} 61} \leftarrow \text{ multiply}$
$1440$
$\underline{\textcolor{w h i t e}{14} 24} \leftarrow \text{ add}$
$1464$

So we now have:

$1464 \times {10}^{7}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$1467 \times {10}^{7}$
$146.7 \times {10}^{8}$
$14.67 \times {10}^{9}$
$1.467 \times {10}^{10} \leftarrow \text{ this is the same format as in the question }$

$1.467 \times {10}^{10} \leftarrow \text{ Scientific notation}$