Oct 17, 2017

$\left(2.3 \times {10}^{7}\right) \left(1.4 \times {10}^{-} 2\right) = 3.2 \times {10}^{5}$

#### Explanation:

Start by looking at the exponents or powers of the two decimal numbers to see that this is a large number (tens of millions) multiplied by a relatively small number (hundredths or 1/100).
So the answer will lay somewhere in the thousands.

$\left(2.3 \times {10}^{7}\right) \left(1.4 \times {10}^{-} 2\right)$

To multiply exponents, we need to add them: ${10}^{7} + {10}^{-} 2 = {10}^{5}$
but we still must be on the look out for additional powers if the decimal numbers multiply to be above $10.0$ - here they do not.

$\left(2.3 \times {10}^{7}\right) \left(1.4 \times {10}^{-} 2\right) = d . d \times {10}^{5}$

and we can solve for: $d . d = 2.3 \times 1.4 = 3.22$ rounded to $3.2$

So: $\left(2.3 \times {10}^{7}\right) \left(1.4 \times {10}^{-} 2\right) = 3.2 \times {10}^{5}$