How do you divide (1.1x10^22)/(6.022x10^23)?

Mar 29, 2015

You can split the fraction as it follows:
$\setminus \frac{1.1 \cdot {10}^{22}}{6.022 \cdot {10}^{23}} = \setminus \frac{1.1}{6.022} \setminus \setminus \frac{{10}^{22}}{{10}^{23}}$

and deal with the two parts separately.

$\setminus \frac{1.1}{6.022}$ is a common numeric division, and the result is $0.1827$

As for $\setminus \frac{{10}^{22}}{{10}^{23}}$, you can see it in two ways: either you expand the powers, having a fraction of the form
$\setminus \frac{10 \cdot 10 \cdot \ldots \cdot 10}{10 \cdot 10 \cdot 10 \cdot \ldots \cdot 10}$, with 22 "tens" at the numerator and 23 at the denominator. So, you can simplify all the "tens", except one at the denominator, obtaining ${10}^{22} / {10}^{23} = \frac{1}{10}$.

In a more formal fashion, you have that ${10}^{22} / {10}^{23} = {10}^{- 1}$, which is again $\frac{1}{10}$.

So, the final answer is $\setminus \frac{1.1 \cdot {10}^{22}}{6.022 \cdot {10}^{23}} = 0.1827 \cdot {10}^{- 1}$.