You can split the fraction as it follows:
\frac{1.1 * 10^22}{6.022 * 10^23} = \frac{1.1}{6.022}\ \frac{10^22}{10^23}
and deal with the two parts separately.
\frac{1.1}{6.022} is a common numeric division, and the result is 0.1827
As for \frac{10^22}{10^23}, you can see it in two ways: either you expand the powers, having a fraction of the form
\frac{10 * 10 * ... * 10}{10 * 10 * 10 * ... * 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=1/10.
In a more formal fashion, you have that 10^22/10^23=10^{-1}, which is again 1/10.
So, the final answer is \frac{1.1 * 10^22}{6.022 * 10^23} = 0.1827 * 10^{-1}.
