Question

Calculate:
$6.022 \times {10}^{23} \times \frac{100}{23}$
$6.022 \times {10}^{23} \times \frac{100}{56}$

Answer 1

You can split the fraction as it follows:
1.1⋅10226.022⋅1023=1.16.022 10221023

and deal with the two parts separately.

1.16.022 is a common numeric division, and the result is 0.1827

As for 10221023, you can see it in two ways: either you expand the powers, having a fraction of the form
10⋅10⋅...⋅1010⋅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 10221023=110.

In a more formal fashion, you have that 10221023=10−1, which is again 110.

So, the final answer is 1.1⋅10226.022⋅1023=0.1827⋅10−1.