The ångström (symbol: Å) is a widely used non-SI unit of length. Its value in SI units is:
$$1\ \mathring{\mathrm{A}}=0.1\ \mathrm{nm}=100\ \mathrm{pm}=10^{-10}\ \mathrm m$$
Thus, the required conversion factor is given by
$$\frac{1\ \mathring{\mathrm{A}}}{10^{-10}\ \mathrm m}=1$$
or
$$\frac{10^{-10}\ \mathrm m}{1\ \mathring{\mathrm{A}}}=1$$
This conversion factor can be used to express the given length of $1.213\cdot10^{-11}\ \mathrm m$ in terms of the unit ångström:
$$1.213\cdot10^{-11}\ \mathrm m=1.213\cdot10^{-11}\ \mathrm m\cdot\frac{1\ \mathring{\mathrm{A}}}{10^{-10}\ \mathrm m}=0.1213\ \mathring{\mathrm{A}}$$
Note that $0.1213\ \mathring{\mathrm{A}}=12.13\cdot10^{-2}\ \mathring{\mathrm{A}}$, which is the answer given in your book.
Also note that you do not simply divide the given length by $10^{-10}$ since the units are part of the conversion factor. You actually divide the value by $10^{-10}\ \mathrm m/\mathring{\mathrm{A}}$.