First of all, we have to know the equivalent decimal number to each of them.
[tex]\begin{gathered} 4\frac{2}{3}=\frac{4\cdot3+2}{3}=\frac{12+2}{3}=\frac{14}{3}=4.66666\ldots \\ 4.7 \\ \sqrt[]{17}=4.12310\ldots \\ 4\frac{3}{4}=\frac{4\cdot4+3}{4}=\frac{16+3}{4}=\frac{19}{4}=4.75 \end{gathered}[/tex]Notice that the interval is from 4.12310... to 4.75.
You can observe that 4.7 falls into this interval, and 4.666... also falls into this interval.