Visualize the representation of $5.3\overline{7}$ on the number line up to $5$ decimal places,that is,up to $5.37777$.

(N/A) To visualize $5.3\overline{7}$ on the number line up to $5$ decimal places,we use the process of successive magnification:
$1$. We know that $5.3\overline{7}$ lies between $5$ and $6$. We divide the distance between $5$ and $6$ into $10$ equal parts and locate $5.3$ and $5.4$. $5.3\overline{7}$ lies between $5.3$ and $5.4$ [Fig $(i)$].
$2$. Next,we divide the distance between $5.3$ and $5.4$ into $10$ equal parts to locate $5.37$ and $5.38$. $5.3\overline{7}$ lies between $5.37$ and $5.38$ [Fig $(ii)$].
$3$. We then divide the distance between $5.37$ and $5.38$ into $10$ equal parts to locate $5.377$ and $5.378$. $5.3\overline{7}$ lies between $5.377$ and $5.378$ [Fig $(iii)$].
$4$. Finally,we divide the distance between $5.377$ and $5.378$ into $10$ equal parts to locate $5.3777$ and $5.3778$. By magnifying this portion,we can represent $5.37777$ on the number line [Fig $(iv)$].