Visualize $4.\overline{26}$ on the number line,up to $4$ decimal places.

(N/A) We can visualize the number $4.\overline{26}$ or $4.2626\ldots$ on the number line using the process of successive magnification.
$I$. The number $4.2626\ldots$ lies between $4$ and $5$. We divide the interval $[4, 5]$ into $10$ equal parts and locate $4.2$ and $4.3$.
$II$. The number $4.2626\ldots$ lies between $4.2$ and $4.3$. We magnify the interval $[4.2, 4.3]$ and divide it into $10$ equal parts to locate $4.26$ and $4.27$.
$III$. The number $4.2626\ldots$ lies between $4.26$ and $4.27$. We magnify the interval $[4.26, 4.27]$ and divide it into $10$ equal parts to locate $4.262$ and $4.263$.
$IV$. The number $4.2626\ldots$ lies between $4.262$ and $4.263$. We magnify the interval $[4.262, 4.263]$ and divide it into $10$ equal parts. We can now locate $4.2626$ on the number line.