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

Hint: In this question we need to sketch \[4.\overline {26} \] on the number line up to 4 decimal places. To spot the number on the number, find the range of the numbers in which the given numbers lie step by step and spot the number on the number line.

Complete step-by-step answer:
Given the number which is to be visualized on the number line is \[4.\overline {26} \]
Since the number is a recurring number we can write this as \[4.2626\]
We know the given number lies between 4 and 5, so we will divide the gap between 4 and 5 in ten parts as
 \[4,4.1,4.2,4.3,4.4,4.5,4.6,4.7,4.8,4.9,5\]

Now if we again see the given number we can say that this number must lie between the numbers \[4.2,4.3\] as shown in the number line
So we will divide the gap between \[4.2\] and \[4.3\] in ten parts as
 \[4.2,4.21,4.22,4.23,4.24,4.25,4.26,4.27,4.28,4.29,4.3\]

Now again if we see the given number we can say that this number must lie between the numbers \[4.26,4.27\]
So we will divide the gap between \[4.26\] and \[4.27\] in ten parts as
 \[4.26,4.261,4.262,4.263,4.264,4.265,4.266,4.267,4.268,4.269,4.27\]

Now again if we see the given number we can say that this number must lie between the numbers \[4.262,4.263\]
So we will divide the gap between \[4.262\] and \[4.263\] in ten parts as
 \[4.262,4.2621,4.2622,4.2623,4.2624,4.2625,4.2626,4.2627,4.2628,4.2629,4.263\]

Now finally we can spot the number \[4.2626\] on the number line.

Note: A number line is usually a horizontal line with zero in the middle and as we move to the right on the line the numbers are positive and increasing and if we move on the left side of the line the numbers increase and get more and more negative. In this question since the number which was to be spotted was positive so we moved to the right side of the number line.