Question

Visualize the representation of $2.6\bar{4}$ on the number line up to 5 decimal places, that is op to 2.64444.

Answer 1

Hint: To represent the number on number line we will have to first draw a number line with interval 2 to 3. Now we will make 10 divisions of the interval and hence first plot 2.6. Now similarly we will take the interval 2.60 to 2.70. Again we will divide the interval in 10 parts and hence mark the point 2.64. Hence doing this repeatedly we will mark the required point on the number line.

Complete step by step answer:
Now consider the given number $2.6\bar{4}$ .
Now we know that the number lies between 2 and 3.
Let us first plot 2.6 on the number line.
First we will divide the line between 2 to 3 in 10 parts. Hence we can say that each part is now of the length 0.1 units. Now to get 2.6 will shift 6 units from 2. Hence we get,

Now let us mark the point 2.64.
Now we know that the point lies between 2.60 to 2.70.
Hence we will divide the length between 2.60 and 2.70 into 10 parts. Hence each part will have length 0.01 units. Hence we will shift 4 units from 2.60 to reach 2.64

Now similarly we will plot 2.644. To do so we will take the number line from 2.640 to 2.650.
Now again we will divide the number line in 10 parts and hence each length will denote 0.001 units. Hence again by shifting 4 units from2.64 we will get 2.644.
Hence doing this 5 times we will be able to plot the number 2.64444 on the number line.

Note: Now note that the while drawing number line always note that the length of an interval is the total length divided by number of divisions. Hence we always divide the length by 10 to get precise intervals for decimals.