Class 9th chapter 1st ex. 1.4question 3

Here's the solution for Class 9th, Chapter 1, .4, Question 3.

Question: Visualize the representation of 5.378 on the number line.

Answer:

To visualize 5.378 on the number line, we will use successive magnification.

1. Step 1: Locate the interval. We know that 5.378 lies between 5 and 6. So, we first consider the number line segment between 5 and 6.

2. Step 2: Magnify the interval [5, 6]. Divide the segment between 5 and 6 into 10 equal parts. This gives us points 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9. We can see that 5.378 lies between 5.3 and 5.4.

3. Step 3: Magnify the interval [5.3, 5.4]. Now, we consider the segment between 5.3 and 5.4 and divide it into 10 equal parts. This gives us points 5.31, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.38, 5.39. We can see that 5.378 lies between 5.37 and 5.38.

4. Step 4: Magnify the interval [5.37, 5.38]. Finally, we consider the segment between 5.37 and 5.38 and divide it into 10 equal parts. This gives us points 5.371, 5.372, 5.373, 5.374, 5.375, 5.376, 5.377, 5.378, 5.379. The point 5.378 is located on this segment.

The visualization involves repeatedly zooming into the relevant segment of the number line.