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Question:

Visualise 3.765 on the number line, using successive magnification.

Solution:

To visualize 3.765 on a number line using successive magnification, we follow these steps:

  1. Initial Visualization: Start with a number line showing the integers from 3 to 4. 3.765 lies between 3 and 4.

  2. First Magnification: Magnify the section of the number line between 3 and 4. This section will now be the focus. We can add markings for 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, and 4. 3.765 lies between 3.7 and 3.8.

  3. Second Magnification: Now, magnify the section between 3.7 and 3.8. Add markings for 3.71, 3.72, 3.73, 3.74, 3.75, 3.76, 3.77, 3.78, 3.79, and 3.8. 3.765 lies between 3.76 and 3.77.

  4. Third Magnification: Finally, magnify the section between 3.76 and 3.77. Add markings for 3.761, 3.762, 3.763, 3.764, 3.765, 3.766, 3.767, 3.768, 3.769, and 3.77. Now 3.765 is clearly visible on the number line.

This process of successive magnification allows us to locate any decimal number on the number line with increasing precision. Each step involves zooming in on a smaller and smaller interval, until the desired number is clearly identified.