Chapter 1: Real Numbers (Exercise 1.4)

Admin 06 Aug, 2026 9 बार पढ़ा गया

Topic: Visualising Real Numbers on the Number Line through Successive Magnification

Question 1:

Visualise $2.874$ on the number line using successive magnification.

Solution:

Step 1: The number $2.874$ lies between $2$ and $3$ .
- Divide the portion of the number line between $2$ and $3$ into $10$ equal parts.
- Locate the interval between $2.8$ and $2.9$ .
Step 2: The number $2.874$ lies between $2.8$ and $2.9$ .
- Magnify the interval $[2.8, 2.9]$ and divide it into $10$ equal parts ( $2.81, 2.82, \dots, 2.89$ ).
- Locate the interval between $2.87$ and $2.88$ .
Step 3: The number $2.874$ lies between $2.87$ and $2.88$ .
- Magnify the interval $[2.87, 2.88]$ and divide it into $10$ equal parts ( $2.871, 2.872, \dots, 2.879$ ).
- The $4^{\text{th}}$ mark after $2.87$ represents the exact location of $2.874$.

Question 2:

Visualise $5.\overline{28}$ ( $5.2828...$ ) on the number line up to $4$ decimal places (i.e., $5.2828$ ).

Solution:

Step 1: The number $5.2828$ lies between $5$ and $6$ .
- Divide the segment between $5$ and $6$ into $10$ equal parts.
- Identify the interval between $5.2$ and $5.3$ .
Step 2: Magnify the interval $[5.2, 5.3]$ and divide it into $10$ equal parts.
- Identify the interval between $5.28$ and $5.29$ .
Step 3: Magnify the interval $[5.28, 5.29]$ and divide it into $10$ equal parts.
- Identify the interval between $5.282$ and $5.283$ .
Step 4: Magnify the interval $[5.282, 5.283]$ and divide it into $10$ equal parts ( $5.2821, 5.2822, \dots, 5.2829$ ).
- The $8^{\text{th}}$ mark after $5.282$ accurately represents $5.2828$.