Samacheer Kalvi Class 9 Maths Solutions Chapter 2 Real Numbers Exercise 2.4

Question 1. Represent the following numbers on the number line.
(i) 5.348
Answer:The number 5.348 is a rational number that lies between 5 and 6. To represent it accurately on a number line, we use a process called successive magnification. This involves zooming in on smaller and smaller segments of the number line.**Steps of Construction:** 1. Start by marking integers 5 and 6 on the number line. Divide the segment between 5 and 6 into 10 equal parts. The number 5.348 lies between 5 and 6. 2. Next, zoom in on the section between 5.3 and 5.4. Divide this segment into 10 smaller equal parts. The number 5.348 lies between 5.3 and 5.4. 3. Then, zoom into the segment between 5.34 and 5.35. Divide this part into 10 even smaller equal parts. 4. Finally, identify the point representing 5.348 in this magnified view. This point will be the eighth mark from 5.340 (or the second mark from 5.350).
In simple words: To show 5.348, first find 5 and 6. Then zoom in to 5.3 and 5.4. Next, zoom closer to 5.34 and 5.35. In the last zoom, find the eighth tiny mark after 5.340; that's 5.348.

🎯 Exam Tip: When using successive magnification, ensure each interval is divided into exactly ten equal parts and label the relevant endpoints clearly for each step.

Question 1. (ii) Represent \( 6.\overline {4} \) upto 3 decimal places on the number line.
Answer:To represent \( 6.\overline {4} \) up to 3 decimal places, we first write it as \( 6.444 \). This number lies between 6 and 7. We use successive magnification to pinpoint its location.**Steps of Construction:** 1. Begin by marking integers 6 and 7 on the number line. Divide the segment between 6 and 7 into 10 equal parts. The number \( 6.444 \) lies between 6 and 7. 2. Next, zoom in on the section between 6.4 and 6.5. Divide this segment into 10 smaller equal parts. The number \( 6.444 \) lies between 6.4 and 6.5. 3. Then, zoom into the segment between 6.44 and 6.45. Divide this part into 10 even smaller equal parts. 4. Finally, identify the point representing \( 6.444 \) in this magnified view. This point will be the fourth mark from 6.440 (or the sixth mark from 6.450).
In simple words: To place \( 6.\overline{4} \) (which is \( 6.444 \)) on the number line, start with 6 and 7. Then, magnify the part between 6.4 and 6.5. Magnify again between 6.44 and 6.45. The fourth mark in this last section is \( 6.444 \).

🎯 Exam Tip: When representing repeating decimals like \( 6.\overline{4} \), remember to expand it to the required number of decimal places before beginning the visualization process.

Question 1. (iii) Represent \( 4.\overline {73} \) upto 4 decimal places on the number line.
Answer:To represent \( 4.\overline {73} \) up to 4 decimal places, we write it as \( 4.7374 \). This number lies between 4 and 5. We will use the method of successive magnification four times to accurately place it on the number line.**Steps of Construction:** 1. Start by marking integers 4 and 5 on the number line. Divide the segment between 4 and 5 into 10 equal parts. The number \( 4.7374 \) lies between 4 and 5. 2. Next, zoom in on the section between 4.7 and 4.8. Divide this segment into 10 smaller equal parts. The number \( 4.7374 \) lies between 4.7 and 4.8. 3. Then, zoom into the segment between 4.73 and 4.74. Divide this part into 10 even smaller equal parts. The number \( 4.7374 \) lies between 4.73 and 4.74. 4. Finally, zoom into the segment between 4.737 and 4.738. Divide this into 10 tiny equal parts. Mark the fourth point from 4.7370 in this magnified view; this point represents \( 4.7374 \).
In simple words: To show \( 4.\overline{73} \) (which is \( 4.7374 \)) on the number line, start with 4 and 5. Then zoom into 4.7 and 4.8. Next, zoom into 4.73 and 4.74. Finally, zoom again into 4.737 and 4.738. The fourth tiny mark in this last zoom is \( 4.7374 \).

🎯 Exam Tip: Always round the repeating decimal to the specified number of decimal places before beginning the visualization, as shown in this example where \( 4.\overline {73} \) becomes \( 4.7374 \).