GSEB Class 9 Maths Solutions Chapter 1 Number Systems Exercise 1.4

Question 1. Visualise 3.765 on the number line using successive magnification.
Answer: We find 3.765 on the number line between 3 and 4. To achieve this, we enlarge the section between 3 and 4 and split it into 10 identical parts, as presented in figure 1(b).
We find 3.765 on the number line between 3.7 and 3.8, so we enlarge the line segment between 3.7 and 3.8 and split this segment into 10 identical parts, as presented in figure 1(c).
Now we notice that 3.765 is between 3.76 and 3.77. Therefore, we again enlarge this segment of the line and split it into 10 identical parts. The exact position of 3.765 is clearly shown on the number line, as illustrated in figure 1(d).
In simple words: To find 3.765 on the number line, you zoom in closer and closer. First, look between 3 and 4, then between 3.7 and 3.8, and finally between 3.76 and 3.77, dividing each section into ten smaller parts until you see 3.765 clearly.

Exam Tip: Always start by identifying the two whole numbers the decimal lies between, then magnify progressively to each decimal place until the number is clearly visible.

Question 2. Visualise \( 4.\overline {26} \) on the number line, up to 4 places.
Answer: We find \( 4.\overline{26} \) rounded to 4 decimal places, which is 4.2626, on the number line. We observe that 4.2626 sits between 4 and 5 on the number line, as depicted in figure 2(a). We split the segment between 4 and 5 into 10 identical parts and label each division point, as illustrated in figure 2(b).
We find 4.2626 within the range of 4.2 and 4.3 and split this segment into 10 identical parts, as shown in figure 2(c).
Next, we enlarge the section between 4.2 and 4.3 using a magnifying glass to pinpoint 4.2626 between 4.26 and 4.27, as presented in figure 2(d).
Finally, we pinpoint the value 4.2626 by enlarging the line segment between 4.262 and 4.263 using a magnifying glass. We then divide this segment into 10 identical parts and highlight 4.2626, as shown in figure 2(e).
In simple words: To locate \( 4.\overline{26} \) (which is 4.2626 when rounded to four places) on a number line, zoom in multiple times. First, find its spot between 4 and 5, then between 4.2 and 4.3, next between 4.26 and 4.27, and finally between 4.262 and 4.263. Each time, divide the section into ten smaller parts to get closer to the exact number.

Exam Tip: When visualizing repeating decimals, always approximate to the required number of decimal places before beginning the successive magnification process.