Practice Questions on Real Number Representation | Class 9 – Chapter 1 Number System
Question 1. Visualize 3.765 on the number line, using successive magnification.
Solution:
Now in the given question, you have to represent 3.765 on the number line using the successive magnification method.
Step 1: We will check the range of the number and magnify it accordingly. That is, 3.765 will lie between 3 and 4 so we will magnify the value between 3 and 4.
Magnify 3 and 4
Step 2: Now 3.76 will lie between 3.7 and 3.8, so we will magnify the value between 3.7 and 3.8.
Step 3: Now as we will magnify we will check the range, that is, 3.765 will lie between 3.76 and 3.77.
Step 4: Now as we will magnify the value between 3.76 and 3.77 we will find the value 3.765.
Hence 3.765 is found between 3.76 and 3.77
Question 2. Visualize [Tex]4.\overline{26} [/Tex] on the number line, up to 4 decimal places.
Now in this question, we have to represent the number [Tex]4.\overline{26} [/Tex] on the number line. The bar sign ( ͞ ) above .26 depicts that the number .26 is repeated continuously after the decimal point. But it is given that we have to represent the number up to 4 decimal places only, that is, we have to represent 4.2626 on the number line.
Step 1: We will check the range of the number and magnify it accordingly.
Step 2: Now 4.2626 will lie between 4 and 5, so we will magnify the value between 4 and 5.
Magnify 4 and 5
Step 3: 4.26 will lie between 4.2 and 4.3, so we will magnify the value between 4.2 and 4.3.
Step 4: 4.262 will lie between 4.26 and 4.27, so we will magnify the value between 4.26 and 4.27.
Step 5: Now at last 4.2626 will lie between 4.262 and 4.263, so we will magnify the value between 4.262 and 4.263.
Step 6: As we will magnify the value between 4.262 and 4.263 we will get 4.2626.
Hence 4.2626 is found between 4.262 and 4.263
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