Locate the following rational numbers on the number line. Class 9

Locate the following rational numbers on the number line. Class 9

Question 1.

Locate the following rational numbers on the number line. Class 9

i. 0.532

ii. $1.1 \overline{5}$

Solution:

i. 0.532 lies between 0 and 1

1. Divide the space between 0 and 1 into ten equal parts. These marks represent the tenths (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, etc.).
2. Locate the mark for 0.5. The number 0.532 lies between 0.5 and 0.6.

1. Further divide the space between 0.5 and 0.6 into ten smaller, equal parts. These represent the hundredths (0.50, 0.51, 0.52, 0.53, 0.54, etc.). Locate the third mark after 0.5, which is 0.53.

1. The number 0.532 lies between 0.53 and 0.54. Further divide the space between 0.53 and 0.54 into ten equal parts. These represent the thousandths (0.531, 0.532, 0.533, etc.). Locate the second mark after 0.53, which represents 0.532.

ii. To represent 1.155555...on the number line, we use the method of successive magnification.

Since

1 < 1.155555...< 2,

the number lies between 1 and 2. Divide the interval from 1 to 2 into 10 equal parts to locate 1.1 and 1.2.

Now,

1.1 <1.155555...< 1.2

So, focus on the interval between 1.1 and 1.2 and again divide it into 10 equal parts to locate 1.15 and 1.16.

Further,

1.15 < 1.155555... < 1.16

Divide this interval once again into 10 equal parts to locate 1.155.

Since the digit 5 repeats endlessly, the number lies between 1.155 and 1.156, very close to 1.156.

Hence, 1.155555...is represented by a point very close to 1.156, slightly to its left, on the number line.