Name: Surds: Introduction
Uploaded: 2019-07-19
Duration: 4 min 21 s
Description: We know that irrational numbers are written in the form of neither terminating nor recurring decimals. Let's learn to write another form of irrational number...

Question

Write any three rational numbers and any three irrational numbers lying between

2.1

and

2.2

Accepted Answer

We are given to write any three rational numbers and any three irrational numbers lying between $2.1$ and $2.2$

First, we shall write the three rational numbers between $2.1$ and $2.2$ .

We know that a rational number between $a$ and $b$ can be written as $\frac{a + b}{2}$ .

Hence, one rational number between $2.1$ and $2.2$ is $\frac{2.1 + 2.2}{2} = \frac{4.3}{2} = 2.15$ .

Also, one rational number between $2.1$ and $2.15$ is $\frac{2.1 + 2.15}{2} = 2.125$ .

And, one rational number between $2.15$ and $2.2$ is $\frac{2.15 + 2.2}{2} = \frac{4.35}{2} = 2.175$ .

Therefore, the three rational numbers between $2.1$ and $2.2$ are $2.125, 2.15$ and $2.175$ .

Now, we shall find three irrational numbers lying between $2.1$ and $2.2$ .

We know that the decimal expansion of irrational numbers are non-terminating and non-repeating. There are an infinite number of irrational numbers between any two rational or irrational numbers. So, there are an infinite number of irrational numbers between $2.1$ and $2.2$ . We can choose any three of them.

Here, we shall choose the numbers $2.101001001000100001 . . . . ., 2.102002000200002 . . . . .$ and $2.103003000300003 . . . . .$ . The chosen numbers are lying between $2.1$ and $2.2$ and also, they are non-terminating and non-repeating.

Therefore, the three irrational numbers lying between $2.1$ and $2.2$ are $2.101001001000100001 \dots \dots, 2.102002000200002 \dots \dots$ and $2.103003000300003 ......$ .

Write any three rational numbers and any three irrational numbers lying between $2.1$ and $2.2$

Important Questions on Number System

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