Question

Find three rational numbers between 0.1 and 0.11

Answer 1

Let x = 0.1 and y = 0.11

Here, x < y and we have to find three rational numbers, so consider, n = 3

∴ `d = (y - x)/(n + 1)`

= `(0.11 - 0.1)/(3 + 1)`

= `0.01/4`

Since, the three rational numbers between x and y are (x + d), (x + 2d) and (x + 3d)

Now, `x + d = 0.1 + 0.01/4`

= `(0.4 + 0.01)/4`

= `0.41/4`

= 0.1025

`x + 2d = 0.1 + 0.02/4`

= `(0.4 + 0.02)/4`

= `0.42/4`

= 0.105

And `x + 3d = 0.1 + 0.03/4`

= `(0.4 + 0.03)/4`

= `0.43/4`

= 0.1075

Hence, three rational numbers between 0.1 and 0.11 are 0.1025, 0.105, 0.1075

Also, without using above formula the three rational numbers between 0.1 and 0.11 are 0.101, 0.102, 0.103