(i) –1 and –2
Three rational numbers between –1 and –2 are –1.1, –1.2 and –1.3.
(ii) 0.1 and 0.11
Three rational numbers between 0.1 and 0.11 are 0.101, 0.102 and 0.103.
(iii) 5/7 and 6/7
5/7 can be written as (5 × 10)/(7 × 10) = 50/70
Similarly,
6/7 can be written as (6 × 10)/(7 × 10) = 60/70
Three rational numbers between 5/7 and 6/7 = three rational numbers between 16/80 and 20/80.
Three rational numbers between 5/7 and 6/7 are 51/70, 52/70, 53/70.
(iv) 1/4 and 1/5
Here, according to the question,
LCM of 4 and 5 is 20.
Let us make the denominators common, 80.
(4 × 20) = 80 and (5 × 16) = 80
Hence,
1/4 can be written as (1 × 20)/(4 × 20) = 20/80
Similarly,
1/5 can be written as (1 × 16)/(5 × 16) = 16/80
Three rational numbers between 1/4 and 1/5 = three rational numbers between 16/80 and 20/80.
Therefore, the three rational numbers are 17/80, 18/80 and 19/80.
