Insert 16 rational numbers between 2.1 and 2.2.

Question

Philoid · Accepted Answer

Let’s take

n= numbers required to be find out

So,

Thus, 16 rational numbers are:

(a + d), (a + 2d), (a + 3d), (a + 4d), (a + 5d), (a + 6d), (a + 7d), (a + 8d), (a + 9d), (a + 10d), (a + 11d), (a + 12d), (a + 13d), (a + 14d), (a + 15d) and (a + 16d)

So,

(a + d) = (2.1 + 0.005) = 2.105

(a + 2d) = [2.1 + (2 × 0.005)] = 2.110

(a + 3d) = [2.1 + (3 × 0.005)] = 2.115

(a + 4d) = [2.1 + (4 × 0.005)] = 2.120

(a + 5d) = [2.1 + (5 × 0.005)] = 2.125

(a + 6d) = [2.1 + (6 × 0.005)] = 2.130

(a + 7d) = [2.1 + (7 × 0.005)] = 2. 135

(a + 8d) = [2.1 + (8 × 0.005)] = 2. 140

(a + 9d) = [2.1 + (9 × 0.005)] = 2. 145

(a + 10d) = [2.1 + (10 × 0.005)] = 2. 150

(a + 11d) = [2.1 + (11 × 0.005)] = 2. 155

(a + 12d) = [2.1 + (12 × 0.005)] = 2. 160

(a + 13d) = [2.1 + (13 × 0.005)] = 2. 165

(a + 14d) = [2.1 + (14 × 0.005)] = 2. 170

(a + 15d) = [2.1 + (15 × 0.005)] = 2. 175

(a + 16d) = [2.1 + (16 × 0.005)] = 2. 180

Thus, the rational numbers between 2.1 and 2.2 are 2.105, 2.110, 2.115, 2.120, 2.125, 2.130, 2.135, 2.140, 2.145, 2.150, 2.155, 2.160, 2.165, 2.170, 2.175, 2.180,