Find five rational numbers between 1 and 2.

1.	Find five rational numbers between 1 and 2.
Answer» We know, one rational number between two numbers m and n = (m+n)/2 Step 1: Rational number between 1 and 2 = (1+2)/2 = 3/2 Step 2: Rational number between 1 and 3/2 = (1+3/2)/2 = 5/4 Step 3: Rational number between 1 and 5/4 = (1+5/4)/2 = 9/8 Step 4: Rational number between 3/2 and 2 = 1/2 [(3/2) + 2)] = 7/4 Step 5: Rational number between 7/4 and 2 = 1/2 [7/4 + 2] = 15/8 Arrange all the results: 1 < 9/8 < 5/4 < 3/2 < 7/4 < 15/8 < 2 Therefore required integers are, 9/8, 5/4, 3/2, 7/4, 15/8.

Answer»

We know, one rational number between two numbers m and n = (m+n)/2

Step 1: Rational number between 1 and 2 = (1+2)/2 = 3/2

Step 2: Rational number between 1 and 3/2 = (1+3/2)/2 = 5/4

Step 3: Rational number between 1 and 5/4 = (1+5/4)/2 = 9/8

Step 4: Rational number between 3/2 and 2 = 1/2 [(3/2) + 2)] = 7/4

Step 5: Rational number between 7/4 and 2 = 1/2 [7/4 + 2] = 15/8

Arrange all the results: 1 < 9/8 < 5/4 < 3/2 < 7/4 < 15/8 < 2

Therefore required integers are, 9/8, 5/4, 3/2, 7/4, 15/8.

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