Question

Find 3 rational numbers between 3 and 4 using method of averages. [3 MARKS]

Answer 1

Concept : 1 Mark
Finding the numbers : 1 Mark
Calculation : 1 Mark

If we take an average of two numbers and then average of the first number and the average, then the number so obtained will always be between first and second number.

The first number is :
$\frac{3+4}{2}=\frac{7}{2}=3.5$

The second number is :
$\frac{3+\frac{7}{2}}{2}=\frac{13}{4}=3.25$

The third number is :
$\frac{3+\frac{13}{4}}{2}=\frac{25}{8}=3.125$

Hence the required set is 3, 3.125, 3.25, 3.5, 4.