Find three rational numbers between 3.1415 and 3.1416. Class 9

Find three rational numbers between 3.1415 and 3.1416. Class 9

Question 1.

Find three rational numbers between 3.1415 and 3.1416. Class 9

Solution:

Given rational numbers with more decimal places:

3.1415 = 3.14150

3.1416 = 3.14160

Now, we can find numbers between them by increasing decimal places:

3.14151, 3.14152, 3.14153

(All these numbers lie strictly between

3.14150 and 3.14160)

∴ Three rational numbers between 3.1415 and 3.1416 are 3.14151, 3.14152 and 3.14153

Question 2.

Can you think of other way(s) to find a rational number between any two rational numbers? Class 9

Solution:

i. Average Method:

Take the average of the two numbers.

Number = $\frac{a+b}{2}$

This always lies between a and b.

ii. Equivalent Fractions Method:

Convert the given rational numbers into equivalent fractions with a common denominator and then choose a rational number between them.

Example: $\frac{1}{2}, \frac{5}{4}$

$\frac{1}{2}=\frac{2}{4}, \frac{5}{4}$

A rational number between them is $\frac{3}{4}$