Question

Find two rational numbers in the form of p/q between the numbers 0.2121121112... and 0.2020020002... .

Answer 1

Step-by-step explanation:

One out of many methods is as follows…

To find any rational number lying between 2 given ratioal numbers..

0.2121121112 &

0.2020020002

Select few digits starting from tenth place in both the given numbers.

I pick 212 & 202

Now, get any number between 212 & 202

Like I pick 206

So required number = 0.206 ( also you may suffix any random digits after 6 , like 0.2063712, or 0.206555. . . etc etc )

= 206/1000

= 103/500

This way, we can find countless numbers lying between two rationals

NOTE: If you want the number exactly lying between them. Then add given 2 numbers & divide the sum by 2. Then convert it in the form of p/q

So, we get 2070570557/ 10^10