Question

(1).simplify 3⅔.3⅕.
(2). check whether 3.142678 is a rational or an irrational number.
(3). can we insert 100 rational number between 2 and 7? if yes, why?​

Answer 1

Step-by-step explanation:

(1) :

This is of the form A^m * A^n = A^(mn).

3^(2/3) * 3^(1/5) ===>

3^[ (2/3) * (1/5) ]

3^ [2/15 ]

Answer : 3^ (2/15).

(2) :

3.142678 = 3142678/1000000.

So,

3.142678 can be expressed in the form p/q (3142678/1000000 ) where p and q are integers (3142678 and 1000000) and q ≠ 0.

This satisfies the condition required for any number to be a rational number.

Therefore, the given number is rational.

(3) :

Yes, we can insert 100 or more rational numbers between 2 and 7.

This is because, one of the fundamental rules of rational numbers which says : There are infinite number of rational numbers between any two rational numbers.

Hope this helps!!!!! Please do mark me BRAINLIEST if you think the answer is worth it ☺️.