Question

Theorem 1.5 :




Let x be a rational number whose decimal expansion terminates. p ,
q

prime factorisation of q is of the form 2
where p and q are coprime, and the n 5 m , where n, m are non-negative integers.

Then x can be expressed in the form

Answer 1

x(rational number) can be expressed in p/q form,and the prime factorisation of q is of the form 2n5m,where n,m are non negative integers.


i hole its ryt

Answer 2

Given : x is a rational number whose decimal expansion terminates . p&q are two integers in which prime Factorisation of q is of the form 2^m5^n where p&q are co-prime & non negative integer

To Find : How x can be expressed

Solution :

• Consider the theorm ,

Let x be a rational number whose decimal expansion terminates.

Then x can be expressed in the form of p/q , where p and q are coprime and the prime factorisation of q is of the form 2^n5^m

, where n, m are non-negative integers.

•According to theorm

X can be expressed in the form of p/q

•Hence , X can be expressed in the form of p/q