Theorem 1.5 Let x be a …
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Theorem 1.5
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 of 2 to the power n ×5 to the power m are non negative integers.
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Gaurav Seth 3 years, 7 months ago
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
2Thank You