REAL NUMBERS
10. Let x be a rational number whose decimal expansion terminates. Then I can be
expressed in the form
where pand q are co-prime and the prime factorization of
qis of the form 25 where m. n are non-negative integers.
norime factorization of qis of the form
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Answer:
Here's the answer.
Step-by-step explanation:
Firstly,
Read Theorem 1.5 of the lesson
' Real Numbers' in your NCERT textbook.
Thereafter, it's quite simple.
Since, a rational number 'x', expressed as p/q, where the prime factorisation of q is of the form 2^n5^m, is having a terminating decimal expansion.
Therefore, if the prime factorisation of q is not of the form 2^n5^n, then X has a 'non- terminating, recurring decimal expansion.
Hope it helps you.
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