Decimal Representation Of Rational Numbers
Theorem:
Let
For example :
Theorem:
Let
For example :
Solved Examples Based on Decimal Representation Of Rational Numbers
Question:
Without actually calculating, state whether the following rational numbers have a terminating or non-terminating repeating decimal expansion.
(i)
Hint: If the denominator is of the form
Solution:
(i)
Since
\ It has non terminating decimal representation.
(ii)
Since q =
\ It has a terminating decimal representation.
(iii)
Since
Question:
What can you say about the prime factorization of the denominators of the following rationales:
(i) 36.12345 (ii)
Solution:
(i) Since 36.12345 has terminating decimal expansion. So, its denominator is of the form
(ii) Since