14
Question
The decimal expansion of the rational number
(a) one decimal place
(b) two decimal place
(c) three decimal place
(d) four decimal place
(a) one decimal place
(b) two decimal place
(c) three decimal place
(d) four decimal place
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Solution
We have,
Theorem states:
Let 
be a rational number, such that the prime factorization of q is of the form
, where m and n are non-negative integers.
Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.
This is given that the prime factorization of the denominator is of the form.
Hence, it has terminating decimal expansion which terminates after 
places of decimal.
Hence, the correct choice is (d).
We have,
Theorem states:
Let be a rational number, such that the prime factorization of q is of the form, where m and n are non-negative integers.
Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.
This is given that the prime factorization of the denominator is of the form.
Hence, it has terminating decimal expansion which terminates after places of decimal.
Hence, the correct choice is (d).
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