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Q.

Choose the option which represents the rational number which is expressible as a terminating decimal.


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a

124 165

b

131 30

c

2027 625

d

1625 462  

answer is C.

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Detailed Solution

Given are some numbers and we need to find which one of them is terminating decimal.
For any rational number ‘n’, if the denominator, has its prime factors of the form ( 2 x × 5 y ) where x and y are positive integers, then that rational number is said to be have a terminating decimal expansion.
So, we have the prime factors of the denominators of the fractions as follows,
For the first option,
124 165 = 124 3×5×11
For the second option,
131 30 = 131 2×3×5
For the third option,
2027 625 = 2027 5×5×5×5 = 2027 5 4 ×1 = 2027 2 0 × 5 4
For the fourth option,
1625 462 = 1625 2×3×7×11
So, we can observe that of all the fractions, 2027 625 has its denominator as 2027 2 0 × 5 4 ,i.e., ( 2 x × 5 y ) .
Thus, it can be expressed as a terminating decimal.
Hence, the correct option is (3).
 
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