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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

124165

b

13130

c

2027625

d

1625462

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,

124165 = 124 3 × 5 × 11

For the second option,

13130 = 131 2 × 3 × 5

For the third option,

2027625 = 2027 5 × 5 × 5 × 5 = 2027 54 × 1 = 2027 20 × 54

For the fourth option,

1625462 = 1625 2 × 3 × 7 × 11

So, we can observe that of all the fractions,

2027625

has its denominator as

2027 20 × 54

,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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