Question

Which of the following rational numbers have terminating decimal?

Options

• \[\frac{16}{225}\]
• \[\frac{5}{18}\]
• \[\frac{2}{21}\]
• \[\frac{7}{250}\]

   

• Non of the above

Answer 1

(i) We have, 

`16/225= 16/(3^2xx5^2)`

Theorem states: 

Let  `x=p/q` be a rational number, such that the prime factorization of q is not of the form `2^mxx5^n`, where mand n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(ii) We have,

`5/18=5/(2xx3^2)`

Theorem states: 

Let `x=p/q` be a rational number, such that the prime factorization of q is not of the form `2^mxx5^n`, where mand n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(iii) We have,

`2/21 = (2/7xx3)`

Theorem states: 

Let  `x= p/q` be a rational number, such that the prime factorization of q is not of the form`2^mxx5^n`, where mand n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(iv) We have,

`7/(250)=7/(2^1xx5^3)`

Theorem states: 

Let  ` x= p/q` be a rational number, such that the prime factorization of q is of the form  `2^mxx2^n `, where m andn are non-negative integers.

Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of mand n.

Then, x has a decimal expression which will have terminating decimal after 3 places of decimal.

Hence the (iv) option will have terminating decimal expansion.

There is no correct option.