Question

which of the following rational number having known terminating decimal expansion 144/225 ,25/36,49/25,7/250​

Answer 1

Answer

49/25 and 7/250 have terminating decimal expansion.

Explanation:

If a fraction has terminating decimal expansion then its denominator should have its prime factors as 2s and 5s only.

Denominator in 144/255 is 255

Prime factorised form of 255 :- 5 × 3 × 17

255 is not of the 2ᵐ5ⁿ, so it's decimal expansion is non-terminating

Denominator in 25/36 is 36

Prime factorised form of 36 :- 3 × 2 × 3 × 2

36 is not of the 2ᵐ5ⁿ, so it's decimal expansion is non-terminating

Denominator in 49/25 is 25

Prime factorised form of 25 :- 5 × 5

25 is of the 2ᵐ5ⁿ, so it's decimal expansion is terminating ( 5²(2⁰)

Denominator in 7/250 is 250

Prime factorised form of 5 × 2 × 5 × 5

250 is of the 2ᵐ5ⁿ, so it's decimal expansion is terminating

Note that m and n are positive Integers.