Express each of the following decimals in form where q ≠ 0 and p, q are integers

i) 0.36 ii) 15.4

iii) 10.25 iv) 3.25

(i). 0.36 = 36/100

Simplify it in the same p/q form,

⇒ 0.36 = 18/50

On further simplifying it,

⇒ 0.36 = 9/25

This cannot be further simplified in p/q form.

9/25 is in p/q form, where p = 9 and q = 25 are integers and q = 25 ≠ 0.

Hence, the answer is 9/25.

(ii). 15.4 = 154/10

Simplifying it in the same p/q form,

⇒ 15.4 = 77/5

This cannot be further simplified in p/q form.

77/5 is in p/q form, where p = 77 and q = 5 are integers and q = 5 ≠ 0.

Hence, the answer is 77/5.

(iii). 10.25 = 1025/100

Simplifying it in the same p/q form,

⇒ 10.25 = 205/20

On further simplifying it,

⇒ 10.25 = 41/4

This cannot be further simplified in p/q form.

41/4 is in the form p/q, where p = 41 and q = 4 are integers and q = 4 ≠ 0

Hence, the answer is 41/4.