Question

Expresss 13.457777.... in p/q form

Answer 1

given :- 13.4577777...

let x be = 13.4577777... ---------(i)

multiplying both sides by 100

➡ x × 100 = 13.4577777... × 100

➡ 100x = 1345.777777... ---------(ii)

subtracting equation (i) from equation (ii)

➡ 100x - x = 1345.777777... - 13.45777777...

➡ 99x = 1332.32

➡ x = 1332.32/99

now, in the form of p/q both p and q must be integers

but here p is not a integer.

so let's multiply both p and q by 100 (since there are two no.s after the decimal point)

➡ x = (1332.32 × 100)/(99 × 100)

➡ x = 133232/900 = 3028/225