Question

Express p/q form o.2353535​

Answer 1

Let us assume, that

x = 0.2353535…

x = 0.235 -- (i)

On Multiplying both sides by 100 of equation (i) we get,

100x = 100 × 0.2353535…

100x = 23.53535 —(ii)

Subtracting equation (i) from equation

(ii) we get,

100x – x = 23.53535 – 0.2353535…

99x = 23.2999965

x = 23.2999965/99

x = 233/990

x = 0.2353535

$\:$

Hence, x = 0.2353535…= 0.235‾ can be expressed in the form of p/q as 233/ 990 and here q=990 (q ≠ zero)

Hence proved .