Show that 0.2353535...= 0.235 can be expressed in the form of p/q, where p and q are integers and q is not equal to zero

Answer:

Given a number 0.2353535…….

We need to prove 0.2353535… = 0.235‾ can be expressed in the form of p/q, where p and q are integers and q ≠zero

Proof:

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.

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