Question

Express 0.235.........,in the form of



, not equal to 0 and p and q are integers.
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Answer 1

Given a number 0.2353535…….

We need to prove0.2353535…= 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…=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,

99x=23.53535…−0.2353535…

x= 23.33 / 99

x= 233/ 990

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