Question

show that 0.23232.... can be expressed in the form p/q , where p and q are integers where q ≠ 0​

Answer 1

let x = 0.23232.... (1)

Multiplying both side by 100.

100 × x = 100 × 0.23232....

100x = 23.2323.... (2)

Subtracting (1) form (2)

we get,

=> 100x - x = 23.2323... - 0.2323...

=> 99x = 23

=> x = 23/99

23/99 is in the form of p/q , where p and q are integers where q ≠ 0

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Answer 2

let x = 0.23232... (1)

Multiplying both side by 100

100x = 100 × 0.23232...

100x = 23.2323... (2)

Subtracting (1) form (2)

=> 100x - x = 23.2323... - 0.23232...

=> 99x = 23

=> x = 23/99

Hence, 23/99 is the required rational number.

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