Question

Convert the following decimal number in the form of p/q
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Answer 1

Let us assume that,

23.4343... = p/q _____ eq.(i)

By multiplying eq.(i) by 100, we get

2343.4343... = 100p/q _____ eq.(ii)

By subtracting eq.(i) from eq.(ii), we get

2343.4343... - 23.4343... = (100-1)p/q

or, 2343 - 23 = 99p/q

or, 2320 = 99p/q

or, 2320/99 = p/q

• Hence proved.