Question

If 2.52525....=p/q (in the lowest form), then what is the value of q/p?

Answer 1

$2.52525.... = 2.\bar{52}$


$\mathsf{Let \: \: 2.\bar{52} = 2 }$


As there are 2 numbers under the bar multiply by 100 on both sides,


$2. \bar{52} \: \times 100 = x \times 100 \\ \\ 252. \bar{52} = 100x$



Then, subtract x from both sides,


$252. \bar{52} \: = 100x \\ \: \: \: \: 2. \bar{52} \: = \: - \: \: x \\ - - - - - - - \\ 250 = 99x \\ - - - - - - - \\ \\ \\ \\ \frac{250}{99} = x \\ \\ \frac{250}{99} = 2. \bar{52}$




Therefore, $2.\bar{52}$ in p/q form is 250 / 99

Answer 2

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