Question

Express 0.1254(bar on 54) in the form p/q

Answer 1

$let \: x = 0.12 \bar{5} \bar{4} \\ \\ or \: x = 0.12545454... \\ \\ 100x = 12.545454... \\ \\ 10000x = 1254.545454... \\ \\subtract : \\ 10000x - 100x = 1254.5454... - 12.5454... \\ \\ 9900x = 1242 \\ \\ x = \frac{9900}{1242} \\ \\ x = \frac{550}{69} \\ \\ thus \: \: \: 0.12 \bar{5} \bar{4} = \frac{550}{69} \:$

Answer 2

Given :      $0.12\overline{54}$

To Find : Express in   p/q form

Solution:

 N = $0.12\overline{54}$

100N = $12.\overline{54}$

10000N = $1254.\overline{54}$

=> 10000N  - 100N  =   $1254.\overline{54}$ - $12.\overline{54}$

=> 9900N = 1242

=> N = 1242/9900

=> N = 621/4950

=> N = 207/1650

=> N = 69/550

 $0.12\overline{54}$ =   69/550

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