Question

Represent in p/q form:0.0238 bar on 38

Answer 1

Question :-

represent $\sf 0.02 \overline{38}$ in the form of p/q .

Solution :-

$\sf \: let \: \: \: x = 0.02 \overline{38} \: ........eq.(1) \\ \\ \sf multiply \: by \: 100 \: in \: eq.(1) \\ \\ \sf \: 100x = 2.\overline{38} \ \: ............eq.(2) \\ \\ \sf \: again \: multiply \: by \: 100 \: in \: eq.(2) \\ \\ \sf \: 10000x = 238.\overline{38} \: ..............\: eq.(3) \\ \\ \bf \: subtract \: eq.(2) \: from \: eq.(3) \\ \\ \sf \: 10000x = 238.\overline{38} \\ \sf \: 100x = 2.\overline{38} \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \:9900x = 236 \\ \\ \sf \: x = \dfrac{9900}{236} \\ \\ \bf x = \frac{59}{2475}$

hence the p/q form of $\sf 0.02 \overline{38}$ is $\bf \frac{59}{2475}$