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Convert the following in p/q form: (i) 5.2 bar (ii) 23.43 bar (iii) 0.32 bar (iv) 0.123 bar

$(i) let x = 5. \bar{2} \Rightarrow 10 x = 52.2222222............. \Rightarrow 10 x - x = 52.222222......... - 5.222222222........ \Rightarrow 9 x = 47 \Rightarrow x = \frac{47}{9} (i i) Let x = 23. \bar{43} \Rightarrow 100 x = 2343.43434343.......... \Rightarrow 100 x - x = 2343.434343......... - 23.4343434343....... \Rightarrow 99 x = 2320 \Rightarrow x = \frac{2320}{99} (i i i) Let x = 0. \bar{32} \Rightarrow 100 x = 32.323232....... \Rightarrow 100 x - x = 32.323232.......... - 0.3232323232........... \Rightarrow 99 x = 32 \Rightarrow x = \frac{32}{99} (i v) Let x = 0. \bar{123} \Rightarrow 1000 x = 123.123123123...... \Rightarrow 1000 x - x = 123.123123123........... - 0.123123123........ \Rightarrow 999 x = 123 \Rightarrow x = \frac{123}{999}$

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