Question

express 0.1234 in p/q form where p and q are integers and q not equal to 0 (34 is bared )

Answer 1

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✧✧Answer✧✧

$\sf Let \: 0.12 \overline{34} = c$

$\sf Then \: 100c= 12. \overline{34}.........(1)$

$\sf and \: 10000c=1234. \overline{34}.........(2)$

$\sf Subtracting \; (1) \; from \: (2):-$

$\implies \sf 10000c-100c= 1234. \overline{34} - 12. \overline{34}$

$\implies \sf 9900c = 1222$

$\implies \sf c = \dfrac{1222}{9900}$

$\implies \sf \therefore 0.12 \overline{34} \: in \: \dfrac{p}{q} \: form = \dfrac{1222}{9900}$

Hope it helps you mate!✧✧

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Answer 2

Let,

x=1.

34

ˉ

x=1.34343434...

100x=134.343434...

⇒100x−x=134.343434...−1.343434...=133

⇒99x=133

∴x=

99

133

hope it helps u ☺️