Question

Expres 0.3 bar as a fraction in simplest form

Answer 1

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let x = 0.3 ------------- 1

multiply equation 1 by 10 in both sides

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10x = 3.3 --------------2

equation 2 - equation 1

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10x - x = 3.3 - 0.3

9x = 3

X = 3/9

X = 1/3

Answer 2

$\huge \tt \underline \orange {Answer}$

$\red{: \implies} \bf \pink{0. \bar3} \\ \\ \red{: \implies} \rm \pink{Let \:x = 0.333.....(i)} \\ \\ \red{: \longrightarrow} \rm \pink {Therefore, \: 10x = 3.333....(ii)} \\ \\ \red{: \longrightarrow} \rm \pink{Substracting (i) from (ii) } \\ \\ \red{: \implies} \rm \pink {3.333-0.333 = 3} \\ \\ \red{: \implies} \rm \pink{10x - x = 3} \\ \\ \red{: \implies} \rm \pink {9x = 3} \\ \\ \red{: \implies} \rm\pink{ \frac{3}{9} } \\ \\ \red{: \implies} \rm \pink{x = \frac{1}{3}} \\ \\ \huge \boxed {0. \bar3 = \frac{1}{3} }$