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# Question and Answer

Show that $$0.3333\cdots =0.\overline 3$$ can be expressed in the form $$\frac {p}{q}$$ where $$p$$ and $$q$$ are integers and  $$q\neq 0.$$
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## QuestionMathsClass 9

Show that $$0.3333\cdots =0.\overline 3$$ can be expressed in the form $$\frac {p}{q}$$ where $$p$$ and $$q$$ are integers and  $$q\neq 0.$$

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4.6
Review from Google Play
4.6
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## Solution

As we do not know what $$0 . \overline{3}$$ is, let us call it  $$x$$and so
$$x=0.3333 \ldots$$
$$\Rightarrow 10 x=10 \times(0.333 \dots)=3.333 \dots$$
So, $$3.3333 \ldots=3+x,$$ since $$x=0.3333 \ldots$$
Therefore, $$10 x=3+x$$
Solving for $$x,$$ we get
$$9 x=3$$
$$\Rightarrow x=\dfrac{1}{3}$$
Hence, $$0 . \overline{3}=\dfrac13$$.