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1
Answer:
0.\overline{729} = \frac{27}{37}\: (\frac{p}{q} \: form )0.
729
=
37
27
(
q
p
form)
Step-by-step explanation:
Let \: x = 0.\overline{729}\: ---(1)Letx=0.
729
−−−(1)
\* Multiply both sides of by 1000 , we get *\
1000x = 729.\overline {729}\: ---(2)1000x=729.
729
−−−(2)
/* Subtract equation (1) from equation (2) , we get*/
\implies 999x = 729⟹999x=729
\begin{lgathered}\implies x = \frac{729}{999}\\=\frac{9\times 3\times 27}{9\times 3\times 37 }\\=\frac{27}{37}\end{lgathered}
⟹x=
999
729
=
9×3×37
9×3×27
=
37
27
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