Decimal to fraction

Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.

Correct answer:

A =  5183
B =  600

Step-by-step explanation:

$$\begin{gathered} 8.638333333={\displaystyle \frac{A}{B}} \\ 8.638333333=8.638+3\cdot 10^{-4}+3\cdot 10^{-5}+3\cdot 10^{-6}+\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}= \\ ={\displaystyle \frac{8638}{1000}}+3\cdot 10^{-4}\cdot {\displaystyle \frac{1}{1-1\mathrm{/}10}}= \\ ={\displaystyle \frac{8638}{1000}}+3\cdot 10^{-4}\cdot {\displaystyle \frac{10}{9}}= \\ ={\displaystyle \frac{8638}{1000}}+{\displaystyle \frac{3}{10000}}\cdot {\displaystyle \frac{10}{9}}= \\ ={\displaystyle \frac{8638}{1000}}+{\displaystyle \frac{3}{9000}}= \\ ={\displaystyle \frac{5183}{600}} \\ 8.638333333={\displaystyle \frac{5183}{600}} \\ A=5183 \\ B=600 \end{gathered}$$

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