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How to change a repeating decimal to a fraction?

How to change a repeating decimal to a fraction?
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How to change a repeating decimal to a fraction?

User MyTimeFinder
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How to change a repeating decimal to a fraction?

Let us consider the recurring decimal


\begin{gathered} 0.622222\ldots\text{ which can be written as} \\ 0.6\bar{2} \end{gathered}
\begin{gathered} \text{Let x = }0.6\bar{2}\ldots.(1) \\ \text{Multiply both sides by 100 (corresponding to the number of decimal places after the decimal point)} \\ We\text{ have;} \\ 100x\text{ = 62. }\bar{2}\ldots\ldots(2) \\ \text{Subtact (1) from (2)} \\ 100x\text{ - x = 62. }\bar{2}\text{ - }0.6\bar{2} \\ 99x\text{ = }61.6 \\ x\text{ = }(61.6)/(99)=\text{ }(616)/(10*99)=(28)/(45) \end{gathered}

User Dbrumann
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