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Question 3 (5 points) Convert the decimal 0.929292... to a fraction. O 92 99 O 92 999 O 92 100 92 1000
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Question 3 (5 points) Convert the decimal 0.929292... to a fraction. O 92 99 O 92 999 O 92 100 92 1000

User Magnus Johansson
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1 Answer

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\begin{gathered} x=\text{ Repeating decimal} \\ n=\text{ Number of repeating digits} \\ x=0.929292\text{ (1)} \\ \text{Multiply by 10}^n \\ 1000x=1000(0.929292) \\ 1000x=929.292 \\ \text{Subtract (1) from the last quation:} \\ 1000x-x=929.292-0.929292 \\ 999x=928.362708 \\ x=(928.362708)/(999)\approx(92)/(99) \\ \end{gathered}

User Shaheed Haque
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