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Write the repeating decimal as a fraction.\newline.807807807.807807807

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Q. Write the repeating decimal as a fraction.\newline.807807807.807807807
  1. Question Prompt: Question_prompt: Write the repeating decimal as a fraction. 0.33333333…0.33333333\ldots\newlineStep 11: Identify the repeating decimal pattern.\newlineThe repeating decimal is 0.33333333…0.33333333\ldots, where the digit '33' repeats indefinitely.\newlineStep 22: Express the repeating decimal as a fraction.\newlineLet x=0.33333333…x = 0.33333333\ldots\newlineThen 10x=3.33333333…10x = 3.33333333\ldots (by multiplying both sides by 1010)\newlineStep 33: Subtract the original equation from the multiplied equation.\newline10x−x=3.33333333…−0.33333333…10x - x = 3.33333333\ldots - 0.33333333\ldots\newline9x=39x = 3\newlinex=39x = \frac{3}{9}\newlineStep 44: Simplify the fraction.\newline39\frac{3}{9} can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 33.\newline0.33333333…0.33333333\ldots11

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