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Write the repeating decimal as a fraction.\newline0.7337337330.733733733

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Full solution

Q. Write the repeating decimal as a fraction.\newline0.7337337330.733733733
  1. Denote Decimal as xx: Let's denote the repeating decimal 0.733733733…0.733733733\ldots as xx.
    x=0.733733733…x = 0.733733733\ldots
    To isolate the repeating part, we multiply xx by 10001000 because there are three digits in the repeating sequence.
    1000x=733.733733…1000x = 733.733733\ldots
    Now, we subtract the original xx from 1000x1000x to get rid of the decimal part.
    1000x−x=733.733733…−0.733733733…1000x - x = 733.733733\ldots - 0.733733733\ldots
    This simplifies to:
    0.733733733…0.733733733\ldots00
    Now, we divide both sides by 0.733733733…0.733733733\ldots11 to solve for xx.
    0.733733733…0.733733733\ldots33
  2. Multiply by 10001000: We check if the fraction can be simplified. The numerator 733733 and the denominator 999999 do not have any common factors other than 11, so the fraction is already in its simplest form.

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