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Convert 0.833‾0.83\overline{3} to a fraction where the 33 is recurring

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Full solution

Q. Convert 0.833‾0.83\overline{3} to a fraction where the 33 is recurring
  1. Multiply by 1010: To get rid of the recurring decimal, multiply xx by 1010 to shift the decimal point one place to the right.\newline10x=8.3333…10x = 8.3333\ldots (with 33 recurring)
  2. Subtract to eliminate: Now, subtract the original xx from 10x10x to eliminate the recurring part.10x−x=8.3333...−0.8333...10x - x = 8.3333... - 0.8333...9x=7.59x = 7.5

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