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Write the repeating decimal as a fraction.\newline.33333333 .33333333\ldots \newline\underline{\hspace{3em}}

Full solution

Q. Write the repeating decimal as a fraction.\newline.33333333 .33333333\ldots \newline\underline{\hspace{3em}}
  1. Multiply by 1010: Multiply xx by 1010 to shift the decimal point one place to the right: 10x=3.333333310x = 3.3333333\ldots
  2. Subtract from 10x10x: Subtract the original number xx from 10x10x to get rid of the repeating decimals: 10xx=3.3333333....33333333...10x - x = 3.3333333... - .33333333...
  3. Do the subtraction: Do the subtraction: 9x=39x = 3
  4. Divide by 99: Divide both sides by 99 to solve for xx: x=39x = \frac{3}{9}
  5. Simplify the fraction: Simplify the fraction: x=13x = \frac{1}{3}

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