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How to Convert Recurring Decimals to Fractions

Fractions contain a numerator and a denominator separated by a horizontal line that represents division. In a proper fraction, where the numerator is smaller than the denominator, that division will result in a decimal answer. Decimals can be exact, such as 0.25, or recurring, such as 0.6666... with the periods representing continuation. If the denominator of a fraction only has the factors of 2 or 5, that fraction will produce an exact answer. All other fractions will produce a recurring decimal.

Instructions

- 1
  Convert a recurring decimal by setting it equal to x then multiplying both sides by the multiple of 10 that would cause the first section of recurring numbers to be on the left side of the decimal point. Solve the equation for x and simplify the resulting fraction.
- 2
  Convert the recurring decimal 0.142857142857... to fraction form. Set it equal to x: x = 0.142857142857..., then count how many places the decimal point has to move to place the first block of numbers, 142857, on the left. Since there are six places, the multiple of 10 used will be 1,000,000.
- 3
  Multiply both sides by 1,000,000: 1,000,000x = 142,857.142857... and eliminate the numbers on the right of the decimal. Do this by subtracting x from both sides: 999,999x - x = 142,857. Solve for x by dividing both sides by: x = 142,857 / 999,999.
- 4
  Simplify the fraction through trial and error. Start by checking to see if the numerator is a multiple of the denominator via division: 999,999 / 142,857 = 7. Write the final answer as 1/7.

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