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How to Teach Kids How to Change a Repeating Decimal to a Fraction

Repeating decimals are numeric values with a pattern of repeating numbers that go on for eternity. Repeating decimals can be written one of two ways, either by drawing a bar over the repeating digit or digits or by using an ellipsis to indicate the pattern continues. Because decimals are rational numbers, they can be expressed as a fraction a/b, where "b" is greater than zero, regardless of whether the digits in the decimal repeat or not.

Instructions

- 1
  Change your repeating decimal into an algebraic equation where "x" equals your repeating decimal. For example, rewrite the decimal 0.33333 as x = 0.33333.
- 2
  Get your repeating digit on both sides of the decimal point by multiplying the repeating digit by 10. If your repeating decimal is a two-digit number, such as 0.424242, multiply by 100. Multiplying the repeating digit 0.33333 by 10 equals 3.3333. Now you have a second equation, 10x = 3.3333.
- 3
  Subtract your two algebraic equations, 10x = 3.3333 and x = 0.33333, to create one new algebraic equation. 10x - x = 3.3333 - 0.3333, so 9x = 3.
- 4
  Isolate your variable, x, by dividing both sides of the algebraic equation by 9: 9x = 3, so x = 3/9.
- 5
  Reduce your fraction into simplest form. The fraction 3/9 can be reduced to 1/3 by dividing both 3 and 9 by 3. So 1/3 is equal to the repeating decimal 0.3333 ...

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