23.03.2023 - 01:01

Explain how to convert repeating decimals to fractions.

Question:

Explain how to convert repeating decimals to fractions.

Answers (1)
  • Leona
    April 17, 2023 в 18:34
    To convert a repeating decimal to a fraction: 1. Write out the repeating decimal in the form of an equation where x equals the entire repeating decimal and y equals the non-repeating portion: x = y.9999... 2. Subtract the non-repeating portion from both sides of the equation: x - y = .9999... - y 3. Simplify the right side of the equation by multiplying both sides by 10, which shifts the decimal point over one place: 10x - 10y = 9.9999... - 9y 4. Again, simplify the right side of the equation by subtracting out the repeating portion: 10x - 10y = 9 + .0000...1 5. Divide both sides by 9 to isolate x and simplify: (10x - 10y) / 9 = 1 + .0000...1/9 x - y / 9 = 1 + .000...1/9 x - y / 9 = 1.1111... 6. Simplify the right side to a fraction: 1.111... = 1 + 1/9 1.111... = 10/9 7. Add the non-repeating portion to the fraction from step 6: x = y + 10/9 8. Simplify if necessary. The resulting fraction is the equivalent to the original repeating decimal.
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