Respuesta :

sqdancefan

Answer:

  124/999

Step-by-step explanation:

A recurring decimal fraction can be expressed as a rational number by using the recurring digits in the numerator and an equal number of 9s in the denominator:

  [tex]0.\overline{124}=\dfrac{124}{999}[/tex]

This fraction cannot be reduced.

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Additional comment

If the recurring digits don't start at the decimal point, then you can determine the fraction by ...

  • Multiply the number by 10^n, where n is the number of recurring digits
  • Subtract the original number. This will cancel the recurring part of the number so the difference is a finite decimal.
  • Divide by (10^n -1) and simplify the fraction.

In this case, you would get ...

  [tex]1000x = 124.\overline{124}\\\\1000x-x=124.\overline{124}-0.\overline{124}=124\\\\x=\dfrac{124}{999}[/tex]

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