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Repeating Decimals

Repeating or Recurring Decimals

deutsch: periodische dezimal zahlen

My Favorite Notation

1/3 = 3/9 = 0.~3

7/12 = 525/900 = 0.58~3

1/7 = 142857/999999 = 0.~142857

3227/555 = 5.8~144

Numbers

irrationals, infinite or never ending

Any number that cannot be expressed as a ratio of two integers is said to be irrational. Their decimal representation neither terminates nor infinitely repeats but extends forever without regular repetition.

Examples of such irrational numbers are π, e and the square roots of 2 and many other numbers.

rational or fraction

  • repeating, recurring or periodic
  • finite

integer

natural or positive

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