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Rational or irrational numbers, step by step

Can the number be written as a fraction of two whole numbers?

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The question

Rational or irrational?

0.222…

0.222…
0.222…
a decimal that repeats forever can still be written as a fraction
0.222…isrational
  1. One question decides it: can this be written as a fraction of two whole numbers? Not "does it look tidy", and not "is there a root sign" — those are the two guesses that go wrong.
  2. Look at what kind of number it is: a decimal that repeats forever can still be written as a fraction.
  3. So it CAN be written as a fraction. That makes it rational.

How it works.

  1. 01

    One question decides it: can this be written as a fraction of two whole numbers? Not "does it look tidy", and not "is there a root sign" — those are the two guesses that go wrong.

  2. 02

    Look at what kind of number it is: a decimal that repeats forever can still be written as a fraction.

  3. 03

    So it CAN be written as a fraction. That makes it rational.

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