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Rational or irrational

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The question

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Rational or irrational?

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a decimal that stops can be written over a power of ten
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  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 stops can be written over a power of ten.
  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 stops can be written over a power of ten.

  3. 03

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

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