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If a number contains decimal places then is it in irrational number?

User Oleg Mazko
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No, it doesn't automatically make it irrational.

A few counter-examples are shown here

  • 0.37373737... = 37/99
  • 0.1111111111... = 1/9
  • 0.1666666.... = 1/6

Notice how when we have a repeating pattern of some kind, it leads to a rational number. A rational number is a ratio or fraction of two integers. The denominator cannot be zero.

An example of an irrational value is pi = 3.1415926535898... where there is no repeating pattern no matter how far we extend the decimal digits out. This means we cannot write pi as a ratio of two integers. We can get close with approximations like 22/7 and 355/113, but we can't get the exact value itself.

User Tommi Kyntola
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