How can I tell a rational and irrational number apart?

Answer 1

Well, an irrational number such as #pi# has an #oo# number of digits after the point and they do not present a recognizable pattern.
A rational number (the result of dividing two integer numbers) either stops after some digits or has #oo# digits but following a pattern (repetitions for example).
Examples:
Rationals:
#5=5/1#
#1/2=0.5#
#2/3=0.6666666666....# always the same number after the point!
#6/11=0.5454545454...# always the same pattern of repeating 54!

An irrational number doesn't follow a pattern after the point, the decimal goes on forever without repeating. Remember that you cannot write your irrational as a fraction of two integers.

You can have "important" irrational numbers as #pi# oe #e# or the result of square roots as #sqrt(2)=1.414213562....#.

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Answer 2

Hazel Anglin

A rational number can be expressed as a quotient or fraction of two integers, where the denominator is not zero. An irrational number cannot be expressed as a fraction of two integers and typically has a non-repeating, non-terminating decimal representation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.