# What is a rational or irrational number?

Any number that has a non-zero denominator and can be expressed as an integer over another integer—all of your fractions—is considered rational.

Hence, set notation represents the set of rational numbers as

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A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, a rational number is any number that can be written in the form ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \neq 0 ).

An irrational number, on the other hand, is a number that cannot be expressed as the quotient or fraction of two integers. In decimal representation, irrational numbers are non-repeating and non-terminating. Examples of irrational numbers include the square root of non-perfect squares, such as ( \sqrt{2} ) or ( \sqrt{3} ), and transcendental numbers like ( \pi ) and ( e ).

In summary, rational numbers can be expressed as fractions of integers, while irrational numbers cannot and have non-repeating, non-terminating decimal representations.

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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.

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.

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.

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