What is a rational or irrational number?

Question

Gabriel Agustin · Accepted Answer

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 #QQ={m/n;m,n in ZZ; n!=0}# An irrational number cannot be expressed as a ratio of integers and include numbers such as #pi, e, sqrt2, ln2#, etc.
The set of irrational numbers #=RR-QQ#.

Noah Archer · Answer

undefined 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.