Rational and Irrational Numbers
Understanding the distinction between rational and irrational numbers is crucial in mathematics. Let's delve into the details of each type:

Rational Numbers:
- Rational numbers are those numbers that can be expressed as a ratio of two integers, where the denominator is not zero.
- They can be written in the form a/b, where a and b are integers and b is not equal to zero.
- Examples of rational numbers include 1/2, -3/4, 5, etc.
- Rational numbers can be terminating (such as 1/2 = 0.5) or repeating decimals (such as 1/3 = 0.333...).

Irrational Numbers:
- Irrational numbers are numbers that cannot be expressed as a simple fraction of two integers.
- They are non-repeating, non-terminating decimals.
- Irrational numbers have an infinite number of decimal places with no repeating pattern.
- Examples of irrational numbers include π (pi), √2 (square root of 2), etc.
- Irrational numbers cannot be expressed as fractions and have decimal representations that go on forever without repeating.

Key Differences:
- Rational numbers can be expressed as fractions, while irrational numbers cannot.
- Rational numbers have either terminating or repeating decimals, whereas irrational numbers have non-terminating, non-repeating decimals.
- The set of rational numbers is countable, while the set of irrational numbers is uncountable.
In conclusion, rational numbers can be represented as fractions, while irrational numbers cannot be expressed as fractions and have non-repeating infinite decimal representations. Understanding these distinctions is fundamental in mathematics and various real-world applications.

A number is rational if we can write it as a fraction where the top number of the fraction and bottom number are both whole numbers.
Alternatively, an irrational number is any number that is not rational. It is a number that cannot be written as a ratio of two integers (or cannot be expressed as a fraction).