Rational Numbers

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where q is not equal to zero. In other words, a rational number is a number that can be written in the form a/b, where a and b are integers and b is not equal to zero.

Rational numbers include integers, fractions, and terminating or repeating decimals. For example, 5, -3, 1/2, 0.75, and 0.333... are all rational numbers because they can be expressed as a quotient of two integers.

Rational numbers can be added, subtracted, multiplied, and divided just like whole numbers and fractions. The result of these operations will always be a rational number, making rational numbers a closed set under addition, subtraction, multiplication, and division.

It's important to note that not all numbers are rational. For example, the square root of 2 (√2) is an irrational number because it cannot be expressed as a fraction of two integers. Irrational numbers are non-repeating, non-terminating decimals and cannot be written as simple fractions.

In summary, rational numbers are a fundamental concept in mathematics and are essential for understanding arithmetic, algebra, and other branches of mathematics.