A rational number is part of a whole expressed as a fraction, decimal or a percentage.
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.
The term rational is derived from the word 'ratio' because the rational numbers are figures which can be written in the ratio form.
Every whole number, including negative numbers and zero, is a rational number. This is because every whole number ‘n’ can be written in the form n/1
For example, 3 = 3/1 and therefore 3 is a rational number.
Numbers such as 3/8 and -4/9 are also rational because their numerators and denominators are both whole numbers.
Recurring decimals such as 0.26262626…, all integers and all finite decimals, such as 0.241, are also rational 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).
For example, the square root of 2 is an irrational number because it cannot be written as a ratio of two integers.
The square root of 2 is not a number of arithmetic: no whole number, fraction, or decimal has a square of 2. Irrational numbers are square roots of non-perfect squares. Only the square roots of square numbers are rational.
Similarly Pi (π) is an irrational number because it cannot be expressed as a fraction of two whole numbers and it has no accurate decimal equivalent.
Pi is an unending, never repeating decimal, or an irrational number. The value of Pi is actually 3.14159265358979323… There is no pattern to the decimals and you cannot write down a simple fraction that equals Pi.
Euler's Number (e) is another famous irrational number. Like Pi, Euler's Number has been calculated to many decimal places without any pattern showing. The value of e is 2.7182818284590452353… and keeps going much like the value of Pi.
The golden ratio (whose symbol is the Greek letter "phi") is also an irrational number. It is a special number approximately equal to 1.618 but again its value is never ending: 1.61803398874989484820...