We will explain rational and irrational numbers, as well as how they are different and can be told apart, one at a time.
What Is a Rational Number?
A rational number is any number that can be written in the form ab, where a and b are integers and b ≠0. The quotient ab can result or not in an integer number. If the quotient does not result in an integer, the rational number can be written either as a terminating or repeating decimal.
Integer number:& 8/4 = 2 [0.8em]
Terminating decimal:& 5/2 = 2.5 [0.8em]
Repeating decimal:& 7/3 = 2.33333... = 2.3
What Is an Irrational Number?
On the other hand, an irrational number is any number that cannot be expressed as the ratio between two integers. In decimal form, irrational numbers do not terminate nor repeat. We can find them, for example, as mathematical constants or as the square root of numbers that are notperfect squares.
Irrational constant:& π = 3.141592...
Irrational square root:& sqrt(2) = 1.414213...
How Are They Different?
Checking if a number can be written as the ratio between two integers or not is the most efficient way to determine whether it is rational or irrational. However, this may not be the easier way. If we can write the number as a decimal, we can use the following guide for telling them apart.
