What Is a Rational Number?
Any number that can be written as a common fraction. Every rational number can be written as a repeating or terminating decimal. The rational numbers have the form a/b, where a and b are integers and b ≠ 0.
A rational number is any number that can be written as a fraction or ratio of two integers. In other words, a rational number is in the form \(\Large\frac{a}{b}\), where a and b are both whole numbers and b is not zero.
For example, these are all rational numbers:
- \(\Large\frac{3}{4}\) (a = 3, b = 4)
- –2 (can be written as \(-\Large\frac{2}{1}\))
- 0.5 (can be written as \(\Large\frac{1}{2}\))
- 0.333… (a repeating decimal that equals \(\Large\frac{1}{3}\))
Every rational number can be written as either a terminating decimal, which is a decimal that ends, or a repeating decimal, which is a decimal with a digit or group of digits that repeats forever.
Unlike rational numbers, irrational numbers like π or √2 cannot be written as fractions and have non-repeating, non-terminating decimal forms.
Rational numbers include:
- Positive and negative fractions
- Whole numbers
- Integers
- Decimals that repeat or terminate
When Do Students Learn About Rational Numbers?
Students begin working with rational numbers in upper elementary school and continue to explore them more deeply in middle and high school.
Grades 4–5 – Early Introduction
Students begin learning that fractions and decimals are different ways of representing rational numbers.
Grades 6–8 – Understanding Rational Numbers
Students compare rational numbers, convert between forms (fractions, decimals, and percents), and perform operations with them.
Grades 9+ – Using Rational Numbers in Algebra
Students apply rational numbers in algebraic expressions, equations, and real-world problem solving.
