What is a Real Number?
The union of the set of rational numbers with the set of irrational numbers.
A real number is any number you can find on the number line. This includes both rational numbers (like fractions and decimals that repeat or end) and irrational numbers (like √2 or π, which are decimal numbers that never end and never repeat).
Real numbers include:
- Whole numbers: 0, 1, 2, 3...
- Integers: –3, 0, 7...
- Fractions: \(\Large\frac{1}{2}\), –\(\Large\frac{1}{2}\)...
- Decimals: 2.75, –0.4
- Irrational numbers: π (pi), √2
In short, if you can locate it on a number line, it’s a real number!
We use real numbers to:
- Measure time and distance
- Record temperatures
- Track money and scores
- Do almost every kind of calculation in school and real life
When Do Students Learn About Real Numbers?
Students begin learning about real numbers as they expand their understanding of rational and irrational numbers, typically in middle school and high school.
Grades 6–7 – Introduction to Real Numbers
Students explore decimals, fractions, and negative numbers, and begin to understand how rational numbers fit into the bigger picture of real numbers.
Grades 8+ – Working with Real Numbers in Algebra
Students learn to compare, order, and use real numbers—including irrational numbers like √2 and π—in algebraic expressions and equations.
