Grade 10 · Theory
The real number system
Algebraic expressions · about 4 min
Visual overview: The real number system1 MIN READ
2 study sections · pause after each one and recall the key ideaEvery number you use in Mathematics sits somewhere in the real number system, and knowing where it sits tells you how it behaves.
Key points- Natural numbers (1, 2, 3…), whole numbers (0, 1, 2…) and integers (…−2, −1, 0, 1, 2…) are counting-based.
- Rational numbers can be written as a fraction a/b — this includes terminating and recurring decimals.
- Irrational numbers (√2, π) cannot be written as a fraction; their decimals never repeat or end.
- A surd is an irrational root such as √3; leave it exact unless the question asks for a decimal.
- Rational — expressible as a fraction of two integers.
- Irrational — a non-terminating, non-recurring decimal.
EXAM TIP
to prove a number is rational, write it as a fraction; recurring decimals always convert (0,3̇ = 1/3).