The real number system

Every number you use in Mathematics sits somewhere in the real number system, and knowing where it sits tells you how it behaves.

• 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.