Concept 1 · free preview
Types of numbers
Understand
Every number belongs to a ‘family’. The condition in a question (natural, integer, rational) tells you which numbers are allowed.
| Type | Simple meaning | Examples |
|---|---|---|
| Natural numbers | Counting numbers | 1, 2, 3, 4… |
| Whole numbers | Natural numbers plus 0 | 0, 1, 2, 3… |
| Integers | Positive, negative and 0 | …−2, −1, 0, 1, 2… |
| Rational numbers | Can be written as p/q with q ≠ 0 | 3/4, −2, 0.5 |
| Irrational numbers | Cannot be written as p/q of integers | √2, √3, π |
| Real numbers | Rational and irrational together | All of the above |
Remember
Here natural numbers start at 1; some mathematical conventions include 0.
Common mistake
Not every square root is irrational. √16 = 4, so it is rational.
Check yourself
Is 0.75 rational?
Answer: Yes. 0.75 = 3/4, which is in p/q form.