What is an integer?
An integer is a whole number. It can be positive (like 1, 2, 3), negative (like −1, −2, −3), or zero (0). Integers have no fractional or decimal part, so 2½ and 0.7 are not integers.
We use integers every day: temperature (−4°C), floors below ground (−2), money owed (−RM50), and steps forward or backward.
Key idea / Key idea
The set of integers is … −3, −2, −1, 0, 1, 2, 3 …. Positive integers are greater than 0, negative integers are less than 0, and 0 is neither positive nor negative.
The number line
A number line helps us picture integers. Negative numbers sit on the left of 0 and positive numbers on the right. As we move right the value increases; as we move left it decreases.
- Any positive integer is greater than any negative integer, so 1 > −100.
- For two negative integers, the one closer to 0 is larger: −2 > −7.
Worked example / Worked example
Arrange −5, 3, 0, −1, 4 in order from smallest to largest.
On the number line the leftmost value is smallest. Reading left to right: −5, −1, 0, 3, 4.
Comparing integers
We compare with the symbols > (greater than), < (less than) and = (equal). For example, −3 < 2 because −3 is to the left of 2. The opposite of an integer has the same distance from 0 but the other sign, so the opposite of 6 is −6.
Remember / Remember
- 0 is an integer but is neither positive nor negative.
- Bigger negative digits mean a smaller value: −9 < −4.
- Positive integers are always greater than negative integers.