Ordering Negative Numbers

On the number line, whichever number sits further left is the smaller one. That rule never changes.

The trap

−8 is less than −3, even though 8 is more than 3. Further left, so smaller.

What it means

−8 °C is colder than −3 °C. A debt of £8 is worse than a debt of £3.

Zero divides them

Every negative number is less than every positive number, whatever the digits.

Further left is always smaller

On the number line, −8 sits to the left of −2, so −8 < −2. This one rule orders every number there is, positive or negative. When ordering negatives confuses you, draw the line and read left to right.

Negatives reverse the familiar order

Among positives, 8 beats 2. Among negatives, −8 loses to −2. The ordering of the digits is mirrored once you cross zero. Noticing this explicitly is more reliable than trying to feel your way through each comparison.

Comparing across zero

Any negative number is less than any positive number, and both are on opposite sides of zero. So −100 < 1 without any further thought. When one number is negative and the other positive, the comparison is settled instantly.

Context can invert what "better" means

A temperature of −2 is warmer than −8, but a debt of £2 is better than a debt of £8, and there the smaller absolute value is preferable. The mathematical ordering is fixed; whether smaller is better depends on what the numbers describe.