On the coordinate plane you have used numbers that start at 0 and grow. But many things go in two directions from a starting point: warmer or colder than zero degrees, above or below sea level, money in or money out.
Key idea
Choose a zero point. Numbers on one side of it are positive, numbers on the other side are negative, written with a minus sign: 8 degrees below zero is $-8$. Zero itself is neither positive nor negative.
Why it works
A measurement like "8 degrees" is not complete until you know which way from zero it goes. The sign carries the direction and the digits carry the size. That lets one number line hold both directions, with 0 as the starting point in the middle.
| Situation | Zero | Positive | Negative |
|---|---|---|---|
| Temperature | 0° | above 0° | below 0° |
| Height | sea level | above | below |
| Money | \$0 | deposit | withdrawal, debt |
| Football | start of play | gain | loss |
Worked example: Write the number
A diver swims 30 feet below sea level. Write a number for the diver’s position.
- Sea level is 0.
- Below sea level is the negative direction.
Answer: $-30$
Worked example: Read the number
A bank statement shows $-15$ for one day. What does it mean?
- Positive numbers are money put in, so negative numbers are money taken out.
- The size is 15.
Answer: \$15 was taken out (a withdrawal of \$15).
Common mistake
Dropping the sign. "A loss of 5 yards" is $-5$, not 5, and "a debt of \$20" is $-20$. Quick check: before writing the number, ask which direction from zero it goes.