Skill: Identify real-world uses of integers

Integers are useful when a real-world quantity can be above or below a meaningful zero.

• A positive integer means the quantity is above, greater than, or in one chosen direction from zero.
• A negative integer means the quantity is below, less than, or in the opposite direction from zero.
• Zero is the reference point.
• The absolute value tells how far the quantity is from zero.

Example:
At noon, the temperature is $(6^\circ\text{C})$ below zero. Write an integer that represents the temperature and explain its meaning.

Step 1: Identify the zero point.
For temperature, $(0^\circ\text{C})$ is the reference point.

Step 2: Decide which side of zero the temperature is on.
The temperature is below zero, so its integer must be negative.

Step 3: Use the number of units from zero.
It is $6$ degrees from zero, so the integer is

$$-6$$

Step 4: Interpret the integer.
The integer $(-6)$ means the temperature is $(6^\circ\text{C})$ below $(0^\circ\text{C})$.

The sign tells which side of zero the temperature is on, and the $6$ tells how far it is from zero. The number $(-6)$ is a value describing the temperature, not just a label or direction. Other examples include $(-20)$ meters for an elevation below sea level or 15)$ for owing money.