Skill: Interpret positive and negative numbers

A signed number tells how a quantity is related to a reference point, usually $0$.

• A positive number, such as $+5$, is above or to the right of $0$.
• A negative number, such as $-3$, is below or to the left of $0$.
• Zero means the reference point or no signed change.
• The magnitude is the distance from $0$. For example, $\vert -3 \vert =3$.
• Opposites are the same distance from $0$ but on different sides. The opposite of $+5$ is $-5$.

Worked example

An elevator starts at the ground floor, labeled $0$. It moves to floor $+5$, then to floor $-3$.

1. Interpret each number.

• $+5$ means the elevator is $5$ floors above the ground floor.
• $-3$ means the elevator is $3$ floors below the ground floor.
• $0$ means the elevator is at the ground floor.

2. Find the magnitude of each position.

The magnitude tells how far the elevator is from floor $0$:

$$\vert +5 \vert =5 \qquad \text{and} \qquad \vert -3 \vert =3$$

So, floor $+5$ is $5$ floors from the ground, and floor $-3$ is $3$ floors from the ground.

3. Compare the two positions.

On a number line, numbers farther to the right are greater:

$$-3 \quad < \quad 0 \quad < \quad +5$$

Therefore,

$$-3<+5$$

Even though $3$ is less than $5$ in magnitude, $-3$ is still less than $+5$ because every negative number is to the left of every positive number on the number line.