Absolute Value of Numbers

The absolute value of a number is its distance from zero on the number line. Because distance cannot be negative, the absolute value of a number is always zero or positive.

We write absolute value using two vertical bars. For example, the absolute value of $-7$ is written as $|-7|$.

Finding the Absolute Value

To find the absolute value, simply count how many units the number is away from zero, regardless of the direction (left or right).

• Find $|-7|$: The number $-7$ is exactly $7$ units away from zero. Therefore, $|-7| = 7$.
• Find $|4|$: The number $4$ is exactly $4$ units away from zero. Therefore, $|4| = 4$.
• Find $|0|$: Zero is exactly $0$ units away from itself. Therefore, $|0| = 0$.

Comparing Absolute Values

You can use absolute value to figure out which number is further from zero.

Example: Which has a greater absolute value: $-12$ or $9$?

1. First, find the absolute values: $|-12| = 12$ and $|9| = 9$.
2. Compare the results: $12 > 9$.
3. Because $12$ is larger, $-12$ is further from zero and has the greater absolute value.

Ordering Absolute Values

When asked to order numbers by their absolute values, always evaluate the absolute values first before placing them in order.

Example: Order $|-3|$, $|5|$, $|-8|$, $|2|$ from least to greatest.

1. Find the value of each expression:
   • $|-3| = 3$
   • $|5| = 5$
   • $|-8| = 8$
   • $|2| = 2$
2. Order these regular numbers from least to greatest: $2, 3, 5, 8$.
3. Write the final answer using the original absolute value expressions: $|2|$, $|-3|$, $|5|$, $|-8|$.