What is an Absolute Value?
The absolute value of a number refers to its magnitude irrespective of the sign of the number. We can use a number line to represent the absolute value of any number. The distance between a number and 0 on the number line is the measure of the absolute value of the given number.
The symbol, || is used to represent absolute value. For instance, the absolute value of a number a is denoted by a and is written as |a|.
Let’s take a look at an example:
Absolute value of 6 and -6:
Mark 6 and -6 on a number line.
The distance between 0 and 6 as well as between 0 and -6 is 6.
So, the absolute values of 6 and -6 are:
|6| = 6 and |-6| = 6.
How do we compare values?
To compare two numbers, plot them on a number line. The number that lies to the left of zero or another number will be lesser, or the number that lies to the right of zero or another number will be greater.
Now let’s solve a few problems on the concept and sharpen our understanding.
Solved Examples
Example 1: Find the absolute value of |-11.6|.
Solution:
Let us use a number line:
Mark -11.6 on the number line.
As you can see, the distance between 0 and -11.6 is 11.6, so, |-11.6| = 11.6.
Example 2: Compare 7 and |-2|.
Solution:
Graph the numbers on a number line.
As we can see, |-2| is to the left of 7.
Hence, |-2| < 7.
Example 3: Ellen and Jake are scuba diving. After some time their dive depths are 30 feet for Ellen and 60 feet for Jake. Who was closer to the surface of the sea?
Solution:
Assume that the surface of the sea is 0.
Use the absolute values of the depths to which Ellen and Jake dived to compare who was closer to the surface of the sea.
According to the problem, Ellen’s dive depth is 30 feet while Jake’s dive depth is 60 feet.
Hence,
Ellen = |-30|
Jake = |-60|
By finding the absolute values,
Ellen: |-30| = 30
Jake: |-6| = 60
Since 30 is less than 60, Ellen was closer to the surface of the sea Jake.
The absolute value of 0 will be 0 itself. As, |0| = 0.
Integers include the set of whole numbers and their negative counterparts. Some examples of integers are -2, 3, -6, 6, -1, and so on.
The absolute value of any integer is defined as its numerical value without considering the negative or positive sign associated with it.
The concept of absolute value is important for us to understand the distance between two points. It is essential for high school math problems and algebraic expressions and equations.