We want to determine which number is greater and which number is farther from 0. We will do these things one at a time.
Greater Number
To find which number is greater, we will start by plotting both numbers on the number line. Let's do it!
We can see on the diagram that 72 is farther to the right than - 3.25. This means that 72 is greater than - 3.25.
Farther From 0
We want to find which number is farther from 0. Let's recall some facts about the absolute value of a number.
The absolute value of a number is its distance from 0 on the number line.
Since distance is always greater than or equal to 0, the absolute value of any number is greater than or equal to 0.
The absolute value of a non-negative number is equal to the number, while the absolute value of a negative number is equal to its opposite.
Let's consider the distances between different numbers and 0 on the number line.
Now, let's calculate the absolute value of both of the given numbers.
|- 3.25|= 3.25 |7/2|= 7/2
We can plot the numbers on a number line to see the order from least to greatest.
Notice that the number that is farther to the left is |- 3.25|. We can also see on the diagram that | 72| is farther to the right. In this case, the following inequality holds true.
| 72|> |- 3.25|
This means that 72 is farther from 0 than - 3.25.
