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 - 45 is farther to the right than - 1.3. This means that - 45 is greater than - 1.3.
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 each of the given numbers.
|- 4/5 |= 4/5 |- 1.3|= 1.3
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 |- 45|. We can also see on the diagram that |- 1.3| is farther to the right. In this case, the following inequality holds true.
|- 1.3|> |- 4/5|
This means that - 1.3 is farther from 0 than - 45.
