Let's approach ordering the given set from least to greatest one number at a time. Notice that we need to compare only the numbers of the same sign. To order the negative numbers, let's rewrite the fractions as decimals.
First Value
First we have - 1 23. Before we convert it to decimal form, let's write it as an improper fraction.
- 5/3 = -1.6
We know that -1.6 lies between - 1.7 and - 1.6 on a number line. Given this information, we can now plot it.
Second Value
Let's now focus on 1.6. Since any positive number is greater than any negative number, we instantly know that 1.6 is the greatest of all three numbers.
Third Value
Next, let's plot -1 45. We will once again convert a fraction to decimal. Before we do that, we first need to write -1 45 as an improper fraction.
-1 45 ⇒ - 9/5
You can use a calculator to evaluate the quotient.
- 9/5 = - 1.8
Let's now plot the point.
Looking at the number line, we can see which of the negative numbers is greater.
-1.8<-1.6 ⇒ -1 45<-1 23
Least to Greatest
We can write the numbers in order from least to greatest all together. Lesser numbers are found on the left and greater numbers are on the right. This gives us the following order.
-1 45, -1 23, 1.6
