Let's approach ordering the given set from greatest to least one number at a time. Notice that two of the given numbers are decimals, so we will try to rewrite 54 and sqrt(3) in this form as well. Let's start with 54.
Rewriting 54
In order to convert a fraction to a decimal, we have to divide the numerator by the denominator.
The fraction 54 written as a decimal is equal to 1.25.
Rewriting sqrt(3)
We could type sqrt(3) into a calculator to help us evaluate it. Or, we can compare it to the square root of two nearby perfect squares. We will show how to do this second option.
Now we know that sqrt(3) is greater than 1 and less than 2. Unfortunately, 1.9 and 54 are also between 1 and 2, so we will need to use a calculator to compare sqrt(3) to these numbers.
sqrt(3)=1.73205...≈ 1.73
Ordering the Numbers
Since - 1.2 is negative, it is the least. For other values we have to compare the decimal parts.
1.9>1.73>1.25
Finally, we can order the given numbers from greatest to least. Remember that 1.73 corresponds to sqrt(3), and 1.25 to 54.
1.9, sqrt(3), 54, - 1.2
