To solve this problem, we want to get all of the possible options into the same form, so that it is easier to compare them. Personally, I prefer comparing in decimals, so that is how I am going to solve this problem.
13/4 - To turn this improper fraction into its decimal equivalent, it is easier to first turn it into a mixed number by dividing the numerator by the denominator.
13/4 = 3 1/4
Because we know that 1/4 = 0.25, we now know that 3 1/4 = 3.25
Therefore, 13/4 = 3.25
3 1/2 - This is similar to the end of the process above. We know that 1/2 = 0.5, so we know that 3 1/2 = 3.5
3 1/2 = 3.5
3.15 is already in its decimal form, so we can leave that be for now.
√9 - To simplify this, we must figure out what number multiplied by itself equals 9. If we start with 2 (2*2 = 4), so that is too small. Next maybe we try 4 (4 * 4 = 16), so that is too large. Now we know we need a number in between 2 and 4, so maybe we try 3. 3 * 3 = 9, so we can conclude that √9 = 3.
√9 =3
If we take all of our decimal equivalents, we have 3.25, 3.5, 3.15, and 3.
Because all of these values have the same whole number value of 3, we need to compare the decimals to find out what order they belong in.
Our final order is (from smallest to largest): 3, 3.15, 3.25, 3.5
But, we need to substitute in the equivalent values we were given for these decimals originally to finish the problem.
This makes your final answer: √9, 3.15, 13/4, 3 1/2
Hope this helps!
