Density: Dimensional Analysis

The volume (in cm3) of 0.55 kilogram piece of iron (Density = 7.9 g/cm3) is _________

When I read a math problem, I often draw a diagram. Of course it doesn’t have to be fancy–it is just to help me understand what each of the facts in the problem mean.

I also list all the facts and label them. This also helps me when I do start solving the problem.


density = 7.9 g/cm3

mass = 0.55 kg  (NOTE: I have to know what each of the units measure and kilograms is a mass unit.)

Problem Map:

This is a plan that shows you where to Start and the units of the answer at the Finish.


UMM! Maybe I need to help you decide where to start.


1. When density is given, you will use it as a conversion factor, this means that it is NEVER the starting point. Instead, it is used to change either grams to cubic centimeters or vise versa.

2. For this problem, the only other fact is the mass of the piece of iron. So this has to be what you will use as your starting point.

3. The answer is to be the volume of the piece of iron measured in cm3.

With this information, you are ready to express your problem map.


0.55 kg———————————————————————–>? cm3


1. The problem is to change the kg unit to cm3

2. Density is a conversion factor that can be used to change the g unit to cm3

3. Since your mass is given in kg, and the density has mass in grams, you will have a second conversion factor, and it is one you must know. This is a conversion between grams and kilograms, which is 1000 g = 1 kg.

3. Write down the starting fact and the multiplication sign (X) , and then draw a line that will separate the numerator from the denominator.

0.55 kg  X =  ? cm3

4. Now you are ready to eliminate the kg unit. You do this by multiplying by a fraction that has the kg unit in its denominator. REMEMBER THAT ANY AND ALL CONVERSION FACTORS ARE FRACTIONS AND CAN BE FLIPPED OVER TO MEET THE NEEDS OF THE PROBLEM.