**Subject:** Using density to solve a dimensional analysis problem.

Dimensional analysis is a procedure for solving problems using a conversion

factor that compares units. Density is a conversion factor that comparing

the mass of a specific volume for a specific substance. YIKES! This sounds

so very complicated, but it really isn’t. Let me give you an example:

**Problem 1:** What is the volume of 38.64 grams of gold?

**Think:
**1. The conversion factor that compares grams of gold to volume (cm^3) is the density of gold, which is 19.32 g/1cm^3

2. Restate the Problem: 38.64 g = ?cm^3

3. Solve by dimensional analysis using the density of gold as the conversion factor.

38.64 g x 1 cm^3/ 19.32 g = 2.00 cm^3

Note: The conversion factor (density) was inverted so that the gram unit is canceled out and only the unit of volume, cm^3 remains.

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**Problem 2:** Determine the mass of 2.00 cm^3 gold using

dimensional analysis, then the calculations would look like this:

2.00 cm^3 x 19.32 g/ 1 cm^3 = 32.64 g

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Let me know if you need more help with this.