**A mole is a chemical unit of measure.**

**Dimensional analysis** is a method used to convert one unit of measurement to another. Conversion factors are mathematical tools for converting between units of measurement. The conversion factor 1 ft = 12 inches is used to convert units of feet to units of inches or vise versa.

**Example:** How many inches are in 3 feet?

Think:

- What conversion factor compares the units of feet and inches?

Conversion factors are ratios between units. 1 ft :12 in; 1 ft/12 in - In the dimensional analysis method, conversion factors are written as fraction.

1 ft/12 in or 12 in/1 ft - Start with the measurement to be converted, which is 3 ft in the problem.

Write this measurement and draw two lines as shown. The horizontal line separates the numerator from the denominator. The vertical line separates factors that are multiplies.

- Next, select the correct version of the conversion factor the converts the unit of feet to the unit of inches.
- Conversion factors are fractions. Remember when working with fractions, the first thing is to simply them: Do this by cancelling factors which are in common between the numerator and denominator. Factors can be numbers and or units of measurement.

- In order to cancel the foot unit, the conversion factor fraction used is 12 in/1 ft.

This is because the foot unit is in the denominator, thus the foot units cancel out as shown. - Remember that the vertical line separates fractions that multiplied.

**Problem 1: **Use Avogadro’s Number (a conversion factor) to decide how many atoms are in 3.05 moles of calcium, Ca.

**Clues:**

- Write the amount that is to be converted.
- Add two lines, one to separate the numerators from the denominators. The second vertical line separates fractions that are multiplied.
- Add the conversion factor.
- Cancel units.
- Multiply factors in the numerator. Divide by factors in the denominator.

Check your work with the following:

**Problem 2: How many moles lithium, Li are equal to 4.2 x 10 ^{ 26} atoms of lithium? **

**Click How Many Atoms in a Mole? to find the answer for this problem. **