Factor-Label Examples & Practice Problems

Factor-Label Examples & Practice Problems

Example:
1. Convert 7.5639 g to kg.
( 7.5639 g x 1 kg) / 1000 g = 0.0075639 kg
The answer has 5 significant figures since 7.5639 g has 5 significant figures.

Most other conversions are not exact. When using non-exact conversions it is a good idea to use at least one more significant figure in the conversion factor than in the data value being converted.

Example: Convert 1.00 gallon to L.
The relevant conversion factors can be obtained from these relationships :
4 qt = 1 gallon (exact) and 1 qt = 0.9464 L (not exact).
Since the value (1.00 gallon) has 3 significant figures, it is a good idea to use at least 4 significant figures in the conversion factor.
1.00 gal x (4 qt/1 gal) x (0.9464 L/1 qt) = 3.79 L

The answer has 3 significant figures because 1.00 gal has 3 significant figures.

Problem Solving Using Units

Many problems in science can be solved by making the units "come out right", even if you don't know the necessary formula to solve the problem. Try the following problems, being very careful with units. Get into the habit of showing all units and how they cancel in every step of a calculation.

Question 1: A piece of metal has a mass of 27.6 g and a volume of 6.72 mL. What is its density in g/cm³?

Question 2: The density of Hg is 13.6 g/cm³. What volume in mL does 195g of Hg occupy?

Question 3: How many square inches are there in 85.0 cm²?

Question 4: The molar mass of O₂ is 32.0 g/mol. How many moles of O₂ are in 0.428 g of the gas?

Question 5: The wavelength of some visible light is 706 nm. What is its frequency in sec^-1 (Hz) ? The speed of light, c = 3.00 x 108 m/sec.

Question 6: A sphere has a volume of 3.75 cm³. What is its diameter in inches? V_sphere = (4/3) r³

Question 7: A piece of aluminum foil is 0.010 mm thick. If it weighs 0.861 g, what is its area in cm²? The density of aluminum is 2.70 g/mL.

Question 8: The radius of a copper atom is 2.556 . How many copper atoms could you line up in a row across a penny 1.85 cm in diameter? How many moles of copper is this?

Use this Scientific Unit Converter to check your answers!