Dr. Walt Volland revised September 29, 2009 all rights reserved 2005-2009

Conversions examples and exercises

The first step is to always identify the unit you want in your answer. Then list all conversion relationships that are of the same "quality". (example is a length conversion so a length relationship was used). After you have practice you will be able to skip this step. The unit you need to cancel out is always on the opposite side of the fraction in the conversion factor. Linear Conversions involve unit labels with "1" for an exponent. This means the conversion only needs to use the conversion factor to multiply once.

EXAMPLE 1: The conversion of one length unit to another can be done the following way. How many millimeters equal 3.8 meters? 3.8 meters = ? millimeters;                   Remember: 1000 millimeter = 1 meter ?  millimeters = 3.8 meters [ 1000 millimeters / 1 meter ] = 3.8 meters [ 1000 millimeters / 1 meter ] ?  millimeters = 3800 millimeters = 3.8 x 103 millimeter The result is rounded off to two significant figure because the 3.8 meters has only two sf even though the definition of 1000 mm = 1 meter is an exact number with an unlimited sf digits. EXAMPLE 2: The conversion of one mass unit to another can be done the following way. How many milligrams equal 2.4 kilograms? 2.4 kilograms = ? milligrams;                   Remember: 1000 milligrams = 1 kilogram ?  milligrams = 2.4 kilograms [ 1000 milligrams / 1 kilogram ] = 2.4 kg [ 1000 mg / 1 kg ] = 2400 mg ?  milligrams = 2400 milligrams = 2.4 x 103 milligrams The result is rounded off to two significant figure because the 2.4 kilograms has only two sf even though the definition of 1000 mg = 1 kg  is an exact number with an infinite number of sf. EXAMPLE 3: The conversion of one weight unit to another can be done the following way. How many pounds equal 78 ounces ? ? pounds = 78 ounces;                   Remember: 1 pound = 16 ounces ? pounds = 78 ounces [1 pounds /16 ounces] = 78 ounces [1 pounds /16 ounces] = 4.875 pounds ? pounds = 4.875 pounds = 4.9 pounds  Here the result is rounded off to two significant figure because the 78 ounces has only two sf. This is true even though the definition  16 oz = 1 pound is an exact number with an unlimited number of sf. EXAMPLE 4: The conversion of one volume unit to another can be done the following way. How many liters equal 27100 millilters ? ? liters = 27100 millilters;                   Remember: 1 liter = 1000 milliliters ? liters = 27100 millilters [1 liter /1000 milliliters] = 27100 milliliters [1 liter /1000 milliliters] = 2.71 liters ? liters = 2.71 liters Here the result is rounded off to three significant figure because the 27100 mL has only three sf.