GED Mathematical Reasoning: Introduction To Measurement

Unit conversion

Standard/Customary Units Metric Units

LENGTH

1 foot = 12 inches 1 centimeter = 10 millimeters
1 yard = 3 feet = 36 inches 1 meter = 100 centimeters
1 mile = 1,760 yards = 5,280 feet 1 kilometer = 1,000 meters

CAPACITY

1 cup = 8 fluid ounces 1 liter = 1,000 milliliters
1 pint = 2 cups 1 kiloliter = 1,000 liters
1 quart = 2 pints
1 gallon = 4 quarts

WEIGHT

1 pound = 16 ounces 1 gram = 1,000 milligrams
1 ton = 2,000 pounds 1 kilogram = 1,000 grams
1 metric ton = 1,000 kilograms
  • When you need to change or convert from one unit to another, first identify the relationship between the units using the conversion chart.
  • Then, from there, to change from a smaller unit to a larger unit will require division and changing from a larger unit to a smaller unit will require multiplication.

smaller to larger means division

larger to smaller means multiplication

 

Example 1

Convert 15 pints to quarts and pints.

 

Note that we are changing from a smaller unit to a larger unit, which means we will divide. Using our conversion chart, we’ll first identify the relationship between pints and quarts. Looking on the left side containing Standard units, we see that one quart equals 2 pints. Since every two pints equals one quart, we will divide 15 by 2 to determine the number of whole quarts. Fifteen divided by two is 7 with a remainder of one. Therefore, 15 pints equals 7 quarts and one pint.

1 quart = 2 pints

15 \div 2 = 7 (Remainder 1)

15 pints = 7 quarts and 1 pint

A popular diagram used to commit the relationship between gallons, quarts, pints, and cups to memory is shown here on the slide.

meas1

A big G contains four smaller Q’s to represent that there are 4 quarts in one gallon.

Two P’s are drawn in each Q to denote that there are two pints in one quart.

Finally, two C’s are drawn in each P to represent that there are two cups in one pint.

Notice that this diagram also helps us see other relationships, too. Like, for example, there are 8 pints in one gallon since there are 8 P’s in the big G.  Or, for another example: there are four cups in one quart, since there are 4 C’s in each Q.

 

Example 2

Convert 6.2 grams to milligrams.

 

Note that we are changing from a larger unit to a smaller unit, which means we will multiply.

Using our conversion chart, we’ll first identify the relationship between grams and milligrams. Looking on the right side containing Metric units, we see that 1 gram equals 1,000 milligrams. Since each gram represents 1,000 milligrams, we’ll multiply 6.2 times 1,000 to determine how many milligrams this is equal to.

1 gram = 1000 milligrams

6.2 * 1000 = 6200

6.2 grams = 6200 milligrams

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