Practice problems for these concepts can be found at:
Measurement Practice Problems: GED Math
Types of Measurements
Units tell us two important things about the object being measured—what is being measured and its size. Are you measuring capacity, weight, length, or temperature? And how big, heavy, long, or hot is the object? For each type of measurement, you must use an appropriate unit of measurement. For example, you might use grams to measure weight, liters to measure capacity, degrees to measure temperature, feet to measure height, and so on.
Today, there are two major systems of measurement. The U.S. customary system is used in everyday life in the United States. The following are the types of measurements used most frequently in the United States:
Units of Length
1 foot (ft.) = 12 inches (in.)
1 yard (yd.) = 3 feet = 36 inches
1 mile (mi.) = 1,760 yards = 5,280 feet
1 square foot (ft.^{2}) = 144 square inches (in.^{2})
1 square yard (yd.^{2}) = 9 square feet
1 square mile (mi.^{2}) = 640 acres = 3,097,600 square yards
1 acre (A) = 4,840 square yards = 43,560 square feet
1 cubic foot (ft.^{3}) = 1,728 cubic inches (in.^{3}) ≈* 7.48 gallons
1 cubic yard (yd.^{3}) = 27 cubic feet
Units of Volume
1 tablespoon (tbs.) = 0.5 fluid ounce (fl. oz.)**
1 tablespoon = 3 teaspoons (tsp.)
1 cup (c.) = 8 fluid ounces
1 pint (pt.) = 2 cups = 16 fluid ounces
1 quart (qt.) = 2 pints = 32 fluid ounces
1 gallon (gal.) = 4 quarts = 128 fluid ounces
1 gallon ≈* 231 cubic inches ≈* 0.1337 cubic foot
Units of Weight
1 pound (lb.) = 16 ounces (oz.)**
1 ton (T) = 2,000 pounds
Units of Time
1 minute (min.) = 60 seconds (sec.)
1 hour (hr.) = 60 minutes
1 day = 24 hours
1 week = 7 days
1 year (yr.) = 52 weeks
1 year = 12 months
1 year = 365 days
*The symbol ≈means about equal to.
**Notice that ounces are used to measure the dimensions of both volume and weight.
The other major system of measurement is the metric system. This system is used in most other industrialized countries outside of the United States. It is also used by doctors and scientists in the United States. The basic units of the metric system are the meter, gram, and liter.
Converting units in the metric system is much easier than converting units in the U.S. customary system of measurement. However, making conversions between the two systems is much more difficult. Luckily, the GED test will provide you with the appropriate conversion factor when needed. Here is a general idea of how the two systems compare:
Conversions between U.S. Customary and Metric Units
1 inch ≈25.4 millimeters ≈2.54 centimeters
1 foot ≈0.3048 meter ≈30.480 centimeters
1 yard ≈0.9144 meter
1 mile ≈1,609.34 meters ≈1.6093 kilometers
1 kilometer ≈0.6214 mile
1 meter ≈3.281 feet ≈39.37 inches
1 square inch ≈ 645.16 square millimeters ≈ 6.4516 square centimeters
1 square foot ≈0.0929 square meter
1 square yard ≈0.8361 square meter
1 square mile ≈2,590,000 square meters ≈2.59 square kilometers
1 acre ≈4,046.8564 square meters ≈0.004047 square kilometer
1 cubic inch ≈16,387.064 cubic millimeters ≈16.3871 cubic centimeters
1 cubic foot ≈0.0283 cubic meter
1 cubic yard ≈0.7646 cubic meter
1 teaspoon ≈5 milliliters
1 tablespoon ≈15 milliliters
1 fluid ounce ≈29.57 milliliters ≈2.957 centiliters
1 fluid ounce ≈0.00002957 cubic meter
1 gallon ≈3.785 liters
1 liter ≈1.057 quarts ≈0.264 gallon
1 quart ≈0.946 liter
Prefixes are attached to the basic metric units to indicate the amount of each unit.
For example, the prefix deci means one-tenth ; therefore, one decigram is one-tenth of a gram, and one decimeter is one-tenth of a meter. The following six prefixes can be used with every metric unit:
1 hectometer = 1 hm = 100 meters
1 millimeter = 1 mm = meter = .001 meter
1 dekagram = 1 dkg = 10 grams
1 centiliter = 1 cL* = liter = 0.01 liter
1 kilogram = 1 kg = 1,000 grams
1 deciliter = 1 dL* = liter = 0.1 liter
*Notice that liter is abbreviated with a capital letter—L.
The following are some common relationships used in the metric system:
Units of Length
1 centimeter (cm) = 10 millimeters (mm)
1 meter (m) = 100 centimeters = 1,000 millimeters
1 kilometer (km) = 1,000 meters
1 square centimeter (cm^{2}) = 100 square millimeters(mm2)
1 square meter (m^{2}) = 10,000 square centimeters = 1,000,000 square millimeters
1 square kilometer (km^{2}) = 1,000,000 square meters
1 cubic centimeter (cm^{3}) = 1,000 cubic millimeters (mm^{3})
1 cubic meter (m^{3}) = 1,000,000 cubic centimeters
Units of Volume
1 liter (L) = 1,000 milliliters (mL) = 100 centiliters (cL)
1 kiloliter (kL) = 1,000 liters = 1,000,000 milliliters
Units of Weight
1 kilogram (kg) = 1,000 grams (g)
1 gram (g) = 0.001 kilogram (kg) = 100 centigrams (cg)
1 centigram (cg) = 0.01 gram (g)
1 gram = 1,000 milligrams (mg)
1 milligram (mg) = 0.001 gram (g)
Converting Units
Units of measure are converted by using either multiplication or division. To change from one unit to another, you need to determine whether more or fewer of the new units are needed. If more are needed, multiply. If fewer are needed, divide. Multiplying ends up with the smaller unit of measurement; dividing ends up with the larger unit.
To change a larger unit to a smaller unit, multiply the specific number of larger units by the number of smaller units in only one of the larger units.
- 5 feet = ? inches
There are 12 inches in one foot. To find how many inches are in 5 feet, multiply 5 by 12: 5 feet × 12 inches = 60 inches.
- Change 3.5 tons to pounds.
There are 2,000 pounds in a ton. To find how many pounds are in 3.5 tons, multiply 3.5 by 2,000: 3.5 tons × 2,000 pounds = 7,000 pounds.
To change a smaller unit to a larger unit, divide the specific number of smaller units by the number of smaller units in only one of the larger units.
Find the number of pints in 64 ounces.
Remember, there are 16 ounces in 1 pint. So, divide 64 by 16 to determine the number of pints: 64 ounces ÷ 16 ounces = 4 pints.
Conversions within the Metric System
An easy way to do conversions with the metric system is to move the decimal point either to the right or left, because the conversion factor is always ten or a power of ten. As you learned previously, when you change from a large unit to a smaller unit you multiply, and when you change from a small unit to a larger unit you divide.
When you multiply by a power of ten, you move the decimal point to the right. When you divide by a power of ten, you move the decimal point to the left. To change from a large unit to a smaller unit, move the decimal point to the right.
To change from a small unit to a larger unit, move the decimal point to the left.
Suppose you are packing your bicycle for a trip from New York City to Detroit. The rack on the back of your bike can hold 20 kilograms. If you exceed that limit, you must buy stabilizers for the rack that cost $2.80 each. Each stabilizer can hold an additional kilogram. If you want to pack 23,000 grams of supplies, how much money will you have to spend on the stabilizers?
Step 1 First, change 23,000 grams to kilograms.
Step 2 Move the decimal point three places to the left: 23,000 g = 23.000 kg = 23 kg.
Step 3 Subtract to find the amount over the limit. 23 kg – 20 kg = 3 kg.
Step 4 Because each stabilizer holds one kilogram and your supplies exceed the weight limit of the rack by three kilograms, you must purchase three stabilizers from the bike store.
Step 5 Each stabilizer costs $2.80, so multiply $2.80 by 3: $2.80 × 3 = $8.40.
Temperature
Much of the world measures temperature in degrees Celsius. The Celsius unit of temperature is based on 0° C as the freezing point and at 100° C as the boiling point of water at sea level. In the United States, temperature is measured in degrees Fahrenheit, which is based on 32° F as the freezing point and 212° F as the boiling point.
Thermometers are used to measure temperature. They show measurements as points on a scale. Positive temperatures are shown as numbers greater than 0. Negative numbers are shown as numbers less than 0.
To find the difference between two temperatures, subtract the lower temperature from the higher temperature. Think of a thermometer as a number line: The difference between two points on a number line is equal to the distance between the points.
Find the difference between 60° F and –15° F. Remember, subtracting a negative number is the same as adding a positive number.
60° F – (–15° F) = 60° F + 15° F = 75° F
To convert from degrees Celsius (° C) to degrees Fahrenheit (° F), use the formula:
F = (C) + 32
Substitute the given number of Celsius degrees in the formula for C.
Multiply by and then add 32.
Example
Convert 40° C into Fahrenheit.
F = (40) + 32 = + 32 = 72 + 32 = 104°
Therefore, 40° C = 104° F.
To convert from degrees Fahrenheit (° F) to degrees Celsius (° C), use the formula:
C = (F – 32)
Substitute the given number of Fahrenheit degrees in the formula for F.
Subtract 32, then multiply by .
Example
Convert 50° F into Celsius.
C =(50 – 32) = (18) = = 10°
Therefore, 50° F = 10° C.
Practice problems for these concepts can be found at:
Measurement Practice Problems: GED Math