Customary Units
Customary Units of Length
- Inch (in): Smallest unit commonly used. 12 inches = 1 foot.
- Foot (ft): 1 foot = 12 inches. 3 feet = 1 yard.
- Yard (yd): 1 yard = 3 feet = 36 inches.
- Mile (mi): 1 mile = 1,760 yards = 5,280 feet.
Customary Units of Liquid Volume
- Fluid ounce (fl oz)
- Cup (c): 1 cup = 8 fl oz
- Pint (pt): 1 pint = 2 cups = 16 fl oz
- Quart (qt): 1 quart = 2 pints = 4 cups = 32 fl oz
- Gallon (gal): 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fl oz
Customary Units of Weight
- Ounce (oz): Smallest unit.
- Pound (lb): 1 pound = 16 ounces
- Ton (T): 1 ton = 2,000 pounds
Perimeter
The distance around a two-dimensional shape.
Example: Perimeter of a rectangle = 2 × (Length + Width)
Area
The number of square units covering a surface.
Example: Area of a rectangle = Length × Width
Volume of a Solid
The amount of space a solid occupies.
Example: Volume of a rectangular prism = Length × Width × Height
Time
- Second (s)
- Minute (min): 1 minute = 60 seconds
- Hour (hr): 1 hour = 60 minutes
- Day: 1 day = 24 hours
- Week: 1 week = 7 days
Temperature
- Degrees Fahrenheit (°F)
- Water freezes at 32°F, boils at 212°F
Metric Units
Metric Units of Length
- Millimeter (mm)
- Centimeter (cm): 1 cm = 10 mm
- Meter (m): 1 m = 100 cm
- Kilometer (km): 1 km = 1,000 m
Metric Units of Liquid Volume
- Milliliter (mL)
- Liter (L): 1 L = 1,000 mL
Metric Units of Mass
- Milligram (mg)
- Gram (g): 1 g = 1,000 mg
- Kilogram (kg): 1 kg = 1,000 g
Perimeter, Area, and Volume of a Solid: Metric
- Perimeter: Sum of side lengths (measured in meters, centimeters, etc.)
- Area: Measured in square meters (m²), square centimeters (cm²), etc.
- Volume: Measured in cubic meters (m³), liters (L), etc.
Conversion Between Units
Changing from Customary Units to Metric Units
- 1 inch ≈ 2.54 centimeters
- 1 foot ≈ 0.3048 meters
- 1 mile ≈ 1.609 kilometers
- 1 pound ≈ 0.454 kilograms
- 1 ounce ≈ 28.35 grams
- 1 gallon ≈ 3.785 liters
- 1 quart ≈ 0.946 liters
Changing from Metric Units to Customary Units
- 1 centimeter ≈ 0.3937 inches
- 1 meter ≈ 3.281 feet
- 1 kilometer ≈ 0.621 miles
- 1 kilogram ≈ 2.205 pounds
- 1 gram ≈ 0.035 ounces
- 1 liter ≈ 0.264 gallons
Key Concepts Explained
What is Measurement?
Measurement is the process of quantifying the physical properties of objects or events using standard units. It helps us compare, estimate, and understand the world around us.
Why Are There Different Systems?
Customary units are mainly used in the United States, while the metric system is used worldwide. The metric system is based on powers of ten, making conversions simpler.
Estimating and Choosing Units
Use smaller units for small objects (like millimeters or inches) and larger units for big distances (like kilometers or miles). Choose units that make sense for what you are measuring.
Temperature Scales
Fahrenheit is common in the U.S., Celsius is used elsewhere. To convert:
°C = (°F − 32) × 5⁄9
°F = (°C × 9⁄5) + 32
Examples
Example 1: Converting Inches to Centimeters
Solution: 10 in × 2.54 = 25.4 cm
Example 2: Area of a Rectangle (Customary Units)
Solution: Area = 5 ft × 3 ft = 15 ft²
Example 3: Volume of a Rectangular Prism (Metric Units)
Solution: Volume = 20 × 10 × 5 = 1,000 cm³
Example 4: Converting Celsius to Fahrenheit
Solution: (25 × 9/5) + 32 = 77°F
Pre-test (40 Questions)
- How many inches are in a foot?
- How many feet are in a yard?
- How many yards are in a mile?
- How many ounces are in a pound?
- How many pints are in a quart?
- How many cups are in a gallon?
- What is the metric unit for mass?
- How many centimeters are in a meter?
- How many millimeters are in a centimeter?
- How many liters are in a kiloliter?
- Convert 5 feet to inches.
- Convert 3 yards to feet.
- Convert 2 miles to feet.
- Convert 24 inches to feet.
- What is the perimeter of a rectangle with length 6 ft and width 4 ft?
- What is the area of a rectangle with length 8 m and width 3 m?
- What is the volume of a box 2 m × 2 m × 2 m?
- Convert 1.5 liters to milliliters.
- Convert 500 grams to kilograms.
- Convert 1000 millimeters to meters.
- How many minutes are in an hour?
- How many seconds in 2 minutes?
- What is the freezing point of water in Fahrenheit?
- What is the boiling point of water in Celsius?
- Convert 10 kilometers to meters.
- Convert 2500 milliliters to liters.
- Convert 3 kilograms to grams.
- Which is greater: 1 pound or 500 grams?
- What metric unit would you use to measure the length of a pencil?
- What customary unit would you use to measure the length of a football field?
- Convert 40°F to Celsius.
- Convert 100°C to Fahrenheit.
- How many gallons are in 16 quarts?
- How many quarts are in 2 gallons?
- What is the perimeter of a square with sides of 7 cm?
- What is the area of a square with sides of 5 m?
- What is the volume of a cube with sides of 3 m?
- How many days are in a week?
- What is the metric prefix for one thousand?
- Which is heavier: 1 kilogram or 2 pounds?
Questions & Answers
How do you convert inches to centimeters?
What is the formula for the area of a rectangle?
What is the difference between mass and weight?
How do you convert Celsius to Fahrenheit?
Which is larger: a gallon or a liter?
How do you find the perimeter of a polygon?
What is the metric unit for temperature?
How many meters are in a kilometer?
Post-test (40 Questions)
- How many quarts are in a gallon?
- How many feet are in a mile?
- How many yards are in 18 feet?
- How many ounces are in 3 pounds?
- How many cups are in a quart?
- What is the metric unit for length?
- How many grams are in a kilogram?
- How many liters are in 3 kiloliters?
- Convert 36 inches to yards.
- Convert 4 feet to centimeters.
- Convert 2 miles to kilometers.
- Convert 16 ounces to grams.
- What is the area of a rectangle 10 ft by 4 ft?
- What is the perimeter of a rectangle 5 m by 8 m?
- What is the volume of a box 3 m × 4 m × 5 m?
- Convert 1200 grams to kilograms.
- Convert 2500 milliliters to liters.
- Convert 5 kilometers to miles.
- Which is more: 1 liter or 1 quart?
- How many minutes are in 2 hours?
- How many seconds are in 5 minutes?
- What is room temperature in Celsius?
- Convert 68°F to Celsius.
- Convert 20°C to Fahrenheit.
- How many millimeters are in 5 centimeters?
- What is the perimeter of a square with sides of 12 m?
- What is the area of a square with sides of 9 cm?
- What is the volume of a cube with sides of 4 cm?
- How many days are in a leap year?
- What is the metric prefix for one hundred?
- Which is heavier: 1 kilogram or 1,000 grams?
- How many pints are in a gallon?
- How many cups are in 2 quarts?
- What customary unit measures a person's weight?
- What metric unit measures the mass of a book?
- Convert 500 ml to liters.
- How many centimeters are in a meter?
- Which is longer: 1 yard or 1 meter?
- How many weeks in a year?
- What is the boiling point of water in Fahrenheit?