PRESENTATION 7 Customary Measurement Units

CUSTOMARY LINEAR UNITS Linear Measurement expresses distance between two points or measurement of lengths 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 yard (yd) = 36 inches (in) 1 rod (rd) = 16.5 feet (ft) 1 rod (rd) = 5.5 yards (yd) 1 mile (mi) = 5,280 feet (ft) 1 mile (mi) = 1,760 yards (yd) 1 mile (mi) = 320 rods (rd) 1 mile (mi) = 8 furlongs

CONVERTING UNITS OF MEASURE Example: Express 76.53 inches as feet Method 1 Since 12 inches = 1 foot, divide 76.53 by 12 76.53 ÷ 12 = 6.3775 76.53 inches ≈ 6.378 feet

CONVERTING UNITS OF MEASURE Method 2 Since 76.53 is to be expressed as feet, multiply by the unity fraction This permits the inch unit to be canceled and the foot unit to remain

CONVERTING UNITS OF MEASURE Example: Express 2.28 yards as inches Method 1 Since 36 inches equal 1 yard, multiply 2.28 by 36 2.28 × 36 = 82.08 2.28 yards ≈ 82.1 in

CONVERTING UNITS OF MEASURE Method 2 Multiply 2.28 by the unity fraction Divide the numerator and denominator by the common factor, 1 yard

SURFACE AREA Two-dimensional measure Computed as product of two linear measures Expressed in square units Unity fractions are used for surface area conversions

SURFACE AREA Customary Units of Surface Area 1 square foot (sq ft) = 144 square inches (sq in) 1 square yard (sq yd) = 9 square feet (sq ft) 1 square rod (sq rd) = 30.25 square yards (sq yd) 1 acre (A) = 160 square rods (sq rd) 1 acre (A) = 43,560 square feet (sq ft) 1 square mile (sq mi) = 640 acres (A)

SURFACE AREA CONVERSIONS Example: Express 728 square inches as square feet Method 1 Since 144 sq in = 1 sq ft, divide 728 by 144 728 ÷ 144 = 5.055 ≈ 5.06 728 sq in ≈ 5.06 sq ft

SURFACE AREA CONVERSIONS Method 2 Use the unity fraction to solve

CUSTOMARY VOLUME UNITS Three-dimensional Computed as product of three linear measures Expressed in cubic units Equivalent units of volume: 1 cubic foot (cu ft) = 1,728 cubic inches (cu in) 1 cubic yard (cu yd) = 27 cubic feet (cu ft)

CUSTOMARY VOLUME UNITS CONVERSION Example: Castings are to be made from 2.250 cubic feet of molten metal. If each casting requires 15.8 cubic inches of metal, how many castings can be made? Since 1,728 cubic inches equal 1 cubic foot, multiply 1,728 by 2.250 1,728 × 2.250 = 3,888 Divide 3,888 ÷ 15.8 ≈ 246; 246 castings can be made

CUSTOMARY UNITS OF CAPACITY Capacity is a measure of volume There are three different kinds of measures of capacity: Liquid measure Dry measure Apothecaries fluid measure (for measuring drugs and prescriptions)

CUSTOMARY UNITS OF CAPACITY CONVERSION English/Metric Units of Capacity: 16 ounces (oz) = 1 pint (pt) 2 pints (pt) = 1 quart (qt) 4 quarts (qt) = 1 gallon (gal) 1 gallon (gal) = 231 cubic inches (cu in) 7.5 gallons (gal) = 1 cubic foot (cu ft) 1,000 milliliters (mL) = 1 liter (L) 1 milliliter (mL) = 1 cubic centimeter (cu cm) 1,000 liters (L) = 1 cubic meter (cu m)

CUSTOMARY UNITS OF WEIGHT CONVERSION English/Metric Units of Weight: 16 ounces (oz) = 1 pound (lbs) 2,000 pounds (lbs) = 1 short ton 2,240 pounds (lbs) = 1 long ton 1,000 milligram (mg) = 1 gram (g) 1,000 grams (g) = 1 kilogram (kg) 1,000 kilograms (kg) = 1 metric ton

CAPACITY/WEIGHT CONVERSIONS Example: How many ounces of solution are contained in a container when full? Since 16 oz = 1 pt and 2 pt = 1 qt, there are 16 × 2 or 32 oz in 1 qt Multiply

COMPOUND UNITS Products or quotients of two or more basic units such as mi/hr or lb/sq in Unity fractions used to convert compound units by placing units on opposite sides of fraction so that they cancel out

COMPOUND UNITS Example: Express 0.283 tons per square foot as pounds per square inch Multiply by the unity fractions

PRACTICE PROBLEMS How many strips, each having an area of 36 square inches, can be sheared from a sheet of aluminum that measures 6 square feet?

PRACTICE PROBLEMS Convert square feet to square inches Divide to determine the number of strips 864 sq in ÷ 36 sq in = 24 A total of 24 strips can be sheared from the sheet of aluminum