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
1 ft
12 in
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
36 in
1 yd
Divide the numerator and denominator by the common factor, 1 yard
2.28 yd 
36 in
1 yd
  Ans  

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
1sq ft
144 sq in
728 sq in 
1sq ft
144 sq in

728 sq ft
144
 Ans

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
32
4
24;
3
4
 Ans

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
0.283 ton
1 sq ft

2,000 lb
1 ton

1 sq ft
144 sq in
 3.93 lb/sq in Ans

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