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Metric Units of Length
milli - means thousandth
1mm = 0.001m
1m=1,000mm

centi - means hundredth
1cm = 0.01m
1m = 100cm

kilo - means thousand
1km = 1,000m
1m = 0.001km
Metric Units of Mass and Capacity
Metric Units of Mass:
1kg = 1,000g
0.001 kg = 1g
1g = 1,000mg
0.001g = 1mg

Metric Units of Capacity
1kL = 1.000L
0.001 kL = 1L
1L = 1,000 mL
0.001L = 1mL
Converting Units in the Customary System
Length:
1foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 mile (mi) = 5,280 feet (ft)

Weight:
1 pound (lb) = 16 ounces (oz)

Liquid Capacity:
1 gallon (gal) = 4 quarts (qt)
1 quart = 2 pints (pt)
1 pint (pt) = 2 cups (c)
Converting Between Measurement Systems
Length:
1 in ≈ 2.54 cm
1 km ≈ 0.62mi
Area:
1 in² ≈ 6.45 cm²
Volume:
1 in³ ≈ 16.39 cm³
Capacity:
1 L ≈ 1.06 qt
Weight:
1 oz ≈ 28 g
1 kg ≈ 2.2 lb
Computing with Customary Measures
When you solve problems with customary units of measure, you must change the units of measurement.
Computing with Time
When you add or subtract units of time, you must convert between the units.
Perimeter
To find the perimeter of a given geometric figure, you add the lengths of the sides.
Example:
Find missing lengths.
8 - 7 = 1
4 - 1 = 3
x = 3 ft
3 + 3 = 6
8 - 6 = 2
y = 2 ft
8 + 7 + 3 + 3 + 2 + 4 + 3 + 8 = 38
Perimeter = 38 ft
Area of Rectangles and Squares
Area = Base x Height
The area is expressed in square + unit such as square inches (in²), square feet (ft²), or square centimeter (cm²).
Area of Triangle
Area = Base x Height ÷ 2
Area of Parallelograms
Area = Base x Height
Area of Trapezoids
Area = 1/2 Height x (Base 1 + Base 2)
Area of Compound Shapes
Circle
The diameter of a circle is the distance across the circle through its center.
The radius is the distance from the center to any point on the circle.
Circumference of the Circle
The perimeter of a circle is its circumference.
C = π (3.14) x Diameter
Area of Circle
Area = π x r²
Surface Area of Rectangular Prisms
Rectangular prisms has two of the same sizes facing each other.
Surface Area of Triangular Prisms
Triangular prisms has two of the same sizes for the top and the base. Find areas of the three rectangular shape sizes. Add them together.
Surface Area of Cylinders
1. Find areas of circle. A = π x r²
2. Multiply circle's area by two. (Top + Base)
3. Find area of rectangle.
Example:
Area of circle = 3.14 x 2² = 12.56
Area of circles = 12.56 x 2 =25.12
Base of rectangle = 3.14 x 4 =12.56
Area of rectangle = 12.56 x 5 = 62.80
Area of cylinder = 25.12 + 62.80 = 87.92 in²
Volume of Rectangular Prisms
V = Area of the Base x Height
V = 3 x 2 x 5 = 30m³
Volume of Triangular Prisms
Base = Triangle
Area of Triangle = (Base x Height) ÷ 2
Volume = Area of triangle x height
Volume of Cylinders
Base = Circle
Area of Circle = π x r²
Volume = Area of circle x height
Connecting Volume, Mass, and Capacity
Mass of Water
1 cm³ = 1 mL = 1 g
Example:
What is the mass of the water that the aquarium can hold?
Find the volume. 20 x 40 x 20 = 16,000 cm³
16,000 cm³ = 16,000 mL
16,000 mL = 16,000 g
16.000 g = 16 kg
The mass of the water the aquarium
will hold is 16 kg