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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)

### 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 = 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

Example: