Math Tools Chapters 9-12
By Ryan Catanese

Directional Measurements

A mile is 5,280 feet while a nautical mile is 6,080 feet.  A knot is a measure of speed, one nautical mile per hour.  When working with time, rate, and distance problems, make sure to keep the units of measurement the same.  Distance = rate x time, Rate = distance / time, and Time = distance / rate.

Speed indicates how fast something is going, while the velocity also indicates the direction.  Average speed = distance / time.  Acceleration is the rate of change of the speed, acceleration = (ending velocity – starting velocity) / time.  In order to determine the ending velocity, (Acceleration x time) + starting velocity = ending velocity.

A g-force is a measure of acceleration, with one “g” represent the force of gravity on the Earth’s surface, or 32.2 feet per second per second.  For reference, a kick exerts about 300 g’s on a soccer ball.

Weight and mass are not the same.  Mass is a measure of amount wile weight is a measure of the force of gravity pulling on an object.  So, mass stays the same regardless of gravity, while the weight changes.

The decibel is a unit of measure for the intensity of sound.  One decibel is the softest sound detectable by the human ear, and the ears begin to hurt at 120 dB.

Question: If a boat is traveling at 20 knots, how many miles per hour is that?

Area Measurements

One way to express measurements is by analogy like “The casino is the size of a football field.”  The other way is with numbers.  The perimeter of an object = (2 x length) + (2 x width).  The area of a rectangle = length x width.  The area of a triangle = .5 base x height.  Area is expressed in a length measurement squared, like 1 square foot.

The circumference of a circle is 2(pi) x radius, while the area = (pi) x radius².

Question:  If a circular plot of land has a radius of 60 yards, how big, in area, is the circle?

Volume Measurements

Liquid Measurements:

2 tablespoons = 1 fluid ounce
½ pint = 8 ounces, one cup
2 pints (32 ounces) = 1 quart
4 quarts (128 ounces) = 1 gallon
1 U.S. standard barrel = 31.5 gallons
1 U.S. gallon = 4/5 Imperial gallons
British or Canadian Barrel = 36 Imperial gallons

For energy consumption, Wattage x time = energy consumed, in watt-hours.

Volume = length x width x height.

Firewood is sold in cords.  A cord is 128 cubic feet when the wood is stacked in a line.  A standard cord would be 8 feet long, 4 feet wide, and 4 feet high.

A short ton is 2,000 pounds.  A long ton, or a British town, is 2,240 pounds, and a metric ton is 1,000 kilograms, or 2,204.62 pounds.

Question:  How many teaspoons are in a U.S. standard barrel?

The Metric System

Everyone except America uses the metric system.  It is based on multiples of 10 (giga, mega, milli, micro, etc.).  The roots of the words are meters (length), grams (mass), and liters (volume).  Each prefix is 10 times bigger than the next smallest one.  So, a centimeter is 1/100 of a meter, a millimeter is 1/1000 of a meter, etc.

Basic metric conversions

Multiply inches by 25.4 to find millimeters or millimeters by .04 to get to inches.
Multiply feet by .3 to find meters or meters by 3.3 to get feet.
Multiply yards by .9 to find meters or meters by 1.1 to get feet.
Multiply miles by 1.6 to find kilometers or kilometers by .62 to get miles.
Multiply ounces by 28 to find grams or grams by .035 to get ounces.
Multiply pounds by .45 to find kilograms or kilograms by 2.2 to get pounds.
Multiply pounds by .7 to get stones.
Multiply short tons by .9 to find metric tons or metric tons by 1.1 to get short tons.
Multiply teaspoons by 5 to find milliliters.
Multiply fluid ounces by 30 to find milliliters or milliliters by .034 to find fluid ounces.
Multiply gallons by 3.8 to find liters or liters by .26 to get gallons.
Celsius = .56 x (Fahrenheit – 32)
Fahrenheit = (1.8 x Celsius) + 32