Math Tools for Journalists Chapters 9-12 Summary
May 6, 2011
It is extremely important to understand different units of measure and how to calculate these measurements. Sometimes reporters have to convert units of measure to find accurate numbers. Here are a few conversions, units of measure and formulas from chapters 9-12 of Wickham’s book.
- Time, distance and rate: make sure to keep units of measurement the same.
Time = distance ÷ rate
Distance = rate x time
Rate = distance ÷ time
- Speed: measures how fast something is going. Speed and velocity are not the same measurement.
Acceleration = (ending velocity – starting velocity) ÷ time
–Instantaneous speed: how fast something is moving at that very second. For example, looking at a speedometer of a car will tell you how fast the car is going at a specific moment.
–Average speed: calculated by dividing the distance traveled by the time it took to got there. Another word for rate.
Average speed = distance ÷ time
- Velocity: indicates the direction something is going.
Ending velocity = (acceleration x time) ÷ starting velocity
- G-force: an acceleration measure. One “g” represents the normal force of gravity on Earth’s surface. Two “gs” represent 2 x 32.2 feet per second per second or 64.4 feet per second and so on. Acceleration produced by gravity is measured at 9.8 meters per second per second or 32.2 feet per second per second.
- Weight: a measure of the force of gravity pulling on an object, changes depending on where it is, which planet an object is on, measured in Newtons
- Mass: a measure of amount, remains the same regardless of gravity, measured in kilograms
- Momentum: the force necessary to stop an object from moving, the produce of mass and velocity, all moving objects have momentum
Momentum = mass x velocity
- Perimeter: the border or boundary of a two-dimensional figure, use the formula below if the object is a square or rectangle, if the object has an irregular shape add the lengths of all sides to determine the size of the perimeter
Perimeter = (2 x length) + (2 x width)
- Area of squares and rectangles: a particular space or surface of an object
Area of squares and rectangles = length x width
Area of triangles = .5 base x height
Note: use the shortest sides as base and height.
- Square feet and square yards: small spaces are measured in square inches or square feet. Large areas are measured in square feet, square yards and square rods. Fields and farms are measured in acres. Cities, states and counties are measured in square miles.
- Radius: the radius of a circle is the distance from any edge to the middle of the circle, knowing the radius is the key to finding the circumference
- Circumference: the circumference of a circle is the distance around the circle, or area of a circle
Circumference = 2π x radius
Area = π x radius2
- Liquid measurements: liquid measurements apply to liquid in recipes, bodies of water and other liquids
- Rectangular solid
Volume = length x width x height
- Cord: firewood is sold by a measurement called a cord, defined by 128 cubic feet when the wood is neatly stacked in a line or row. A standard cord would be a stack of wood 8 feet long, 4 feet wide and 4 feet high.
- Ton: there are three different types of tons.
-a short ton = 2,000 pounds
-a long ton (or British ton) = 2,240 pounds
–metric ton = 1,000 kilograms or 2,204.62 tons
- Meter/the metric system: the basic unit for length. Mass is also derived from the meter. One gram is the mass of one cubic centimeter of water at 0 degrees Celsius. The metric system is based on the decimal system. One unit to another can be changed by multiplying or dividing by 10, 100, 1,000 or other multiples of 10. Unit names are meter (length), gram (mass) and liter (volume).
-Newton: metric unit of force, one newton applied to a one-kilogram object will give the object an acceleration of one meter per second per second. The force of gravity is what gives objects weight, so the Newton can also be used as a measure of weight. One kilogram weights 9.8 Newtons on Earth.
-Prefixes: when added to a unit name they create larger or smaller factors.
micro (1 millionth) = 0.000001
milli (1 thousandth) = 0.001
centi (1 hundredth) = 0.01
deci (1 tenth) = 0.1
no prefix = 1.0
deka = 10
hecto = 100
kilo = 1,000
mega = 1,000,000
giga = 1,000,000,000
tera = 1,000,000,000,000
- Length: to convert American lengths to metric multiply
-inches by 25.4 to find millimeters or 2.5 to find centimeters
-feet by 30 to find centimeters or 0.3 to find meters
-yards by 90 to find centimeters or 0.9 to find meters
-miles by 1.6 to find kilometers
To convert metric lengths to American multiply:
-millimeters by 0.04 to get inches
-centimeters by 0.4 to get inches
-centimeters by 0.033 to get feet
-meters by 39 to get inches
-meters by 3.3 to get feet
-meters by 1.1 to get yards
-kilometers by 0.62 to get miles
- Area: to convert American area measurements to metric multiply:
-square inches by 6.5 to find square centimeters
-square feet by 0.09 to find square meters
-square yards by 0.8 to find square meters
-square miles by 2.6 to find square kilometers
-acres by 0.4 to find hectares
To convert metric measurements to American multiply:
-square centimeters by 0.16 to get square inches
-square meters by 11 to get square feet
-square meters by 1.2 to get square yards
-hectares by 2.5 to get acres
-square kilometers by 0.4 to get square miles
- Mass: to convert American mass measurements to metric multiply:
-ounces by 28 to get grams
-pounds by 0.45 to get kilograms
-pounds by .07 to get stones
-short tons (2,000 pounds) by 0.9 to get metric tons
To convert metric mass measurements to American multiply:
-grams by 0.035 to get ounces
-grams by 0.002 to get pounds
-kilograms by 35 to get ounces
-kilograms by 2.2 to get pounds
-metric tons by 1.1 to get tons
- Volume: to convert American volume measurements multiply:
-teaspoons by 5 to find milliliters
-tablespoons by 15 to find milliliters
-fluid ounces by 30 to find milliliters
-cups by 0.24 to find liters
-pints by 0.47 to find liters
-quarts by 0.95 to find liters
-gallons by 3.8 to find liters
-cubic feet by 0.03 to find cubic meters
-cubic yards by 0.76 to find cubic meters
To convert metric volume measurements to American multiply:
-milliliters by 0.034 to get fluid ounces
-milliliters by 0.002 to get pints
-liters by 2.1 to get pints
-liters by 1.06 to get quarts
-liters by 0.26 to get gallons
-cubic centimeters by 0.06 to get cubic inches
-cubic meters by 35 to get cubic feet
-cubic meters by 1.3 to get cubic yards
- Temperatures: to convert Fahrenheit to Celsius
Celsius = .56 x (Fahrenheit – 32)
To convert Celsius to Fahrenheit
Fahrenheit = (1.8 x Celsius) + 32
Some measurements and conversions:
- Mile = 5,280 feet
- Nautical mile = 6,080 feet
- Knot = one knot is one nautical mile per hour
- Acceleration of gravity = 9.8 meters per second per second or 32.2 feet per second per second
- Newton = equal to 0.225 lb. on Earth
- 144 square inches = 1 square foot
- 9 square feet = 1 square yard
- 30 square yards = 1 square rod
- 160 square rods = 1 acre
- 1 acre = 43,560 feet
- 640 acres = 1 square mile
- π or pi is rounded off to 3.14
- wattage x time = energy consumed in watt-hours
- ton conversions:
-short to long ton: multiply by .89
-short to metric ton: multiply by .9
-long to short ton: multiply by 1.12
-long to metric ton: multiply by 1.02
-metric to short ton: multiply by 1.1
-metric to long ton: multiply by .98
Some AP Style rules:
The National Institute of Standards and Technology suggests the news media use certain style rules.
- Units: the names of all units start with lowercase letters, except at the beginning of sentences and for degrees Celsius and degrees Fahrenheit.
- Symbols: unit symbols are written in lowercase letters except for liter and those derived from the name of a person or country (Ex. Newton, N)
- Prefixes: symbols of prefixes that mean a million or more are capitalized and those less than a million are in lowercase (Ex. M for mega, m for milli)
- Plurals: names of units are plural only when the numerical value that precedes them is more than 1 (Ex. 0.25 liter or 1/4 liter, but 250 milliliters), symbols for units are never pluralized
- Spacing: a space is used between number and symbol to which it refers (Ex. 7 m, 28 kg)
- Hyphen: when a metric value is used as a one-thought modifier before a noun, hyphenating the quantity isn’t necessary. But if a hyphen is used, write out the name of the metric quantity with the hyphens between the numeral and quantity.
Ex. a 2-liter bottle, but a 2 L bottle or a 78-millimeter film, but a 78 mm film
- Period: don’t use a period with metric unit names and symbols except at the end of a sentence
- Decimal point: the dot or period is used as the decimal point within numbers. In numbers less than one, zero should be written before the decimal point.
Mary Longwalker was taking a hike for 15 miles. If she walked five miles an hour for eight hours, how far did she hike?
5 miles/hour x 8 hours = 40 miles
So Longwalker hiked a distance of 40 miles.
Bobby Earl rides his bicycle all around town. He can pedal from zero to 30 miles per hour in two minutes. What is his rate of acceleration?
(30 mph – 0 mph) ÷ 2 minutes = 15 miles per hour per minute
So Bobby Earl’s bicycle increases in speed 15 miles every minute he pedals.
Michael Yoseph was driving a Jeep weighing 275 kilograms when it crashed into the median. What was the momentum of Yoseph’s Jeep as it hit the median if it was traveling 78 mph? Yoseph was injured, but survived the crash.
First, miles per hour need to be converted to kilometers per hour, so all the units of measure are metric.
78 mph x 1.6 = 124.8 kph
275 kilograms x 124.8 kilometers per hour = 34,320 kilogram kilometers per hour
Jilly Thomas wants to know the distance around her favorite swimming pool. The distance from the edge of the pool to the middle is 27 feet.
2π x 27 = 169.56 feet