Math Tools For Journalists #3

Summary of Chapters 9-12

By Hannah Williams

3.1 Directional Measurements

Journalists need to know how to calculate directional measurements to both check the math of their sources and enhance the understandability of their stories for their readers. This relatively simple math can add a lot of oomph to your reporting.

Three common calculations include distance (how far), rate (at what speed) and time (for how long).

Distance = rate ´ time

Rate = distance ¸ time

Time = distance ¸ rate

Make sure to use comparable units in your calculations, which may mean converting yards to miles or minutes to hours before you proceed.

Common distance, speed and time conversions:

	Miles/hour	Meter/second	Feet/second	Knots
Miles/hour	–	.447	1.47	.868
Meter/second	.0224	–	.0328	.0194
Feet/second	.0682	.305	–	.592
Knots	1.15	.515	1.69	–

To use the chart above from Math Tools for Journalists, multiply the figure in the unit of measure in the left column by the number in the column of the desired measure.

Speed is another word for rate and measures how fast an object is moving,  whereas velocity refers to how fast and in what direction.

If a car goes “from zero to 60 in less than 15 seconds” that is referring to its acceleration, rather than its speed.

Acceleration = (ending velocity – starting velocity) ¸ time

In cases where acceleration, starting velocity and time are know, i.e., car accidents, freefalls, etc., it may be  of interest to readers to calculate the ending speed.

Ending speed = Ö[2(acceleration ´ distance)]

Momentum is another useful measurement, as it indicated the force necessary to stop a moving object.

Momentum = mass ´ velocity

3.2 Area measurements

Only so many areas are “about the size of a football field,” and analogies can only go so far to convey how large (or small) an area is.  Sometimes its necessary to include the figures themselves for readers to best understand the space described.

The perimeter of an object is the sum of the lengths its sides. For a rectangular object, perimeter = 2 ´ length + 2 ´ width.

Area is the two-dimension space an object spans. For a rectangular object, area = length ´ width. For a triangular object use the two smallest sides, area = ½ base ´ height.

Usually, measurement of area will result in square units of some kind. The following is a common list of area conversions:

·      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 square feet

·      640 acres = 1 square mile

Not all objects have distinct measurable sides, and thus require unique formulae for measurements – a circle being one of them.

The radius of a circle is the distance from any point on its edge to the center. It is half of the diameter, or the distance from one side of the circle to the other. The radius is key to calculating all other measures of a circle.

The perimiter of a circle is its circumference = 2p ´ radius, where pi (p) = 3.14.

For a circle, area = p ´ radius².

3.3 Volume Measurements

 Volume measurements also play a large role in reporting specific figures, be it discussing food, fertilizer, fuel or floods.

Common liquid measurements can be used for any fluid.

·      2 tablespoons = 1 fluid ounce

·      ½ pint = 8 ounces = 1 cup

·      1 pint = 16 ounces = 2 cups

·      2 pints = 32 ounces = 1 quart

·      2 quarts = 64 ounces = ½ gallon

·      4 quarts = 128 ounces = 1 gallon

·      1 U.S. standard barrel = 31.5 gallons

·      1 U.S. gallon = 4/5 Imperial gallon

·      British or Canadian barrel = 36 Imperial gallons

·      Note: When used to reference crude oil on the international market, a barrel contains 42 U.S. gallons or 35 Imperial gallons

For a rectangular solid, volume = length ´ width ´ height.

Firewood is sold in cords, or 128 cubic feet when the wood is stacked neatly in a pile 8 feet long, 4 feet wide and 4 feet high.

A ton is a ton is a ton, right? Wrong. There are three types of tons as follows:

·      Short ton = 2,000 pounds

·      Long (British) ton = 2,240 pounds

·      Metric ton = 1,000 kilograms = 2,204.62 pounds.

3.4 Metric System

The metric system is actually much more logical than the English system of measurement and is based on multiples of 10. Thus, once learned, it is much easier to use.

The metric system’s core unit is the meter – a measure that equals one 10-millionth of the distance from the North Pole to the Equator.

The basic unit of metric mass, the gram, is also derived from the meter. One gram is the mass of one cubic centimeter of water at 0 degrees Celsius.

The metric unit of force is the Newton, which when applied to a one-kilogram object will accelerate the object one meter per second per second.

The basic metric unit names are meter (length), gram (mass) and liter (volume).

Adding prefixes adjusts the units by factors of 10. Basic prefixes are as follows:

·      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

The following are metric to English approximations:

·      1 meter (m) = 39.5 inches

·      1 kilometer(km) = 0.6 mile

·      1 square meter = 1.2 square yards

·      1 kilogram = 2.2 pounds

·      1 liter = 33.8 ounces > 1 quart

There are many online sites that aim to make metric to English conversion a mouse-click away. Try this one from Poseidon Software and Invention.

Temperature is also measured differently in the metric system – in degrees Celsius versus degrees Fahrenheit.

·      Celsius = .56 ´ (Fahrenheit -32)

·      Fahrenheit = (1.8 ´ Celsius) + 32

Using metric does not mean you can sacrifice style. The National Institute of Standards and Technology suggests the following style rules:

·      Capitals:

o   Units: use lowercase except at the beginning of a sentence or degrees Celsius.

o   Symbols: use lowercase unit symbols, except liters (L) and those derived from proper nouns, like a Newton (N).

o   Prefixes: use lowercase symbols for prefixes that mean less than a million and uppercase for those that mean a million or more.

·      Plurals: use plurals only when the preceding numerical value is more than one, with the exception of zero degrees Celsius; never use plurals for symbols.

·      Spacing: leave a space between the numerical figure and the unit or symbol, except when a numeral and unit are used as a hyphenated, compound modifier, and then replace the space with a hyphen.

·      Period: do not punctuate symbols.

·      Decimal points: use zero before a decimal point for numbers less than one.

Problems

2.1 If Elaine drove the 52.6 miles from Elon University to Raleigh Durham Airport in 45 minutes, what was her average speed? Was she likely speeding on I-40 where the speed limit is 65 mph?

a.     Rate = distance ¸ time = 52.6 ¸ 0.75 hour = 70.1 mph

b.     Yes, Elaine was likely speeding on I-40.

2.2 If your dorm room is 10 feet by 12 feet, how many square yards do you have on which to arrange your furniture?

a.     Area = length ´ width = 10 feet ´ 12 feet = 120 square feet ¸ 9 square feet/square yard = 13.3 square yards.

2.3 If your recipe calls for a quart of milk, but you’re halving it, how much milk do you need: in pints? In cups? In ounces?

a.     1 quart = 2 pints ´ ½ = 1 pint.

b.     1 pint ´  2 cups/pint = 2 cups.

c.      2 cups ´ 12 ounces/cup = 24 ounces.

2.4 If you are 5-foot-8-inches tall, how tall are you in centimeters?

a.     5 feet ´ 12 inches/foot = 60 inches + 8 inches = 68 inches

b.     68 inches ¸ 39.5 inches/meter = 1.72 meters ´ 100 centimeters/meter = 172 centimeters.