By Matt Holzapfel

This part of the Abridged Math Tools for Journalists Series will be focused on Chapters 9-12 of the book “Math Tools for Journalists” by Kathleen Woodruff Wickham.

## Chapter 9: Directional Measurements

What are directional measurements, you ask? Great question. Directional measurements are time problems, distance problems, rate problems. All of those problems you saw in middle school, they’re back. While checking the numbers in time, rate and distance problems usually involves just some basic math, it’s still important for reporters to double-check any numbers that will appear in their reporting.

When working with time, rate and distance problems, it is important to keep the units of measurement the same. The formulas are as follows: Distance = rate x time, Rate = Distance x Time, and Time = Distance/Rate. Other directional measurements include speed, velocity, acceleration, g-force, and momentum. While many people do not know the difference between the two, speed and velocity are **not** the same measurement. Speed measures how fast something is going, while velocity **also** indicates its direction.

The most useful of these measurements to a reporter is average speed, which is calculated by dividing the distance traveled by the time it took to get there. Ending velocity can be found by doing the following equation: (Acceleration x time)/Starting velocity. It is also important to know the difference between weight and mass for all of these equations. Mass is an object’s total amount of matter while weight is dependent on the gravitational force pulling the object towards Earth (or any other planet). Next is momentum, which is the force necessary to stop an object from moving. All moving objects have momentum, which is a product of mass and velocity (mass x velocity).

Practice Problems:

- Charlie drove for 2 hours at a constant speed of 65/mph. How far did Charlie travel?
- Considering the gravitational force of Earth and the gravitational force of the Moon, would an object have more mass on Earth or the Moon?

## Chapter 10: Area Measurements

Measurement statistics pop up in all kinds of news stories and knowing how to express measurements in an accurate, clear way is vital to good journalism. There are two ways to explain measurements, one is analogy (The casino is as big as a football field) and the other is with simple, accurate numbers (472 square feet). The perimeter is the total distance around the edge of a square or a rectangle and can be found simply by adding up the length of all the sides. The area is the number of unit squares that can be contained within a square or a rectangle and is found by multiplying an object’s length by its width. The radius of a circle is the distance from any point on the edge of the circle to the exact center. The circumference of a circle is the distance around the circle. It is the circle’s **perimeter**. The circumference can be found with the following formula: 2π x radius.

Practice Problems:

- A rectangle has one side with a length of 8 inches and another with a length of 10 inches. What is the perimeter of the rectangle? The area?
- An object has a perimeter of 56 inches, if the object is a square, what is the length of each side?

## Chapter 11: Volume Measurements

Volume measurements play a key role in many articles because they can be used to provide the public with invaluable information. How many tons of rock salt does a town need to handle a rough winter/ How much salt can each truck hold? All sorts of important details like these can add important context to articles. First, there are liquid measurements. Some of the most common liquid measurement conversions that one might need in the kitchen or elsewhere can be found to the right. To find the volume of a rectangular object (must be 3D), you multiply the length of the object by the width of the object by the height of the object. Some common units of measurement:

- Cord: A common measurement of firewood. 128 cubic feet when the wood is “neatly stacked in a line/row” = 1 cord
- Ton: There are three different types of tons, a short ton = 2,000 pounds, a long ton/a “British ton” = 2,240 pounds, and a metric ton = 1,000 kilograms (2,204.62 pounds)

Practice Problems:

- How many ounces are in 6 gallons? 10 gallons?
- How many milliliters are in a quart?

## Chapter 12: Metric System

In America, many people think the metric system is silly. This is either because they simply don’t understand it, or they just like their way of measuring things better, sometimes both. Unfortunately, basically the entire rest of the world uses the metric system, so as journalists we must have a good grasp of it. The international decimal-based metric system is based on multiples of 10, and every measurement uses standard language for each level (giga, mega, milli, micro, etc.) Once you learn the language, it becomes simple to use the metric system. Because the metric system is based on the decimal system, users can change from one unit to another by multiplying or dividing by 10, 100, 1,000 or other multiples of 10. Each unit is 10 times as large as the next smallest unit. The unit names are meter (length), gram (mass) and liter (volume).

Prefixes can create larger or smaller factors, the prefixes and their values are:

- 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
- Kilo 1,000
- Mega 1,000,000
- Giga 1,000,000,000
- Tera 1,000,000,000,000

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 find inches
- Centimeters by 0.4 to get inches
- Centimeters by 0.033 to get feet
- Meters by 39 to find inches
- Meters by 3.3 to find feet
- Meters by 1.1 to find yards
- Kilometers by 0.62 to find miles

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 American **mass measurements** to metric, multiply:

- Ounces by 28 to find grams
- Pounds by 0.45 to find kilograms
- Pounds by 0.07 to find stones
- Short tons by 0.9 to find metric tons

Practice Problems:

- 50 pounds is how many kilograms? Stones?
- Jimmy buys 20 acres of land, when his mom, who lives in England, asks him how much land he bought, he has to tell her using a unit of metric measurement, what should she tell her?

Answers to Practice Problems:

Chapter 9: 1. 130 miles 2. The problem cannot be solved with the given information. Mass doesn’t change based on a planet’s gravitational force, only weight does.

Chapter 10: 1. Perimeter = 36 Area = 80 2. 28 inches

Chapter 11: 1. 768 ounces and 1,280 ounces 2. 960 millileters

Chapter 12: 1. 22.5 kilograms and 3.5 stones 2. He should tell her that he bought 8 hectares of land