About Measurement

How do you choose the right unit for measurement?

There are myriad units for measuring, such as inches, ounces, hours, cups, kilometers, amps, and bushels. Some units are products of two measures such as foot-pounds. Other units are ratios of two measures such as miles per hour, threads per inch, dollars per gallon, people per square mile, and furlongs per fortnight.

Because there are so many units of measurement to choose from, it is important that we know how to choose the appropriate unit to use for a particular measurement. One thing we must consider in choosing a unit to measure length, area, or volume is the number of dimensions the item being measured has. The measurement unit must have the same number of dimensions as the item. For instance, area of a rectangle uses two dimensions: length and width, so it needs a two-dimensional measurement unit, such as square centimeters.

Length

Length is 1 dimension. Some of the common units used to measure length are inches, miles, centimeters, meters, feet, kilometers, yards, and millimeters.

Area

Area has 2 dimensions (length and width). Some of the common units used to measure area are square inches, square miles, square centimeters, square meters, square feet, square kilometers, square yards, and square millimeters.

Volume

Volume has 3 dimensions (length, width, and height). Some of the common units used to measure volume are cubic inches, cubic miles, cubic centimeters, cubic meters, cubic feet, cubic kilometers, cubic yards, and cubic millimeters.

How do you convert from one unit of measure to another?

There are a number of ways to convert between units. One common method of conversion is called unit analysis. This process uses ratios and the cancellation properties evidenced in fraction multiplication. Simply put, unit analysis is nothing more than multiplication by forms of the number 1. Multiplying a quantity by 1 does not change its value, so we repeatedly multiply our original quantity by ratios, each of which is equivalent to 1. We select the particular ratios to use in such a way that the undesired units will appear in both the  numerator and denominator and cancel, leaving us with a string of numbers which we can then multiply. To perform unit analysis, you will need to know some unit equivalents.

Unit Equivalents

1 mile = 5,280 feet

1 meter = 100 centimeters

1 quart = 4 cups

1 yard = 3 feet

1 kilometer = 1,000 meters

1 cup = 8 ounces

1 foot = 12 inches

1 kilogram = 1,000 grams

1 ounce = 2 tablespoons

1 inch = 2.54 centimeters

1 gallon = 4 quarts

1 tablespoon = 3 teaspoons

Converting Units

What is 25 miles per hour converted to centimeters per second?

Convert the units using ratios of equivalent quantities. Because we set up each ratio so that it is equal to one, the amount being measured will stay the same, only the standard by which we quantify that amount will change. Keep your eye on reducing the units so that you end with your goal of centimeters per second.

Multiplying the fractions together will converts 25 miles per hour to 1,117.6 centimeters per second.

Review of New Vocabulary and Concepts

• measurement unit must have the same number of dimensions as the quality being measured.
• The unit of measurement can be converted by multiplying the measurement by ratios of equivalent units and reducing those units, just as you do in fraction multiplication.