Basic Math and Pre-Algebra

APPENDIX E. Measurement

 

Throughout this book, you’ve encountered units of measurement from both the customary and the metric system. This appendix covers the key information you need to function in each system and just a word or two about shifting from one to the other. In each system, you measure three basic quantities: length (or distance), mass (which, with gravity, determines weight), and volume.

 

Metric System

 

The metric system of measurement (also called the International System of Units) is used around the world, and its popularity likely stems not just from the idea of a universal system but from the consistent decimal logic of the system. Everything is based on tens. There are base units of length, mass, and capacity. The larger and smaller units are created by dividing a base unit by 10 or 100 or 1,000 (and so on) or by multiplying by 10 or 100 or 1,000 (and so on).

 

 

Basic Unit

Approximation

Official Definition

Length:

meter

The distance from a doorknob to the floor

The path length travelled by light in a given time

Mass:

gram*

The mass of a paperclip

The mass of one cubic centimeter of water at 4°C

Capacity:

liter

The volume of a mediumsized bottle of soda or water

The capacity of a container with a volume of 1,000 cubic centimeters

*The current standard defines the kilogram as the base unit and the gram as one one-thousandth of a kilogram, but the system is easier to understand if you begin with gram, the original base unit.

 

Notice that the units of length, mass, and capacity are linked. The liter is the capacity of a cube 10 centimeters wide by 10 centimeters long by 10 centimeters high, connecting length and volume to capacity. The gram is the mass of a cubic centimeter of water, which associates mass with volume and length and capacity.

From the basic units, you can break into smaller units or build into larger units, always multiplying or dividing by powers of ten. The naming of those units follows the same system of prefixes whether the base unit is meter, liter, or gram. Here are the prefixes and some ideas to help you imagine some of the commonly used units.

 

Smaller

1/1,000

milli-

Millimeter: approximately the thickness of 10 sheets of paper

Milligram: the mass of a grain of salt

Milliliter: about 20 drops of water

1/100

centi-

Centimeter: approximately the diameter of a pencil eraser, or the diameter of a AAA battery

Centigram: the approximate mass of a U.S. dollar bill, or about two raisins.

Centiliter: about half a teaspoon

1/10

deci-

Decimeter: approximately the length of a crayon

Decigram: two nickels

Deciliter: about one-fourth of a can of soda

Larger

10

deca-

(or deka-)

Decameter: a long bus or train car

Decagram: about half the mass of a small mouse

Decaliter: approximately the capacity of a teapot

100

hecto-

Hectometer: about a city block

Hectogram: the mass of an orange

Hectoliter: about the capacity of a small refrigerator

1,000

kilo-

Kilometer: about 2.5 laps on a stadium track

Kilogram: mass of a dictionary or large textbook

Kiloliter: the capacity of about eight large trash cans

 

When you’re changing units within a system, the thing to remember is balance. If you’re changing to a unit of a smaller size, you’ll have more of them. If your new unit is bigger, you’ll have fewer. And always, it’s about 10. Multiply by 10 if you’re going to a smaller unit, and divide by 10 to get to a bigger unit.

 

 

 

 

Base

 

 

 

1,000 millimeters

100 centimeters

10 decimeters

1 meter

0.1 decameter

0.01 hectometer

0.001 kilometer

1,000 milligrams

100 centigrams

10 decigrams

1 gram

0.1 decagram

0.01 hectogram

0.001 kilogram

1,000 milliliters

100 centiliters

10 deciliters

1 liter

0.1 decaliter

0.01 hectoliter

0.001 kiloliter

 

Customary System

 

What’s commonly called the customary system is a system that developed over time and remains popular in the U.S. and a few other spots around the world. It is very similar to the British imperial system, as both were derived from English units. The customary system was not designed as a unified system, so there are many different rules to remember.

 

Length

In the customary system, length is measured in units like inches, feet, yards, and miles.

 

Unit

Approximation

Conversion

Inch

From the knuckle to the tip of your thumb

 

Foot

The length of a large man’s foot

12 inches = 1 foot

Yard

The height of the kitchen counter

3 feet = 1 yard

Mile

A 20-minute walk

5,280 feet = 1,760 yards = 1 mile

 

Mass (Weight)

The customary system measures mass (but often calls it weight) in ounces, pounds, and, for really heavy things, tons.

 

Unit

Approximation

Conversion

Ounce

Ten pennies

 

Pound

A package of butter or bacon, or a football

16 ounces = 1 pound

Ton

A car

2,000 pounds = 1 ton

 

Capacity

The customary system uses ounce to measure capacity, but an ounce measured by capacity is not necessarily equivalent to an ounce of mass. If you have an ounce of something (capacity), whether it weighs an ounce or not depends on what it is.

 

Unit

Approximation

Conversion

Ounce

A little container of coffee cream

 

Cup

A container of coffee

8 ounces = 1 cup

Pint

A small container of ice cream

2 cups = 1 pint

Quart

A container of milk

2 pints = 1 quart

Gallon

A large can of paint

4 quarts = 1 gallon

 

Conversion

 

Although you may not often need to convert from one system of measurement to another, when you are, you may not have the tools or formulas handy to make an exact conversion. Here are some rules of thumb that can help you make an approximate conversion.

• An inch is about 2.5 centimeters.

• A meter is a little more than a yard. A meter is about 39 inches and a yard is 36 inches.

• A mile is about 1.6 kilometers.

• A liter is a little more than a quart.

• A kilogram is about 2.2 pounds.

 

WORLDLY WISDOM

A famous number sequence, called the Fibonacci sequence, is easy to re-create and can be used for quick, approximate conversions of length and distance. The Fibonacci sequence begins with two ones, then forms each of the next terms by adding the two previous terms.

1, 1, 1 + 1

1, 1, 2, 1 + 2

1, 1, 2, 3, 2 + 3

1, 1, 2, 3, 5, 8, 13, 21,...

Two adjacent terms of the Fibonacci sequence can give you a rough conversion of miles and kilometers. For example, 5 kilometers is approximately 3 miles, (3.10686 miles) and 8 kilometers is approximately 5 miles (4.97097).