Chapter 15 Measurement

Contemporary Measurement Systems

Measurement SystemsThere are two commonly used systems of measurement today: the U.S customary system and the metric system.

U.S. Customary System The U.S. Customary system of measurement is in many cases, difficult to work with because of the odd relations between the various units.

Primarily due to long the historical development of the system.

U.S. Customary System As we examine the table, we are unable to identify a clear and logical pattern of relations among the various units.

The growth of science and industry in the eighteenth century, however, required an efficient and convenient way to measure length, weight, and volume. The metric system of measurement was created.

Almost all countries of the world have adopted the metric system and made it the official system of measurement.

International System of units

The metric system has evolved over the decades and has been modified into what it is today.The metric system, called le system international d’unites, is known as SI.SI provides eighth basic units listed in the table below

The basic metric units are meters (for length), grams (for mass or weight), and liters (for volume). In elementary and middle school measurement, we commonly teach only length, capacity, mass, temperature, and time.

The basic unit of linear measurement (length) in the metric system is the meter

The other units of length in the metric system are related to the meter by powers of ten.The names of the units of length based on the meter are composed of two parts, the base meter and a prefix that indicates the relation of the unit to the meter

For example kilo is a prefix meaning “one thousand”

So the term kilometer designates a unit of length equal to one thousand meters

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ConversionBecause the units of the metric system are related in a simple and logical way by powers of ten, it is easy to change from one to another. We need only to multiply or divide by the appropriate power of ten.

You can convert between the various different sizes by merely moving the decimal point the correct number of places.

There are many metric-unit prefixes, but the usual ones required in school are these: kilo-, hecto-, deka-, deci-, centi-, and milli-. To convert between the various prefixes, and thus the variously-sized units, you just move up and down this list of prefixes, moving the decimal point as you go.

To remember the prefixes in order, you can use the following sentence:King Henry Doesn't [Usually] Drink Chocolate Milk

kilo-  hecto-  deka-  [unit]  deci-  centi-  milli-

Covert 12.5 Kilometers to Centimeters

How many jumps is it from “kilo” to “centi” Kilo- Hecta- deka- {unit} deci- centi- milli-

1 32 54

So I move the decimal point five places to the right, filling in the extra space with zeroes

Let’s Fill in the Decimal Points

1 2 5 4 0000

12.54 kilometers = 1,254,000 cm

Two farmhouses that are 1300 meters apart.Suppose we want to express this distance in kilometers. We know that 1000 meters is equal to 1 kilometer and that each meter is equal to of a kilometer. Therefore we can multiply 1300 by or (0.01) and obtain 1.3, which is the distance between the 2 farmhouses in kilometers.

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ConversionThe U.S. Customary system, however it is much more cumbersome to change units.

Suppose, for example, that 2 farmhouses are 1.3 miles apart and that we wish to express this distance in feet.

There are 5280 feet in one mile. So, we must multiply 1.3 by 5280 to find the distance in feet between the 2 farmhouses.

1 mile = 5280 feet1.3 miles = 1.3 5280 =6864 feet 5280 1.31584.4 (.3 ) 5280 (1 5280)6868.0

To convert 1.3 miles into 6864 feet we had to perform a three-step mathematical operation.

Converting one metric measure to another measure is a process that often requires only a minimal amount of mental mathematics.

Even though the conversion of measurement within a given system of measure is essential, conversion of measurement from system to a different system is not normally taught as part of the elementary school mathematics. Usually if a measure is given in metrics units, the calculating will also be done in metric measure.