# Using the Metric System

## Introduction

The metric system is an internationally agreed system of units of measurement. It has been adopted as the official system of units in every country except for the United States, Myanmar, and Liberia. It was first developed in France in the 1790's and has undergone many refinements. The current refinement which was published in 1960 is called the "International System of Units" or "SI" for short.

The metric system is easy to learn and easy to use, largely because it is based on the decimal system and is rationally designed to be self-consistent and coherent.

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From its beginning, the main features of the metric system were the standard set of inter-related base units and a standard set of prefixes in powers of ten. These base units are used to derive larger and smaller units that replace a huge number of other units of measure in existence. Although the system was first developed for commercial use, the development of coherent units of measure made it particularly suitable for science and engineering.

Objectives

The objective of this course is for students to learn to use the metric system of units when taking, recording, communicating, or using measurements.

All students are welcome; this course is especially oriented toward United States students who may not have used the metric system often.

## Symbols and abbreviations

When unit names are shortened in SI, symbols are used, not abbreviations. The difference is that symbols are the same in every language whereas abbreviations change from language to language. Thus "kilometers per hour" is written as "km/h" in both English and Italian even though the Italian for "kilometers per hour" is "chilometri orari". In contrast, "Valued added tax" is abbreviated "VAT" in English, but in Italian, it is called "Imposta sul valore aggiunto" and is abbreviated as "IVA".

## Length

The meter ("metre" in UK English) is the basic unit of length. A meter stick, shown in the image to the right, is one meter long. The millimeter, one one-thousandth of a meter, is convenient when smaller lengths are measured. The kilometer, one thousand meters, is convenient when longer lengths are measured. Students may also encounter the centimeter, equivalent to 10 millimeter or 1/100 meter

The most common of these units and their associated symbols are shown in the following table:

Unit Symbol Equivalence
Millimeter mm 1/1,000 of a meter
Centimeter cm 1/100 of a meter
Meter m
Kilometer km 1,000 meters

Automobile speeds are typically measured in kilometers / hour.

### Assignment

1. Obtain measurement devices marked in millimeters. Download and use this millimeter scale if you prefer to use it instead of some other scale.
2. Obtain a meter stick, a measurement device one meter long often subdivided into millimeters.
3. Obtain a device with distances marked in units of kilometers to use in measuring longer distances. This may be the odometer of a car, a cyclometer on a bike or a device specifically made for measuring such distances.
4. Measure several objects you commonly encounter. Consider measuring your height, the dimensions of rooms where you live, the diameter of a tea cup or plate, the height of a table, the length of your thumb, the diameter of various coins, the thickness of various coins, the length of your house, the dimensions of some section of land, the length of the street you live on, the distance to a nearby house, store or school, etc.
5. Write down the measurements as you take them.
6. What units, millimeters, meters, or kilometers, are most convenient for each of the measurements you have taken?
7. Notice if your automobile speedometer includes markings in kilometers / hour (e.g. km/h) If so, notice the speed measured in these metric units as you travel.
8. Check the speed limits in the area where you live. If they are given in miles per hour (for example in the United Kingdom or the United States), convert them to kilometers per hour by multiplying them by 1.609.

## Area

The square meter is the basic unit of area. This is an area equivalent to a square measuring one meter on each side. Large areas, such as land areas, are measured in hectares. One hectare is 10,000 square meters. Larger areas are measured in square kilometers.

The most common of these units units and their associated symbols are shown in the following table:

Unit Symbol Equivalence
Square Meter m2
Hectare ha 10,000 m2
Square Kilometer km2 1,000,000 m2 or 100 ha

### Assignment

1. Use the measuring devices obtained for the previous assignment in this assignment.
2. Measure various areas you commonly encounter. This may include the floor size of various rooms in your house, the area of your front porch, the area of a driveway, a playground, a park, and various parcels of land. These may include land areas near where you live, work, or play.
3. Are square meters or hectares the more convenient units in each case?
4. Write down the measurements as you take them.
5. Look up the area of various parks, lakes, towns, cities, counties, states, or countries you are familiar with. Note how these are expressed in hectares or square kilometers.
6. Find out the dimensions of the playing area for your favourite sport. (Avoid golf.) This can be found in the rule book for the sport or in Wikipedia. Calculate the size of the playing area.

## Volume

The liter ("litre" in UK English) is the basic unit of volume. The milliliter, one thousandth of a liter, is convenient when smaller volumes are measured.

The most common of these units and their associated symbols are shown in the following table:

Unit Symbol Equivalence
Milliliter ml 1/1,000 liter
Liter L 1/1,000 cubic meter

### Assignment

1. Obtain a measurement device marked in milliliters. This may be a measuring cup used in baking or some other device.
2. Measure the volume of several objects you commonly encounter. Consider measuring a glass of water, a bottle of soda, or a spoonful of water.
3. Write down the measurements as you take them.
4. What units, milliliters, or liters are most convenient for each of the measurements you have taken?
5. Look on the labels of various liquids you have around the house. This might include beverages, cleaning fluids, lubricants, or other liquids. It might also include purchases of gasoline, heating oil, or other bulk liquids. Note how these volumes are expressed in milliliters or liters.

## Mass

The kilogram is the basic unit of mass. The gram, equal to 1/1000 of a kilogram is convenient when smaller masses are being measured. The tonne, equal to 1,000 kilogram is used for larger masses. The kilogram is defined as being equal to the mass of the International Prototype of the Kilogram, from which the US prototype shown in the figure on the right was derived.

The most common of these units and their associated symbols are shown in the following table:

Unit Symbol Equivalence
gram g 1/1,000 kilogram
kilogram kg
tonne t 1,000 kilogram

### Understanding Mass and Weight

In everyday usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. In scientific contexts, mass refers loosely to the amount of "matter" in an object, whereas weight refers to the force experienced by an object due to gravity. When an object's weight (its gravitational force) is expressed in "kilograms", this actually refers to the kilogram-force (kgf or kg-f), also known as the kilopond (kp). This distinction is commonly ignored, and informally it is acceptable to express weights in kilograms, even when kilopounds would be the correct units.

### Correspondence with Volumes

The metric system was originally designed so that one liter of water (at 0 °C) weighed exactly one kilogram. Also, one milliliter of water weighs one gram and one cubic meter of water weighs one metric tonne. This allows simple conversion from volume to mass of water and can be used to estimate the conversion for fluids with similar density. A 2 liter bottle of soda weighs approximately 2 kilograms (plus the weight of the container).

### Assignment

1. Obtain measurement devices, such as a postal scale, a kitchen scale and a bathroom scale marked in grams and kilograms.
2. Measure the weight of several objects you commonly encounter. Consider weighing a bottle of milk, a piece of fruit, a letter in an envelope, a small stone, and yourself.
3. Write down the measurements as you take them.
4. What units, grams, or kilograms are most convenient for each of the measurements you have taken?
5. Look on the labels of various food items you have around the house. This might include beverages, or packaged food items. Note how these weights are expressed in grams or kilograms.
6. Find out the weight of a litre of water. [Ans: It should be one kilogram].
7. Look up the mass of various brands of automobile. Also look up the mass of an elephant, of a cow, horse, sheep, chicken, hampster, mouse and of a bee. Check which masses are given in tonnes, kilograms, grams or milligrams.

## Prefixes

In the metric system, multiples and sub-multiples of units follow a decimal pattern. A common set of decimal-based prefixes that have the effect of multiplication or division by a power of ten are applied to units which are themselves too large or too small for practical use. We have seen examples of this where the prefix milli, as in milliliter refers to 1/1000 of a liter, and kilo as in kilometer refers to 1,000 meters.

Metric prefixes that are regularly used in electrical and IT environments are shown in the table on the right with those that are used for normal everyday purposes are underlined.

Metric prefixes in everyday use
Text Symbol Factor
tera T 1000000000000
giga G 1000000000
mega M 1000000
kilo k 1000
hecto h 100
deca da 10
(none) (none) 1
deci d 0.1
centi c 0.01
milli m 0.001
micro μ 0.000001
nano n 0.000000001
pico p 0.000000000001

## Temperature

For everyday purposes, temperature is measured in degrees Celsius, known in earlier years as degrees centigrade. From 1744 until 1954, 0 °C was defined as the freezing point of water and 100 °C was defined as the boiling point of water. For many scientific purposes, temperature is measured in kelvins. Zero kelvins is also known as absolute zero which is the lowest possible temperature that can be achieved. Kelvins and degrees Celsius are related by the relationship K = 273.15 + °C. Thus absolute zero is -273.15 °C and water freezes at 273.15 K.

Today a more precise definition based on quantum mechanics is used, but for all practical purposes the original definition holds.

Useful references to keep in mind are:

Reference Celsius Degrees
Melting Ice 0 °C
Room temperature ~20 °C
Normal Human Body Temperature 37 °C
Boiling Water (at sea level) 100 °C

### Assignment

1. Obtain a thermometer calibrated in degrees Celsius for use in this assignment.
2. Measure the temperature of several items you commonly encounter. Consider measuring the temperature of melting ice, a freezer, a refrigerator, outdoor temperature, warm water, soup, boiling water, your body temperature.
3. Write down the measurements as you take them.

## Time

The metric system has adopted the second as its unit of time. Although minutes, hours and days are not decimal multiples of seconds, they are classed as "Non-SI units accepted for use with the SI Units". The reason for this is that there was world-wide agreement about what these units of measurement meant.

### Assignment

1. Measure out a distance between two points on a sidewalk. If you are allowed to do so, make your own marks using chalk. If you make your own marks, they should be 20 metres apart. Measure how long it take for people to walk between the two marks using a stopwatch or the seconds hand on a watch . Work out their speed in metres per second.

## Electrical units

Did you know that electrical units are part of the metric system? The main electrical units are volts (V), amperes (A), watts (W) and ohms (Ω). They were all named after famous scientists. ("Ω", pronounced "omega", is the last letter in the Greek alphabet".)

### Assignment

1. Examine several batteries. See if you can find batteries that have "1.5 V" or "9 V" on them.
2. Look at the packaging of a new light bulb. Can you find out what voltage it uses (Usually 3 to 6 V on a torch, 12 V on motor car light bulbs and 115 V or 230 V on mains light bulbs.) Also see if you can find out how much power the bulb uses – the power is measured in watts.
3. With an adult's help, unplug a kettle, empty it and look for the manufacturer's label. See if you can find out how what voltage in needs (115 V in the United States, 230 V in the United kingdom). See if you can find out how much power it uses (between 1.5 and 3 kilowatts – symbol "kW")

## Other units of measure

The International System of Units, abbreviated SI, is the modern form of the metric system. It comprises a coherent system of units of measurement built on seven base units. It defines twenty-two named units, and includes many more unnamed coherent derived units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. (Twelve of these prefixes are listed above).

### Assignment

1. As you encounter units in the SI system beyond those covered above, learn the definitions of those additional units and practice using them.

## Interesting Facts

Here are several facts about the metric system that may interest you:

1. The symbols for metric units are the same in all languages. For example "kilometers per hour" is "Chilometro orario" in Italian, but road signs and car speedometers all over the world (including Italy), use the symbol "km/h" for "kilometres per hour".
2. The symbols for metric units that are named after people start with a capital letter such as "W" for watts, named after James Watt while units that were not named after people start with a small letter symbols such as "m" for "metres"
3. Because it is easy to confuse the number "1" and the lower case letter "l", the litre is an exception to the capital letter rule, so the symbol for "litres" is often written as "L". On April fool's day, 1978 Ken Woolmer of the University of Waterloo wrote a spoof article about "Claude Émile Jean-Baptiste Litre" after whom the litre said to have been was named. Many people were fooled by this joke.
4. The metre was originally meant to be 1/10,000,000 of the distance between the North Pole and the Equator. Although it ended up being 0.03% less than this amount, it is useful to remember that one quarter of the earth's circumference is about 10,000 km.
5. The kilogram was originally meant to be the mass of one litre of water at its maximum density (4°C). It ended up as being 0.003% too light, but for practical purposes, it is useful to remember that one litre of water has a mass of about one kilogram, that one cubic centimeter of water has a mas of about one gram and that one cubic meter of water has a mass of about one tonne (1000 kg).
6. It is important not to mix up upper case and lower case letters for metric prefixes. A "2 mW" (milliwatt) battery has enough power to operate a hearing aid (note – lower case "m" in "mW"), but a suburban train will require "2 MW" (megawatts) to operate (note – uppercase "M" in "MW"). There are 1,000,000,000 mW in one MW.

## Going Metric

To strengthen your understanding of the metric system, complete the following optional assignment.

### Optional Assignment

1. Read John Kasson’s Down Home Ye Olde Iowa Metric Cookbook.
2. Dispose of all measuring devices that use units that are not metric.
3. Replace them with measuring devices that use only metric units.
4. Only use metric units when expressing measurement information.