1 ESO - UNIT 06 - THE METRIC SYSTEM AND THE IMPERIAL UNITS

1. Unit 06 February
1. THE METRIC SYSTEM.
In our everyday life we Measure many things. Measurement gives an indication
of the size of a Quantity. The more common types of measurement are:
The Metric System, also known as the Système International d’Unités (SI), was
developed in the late 1700s to standardize units of measurement in Europe. It is the
official system in almost every country in the world.
The United States is the only industrialized country that has not adopted the
metric system as its official system of measurement. Although the United Kingdom
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uses the metric system for most official purposes, the use of the Imperial System of
measure is widespread. At the end of the unit, we will learn more about the imperial
units.
The simplicity of the Metric System stems from the fact that there is only one
Unit of measurement (or Base Unit) for each type of quantity measured (length, mass,
etc.).
The three most common base units in the metric system are the Metre, the
Gram, and the Litre. With these simple measurements we can measure nearly
everything in the world.
But what if we want to talk about really big or really small objects? The
measurement of very large and very small objects is expressed as Multiples of Ten of
the base unit.
1.1. METRIC NUMBERS.
In the Metric System we use Metric Number Prefixes like ‘kilo’ (a thousand),
‘milli’ (one thousandth) and so on. The table below shows the prefixes used for talking
about big and small numbers.
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The doctor wants you to take 15 thousandths of a litre of medicine (a
thousandth is one thousand times smaller), he is more likely to say ‘take 15 millilitres?
or write it down as 15 ml.
1.2. CONVERTING UNITS.
The Metric System is called a Decimal-Based System because it is based on
multiples of ten. Any measurement given in one metric unit can be converted to
another metric unit in a simple way.
This is the metric conversion ladder:
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For every step upward on the ladder you are dividing by 10 or moving the
decimal one place to the left. When you move down the ladder you are multiplying by
10 for each step or moving the decimal one place to the right.
4.3 𝑘𝑘𝑘𝑘 = 4,300 𝑔𝑔
4.3 𝑔𝑔 = 0.0043 𝑘𝑘𝑘𝑘
MATH VOCABULARY: Metric System, Imperial Systems, Base Unit, Metre, Meter, Litre,
Liter, Gram, Multiples of Ten, Metric Number Prefixes, Metric Ladder.
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2. LENGTH MEASUREMENT.
Length is a measure of distance. You can measure how long things are, or how
tall, or how far apart they are. Those are all examples of length measurements.
The base unit for length is the Metre. One metre is one ten-millionth of the
distance from the Earth’s equator to the North Pole. The most common length
measurements are Millimetres, Centimetres, Metres and Kilometres. To calculate one
distance from other we use the metric system ladder as above.
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There are many instruments which are used for measuring. They usually have a
Scale marked on them. We are all familiar with a ruler for measuring lengths. Rulers
have a scale marked in both millimetres and centimetres.
2.1. COMPLEX AND NO-COMPLEX FORM.
When we have a quantity expressed in several units, we say the quantity is in
Complex Form. When we have only one unit we say the quantity is in No-Complex
Form.
2 𝑚𝑚 5 𝑑𝑑𝑑𝑑 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 → 2.5 𝑚𝑚 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 𝑁𝑁𝑁𝑁 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹
2.2. VERY SMALL LENGTH QUANTITIES.
There are quantities very small:
• Micron:
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• Nanometer:
• Angstrom:
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2.3. VERY LARGE LENGTH QUANTITIES.
There are also quantities very large:
• Astronomical Unit:
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• Light Year:
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• Parsec:
MATH VOCABULARY: Length, Distance, Millimetres, Centimetres, Kilometres, Scale,
Ruler, Complex Form, Micron, Nanometer, Angstrom, Astronomical Unit, Light Year,
Parsec.
3. VOLUME AND CAPACITY MEASUREMENTS.
Volume and Capacity are very similar terms. The word Capacity is usually used
when referring to either a liquid or gas. The Capacity of a container is a measure of the
amount of fluid it can contain. The units for capacity are closely related to those of
volume.
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The most commonly used units of capacity are Liter (L) and milliliter (mL). For
larger capacities such as reservoirs and swimming pools, the units of kiloliter (kL) and
megaliter (ML) are used. But sometimes we use Volume measurements for larger
capacities.
The unit of Volume is 1 m3
(Cubic metre). It is a cube that is 1 metre on each side.
Volume is the amount of space a 3-D shape or substance occupies or contains.
We can also use complex and no-complex form to write a capacity or a volume
quantity.
MATH VOCABULARY: Volume, Capacity, Liquid, Gas, Amount, To Measure, To Contain,
Cubic Metre, Shape.
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4. MASS MEASUREMENT.
The Mass of an object is the amount of matter it contains. In everyday use the
terms Mass and Weight are interchanged. In fact, they have different meaning. The
Mass of an object is constant; it is the same no matter where the object is. In contrast,
the Weight of an object is the force upon it due to gravity. For this reason, an object
will have less weight on the moon than on the earth although the mass remains the
same.
The Kilogram (kg) is the base unit of mass in the metric system. Other units of
mass which are commonly used are the milligram (mg), gram (g), and tonne (t). 500 kg
are also called “quintal”.
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We can also use complex and no-complex form to write a mass quantity.
MATH VOCABULARY: Mass, Weight, Tonne.
5. AREA MEASUREMENT.
In any house or apartment there are Surfaces such as carpets, walls, ceilings,
and shelves. These surfaces have Boundaries which define the Shape of the surface.
Area is the amount of surface inside a region. The Area of a closed figure, no matter
what shape, is the number of Square Units (unit2
or u2
) it encloses.
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In the Metric System, the units of measurement used for area are related to
the units we use for length. The base unit for area is the Square Metre. A Square
Metre is the area of a square that is 1 m on each side.
Multiples and divisors of the square meter are shown in the following table:
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5.1. OTHER AREA MEASUREMENTS.
• A Hectare (ha) is an area equal to a square that is 100 metres on each side.
Hectares and square hectometres are the same.
• “Fanega” is a special Spaniard measurement for seed.
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𝟏𝟏 𝒇𝒇𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 = 𝟏𝟏𝟐𝟐 𝒄𝒄𝒆𝒆𝒆𝒆𝒆𝒆 𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆𝒆 = 𝟓𝟓𝟓𝟓, 𝟓𝟓 𝒍𝒍𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊
• “Yugada” is a special Spaniard measurement for seeing how much surface we
have worked in agriculture. It is the quantity of surface that workers seed or
work in a day or a week using a couple of oxen.
MATH VOCABULARY: Area, Surface, Boundaries, Square Metre, Hectare.
6. IMPERIAL UNITS.
The Imperial Units are an irregularly Standardized System of units that have
been used in the United Kingdom and its former colonies, including the
Commonwealth countries. The Imperial system is also called the British System. It is
the primary alternative to the metric system.
Today the Imperial units are widely used only in the United States, under the
name of the U.S. Customary Units (and in some cases with different definitions). They
have been replaced elsewhere by the SI (metric) system. Most Commonwealth
countries have switched entirely to the SI system of units. The United Kingdom
completed its legal transition to SI units in 1995, but a few such units are still in official
use: for example, draught beer must still be sold in Pints; most road sign distances are
still in Yards and Miles, and speed limits are in Miles per Hour.
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The use of SI units is increasingly mandated by law for the retail sale of food
and other commodities, but most British people still use Imperial units in colloquial
discussion of distance (miles and yards), speed (miles per hour), weight (Stones and
Pounds), liquid (pints and Gallons) and height (Feet and Inches). British law requires all
cars to use miles.
In the United States, the adjective imperial is only used with those new units of
volume introduced in 1824, the imperial gallon and its subdivisions (pints, Fluid
Ounces) and multiples (Bushels, Barrels).
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Most Imperial units had the same names as the units that are still
predominantly used in the United States. Unfortunately, the detailed definitions
differed, and in some cases the differences are substantial. A further difference
between the systems in use in the two countries is that in cooking weights and
measures, much more use is made of volume measures (Cups and Spoons) in the US,
whereas in the UK quantities of dry ingredients are usually specified by weight; cup
and spoon measurements are sometimes given, but these are not the same as the US
standard cups and spoons.
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6.1. METRIC AND IMPERIAL CONVERSION.
MATH VOCABULARY: Imperial Unit, Irregular, Standardized System, Pint, Yards, Miles,
Miles per Hour, Stone, Pound, Gallon, Feet, Inches, Fluid Ounces, Bushels, Barrels, Cups,
Spoons, Ounce. Quart.
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