The International System of Units

The image shows the remains of a cubit, an instrument used in Ancient Egypt. A cubit measures a little over 50 cm. The base of the Great Pyramid of Giza has sides with a length of 440 cubits.

In the times of Ancient Egypt or the Roman Empire, there were many reasons to keep a stable measurement system. Trade between different regions made it necessary.

When a merchant in Rome closed a deal with a seller in Sicily, he or she needed to know that they were using the same units. Otherwise, there was no way to know if the deal was good... or very bad!

The field used in an American football game measures 100 yards.

How long is a yard?

Most countries in the world use the International System of Units. Only a few countries, like the United States or the United Kingdom, still use some units from other standardization systems.

A yard is a unit of length in the United States customary system. Other units from this system are the foot (30.48 cm), the pound (a little over 0.45 kg) or the gallon (3.78 L approximately).

Only Three Countries in the World (Officially) Still Use the Imperial System

The International System of Units (SI) was established in order to make understanding easier within the scientific community. Scientists from all over the world can share a common system and therefore avoid misunderstandings.

To find out more about the SI, watch this video

The SI consists of seven base quantities and their respective units.

All the others are called derived quantities and can be expressed in terms of the fundamental quantities.

Base quantities are the most basic. All the others are called derived quantities and can be calculated and expressed in terms of basic quantities.

Quantities		Units
Name	Symbol	Name	Symbol
Length	l	metre	m
Mass	m	kilogram	kg
Time	t	second	s
Temperature	T	kelvin	K
Current intensity	I	ampere	A
Luminous intensity	I_v	candela	cd
Amount of substance	n	mole	mol

The SI establishes which are the derived magnitudes and their units:

Sometimes the unit of the derived magnitude has a proper name, such as newton (N), which is the unit of force.
Other times we name the unit from its relation to units of fundamental magnitudes; for example, speed is measured in m/s.
Some magnitudes are also usually expressed in non-SI units. Thus, it is common to express speed in km/h.

Derived quantities and the International System
Quantity	Symbol	Unit	Other accepted units
Area	A	m²	ha (hectare) ; 1 ha = 10,000 m²
Volume	V	m³	L (dm³)
Density	d, $rho$	kg/m³	g/L
Speed	v	m/s	km/h
Acceleration	a	m/s²
Force	F	N (newton)	kgf
Pressure	P, p	Pa (pascal)	mmHg, atm
Energy	E	J (joule)	kWh

Read the following text.

Fragment of a trade manual written by a Venetian merchant in the XVI century

In Sarai (ancient city in the Mongol kingdom) all linen is sold by picho. And 100 pichi are equal to 118 braza in Venice.

Also, all silks are sold by mena. A mena is equal to 6 pounds 2 ounces, which is a minute in Venice.

What was a picho? What kind of unit was it? What magnitude did it measure?

Do some research

Make a list of measurement units used in the past, like the picho and braza from the fragment. Find out their corresponding magnitudes and equivalents in the International System (SI).

We will use that list in class.

Scientists often handle very large or very small quantities in relation to the basic unit. For example:

The size of some cells is 0.000003 m.
The distance from the Earth to the Sun is 149,597,870,700 m.

The International System also indicates the name and symbol of the multiples and submultiples that will facilitate their writing.

International System Prefixes
Factor	Prefix		Factor	Prefix
10¹⁵	peta	P	10^–15	femto	f
10¹²	tera	T	10^–12	pico	p
10⁹	giga	G	10^–9	nano	n
10⁶	mega	M	10^–6	micro	$normal mu$
10³	kilo	k	10^–3	mili	m
10²	hecto	h	10^–2	centi	c
10	deca	da	10^–1	deci	d

The quantities of the examples above can thus be expressed more simply:

The size of some cells is 3 nm.
The distance from the Earth to the Sun is 149.6 Gm.

Discuss

Do you think these multiples and submultiples were as useful or necessary in the times of the XIV century Venetian merchant?

Which are magnitudes, and which are units?

Magnitude

Unit

Match each magnitude with its corresponding SI unit.

Surface
Temperature
Luminous intensity
Speed
Length
Mass
Current intensity
Force
Time

newton
kelvin
metre per second
candela
metre
ampere
kilogram
second
square metre

Which of these are SI units?

Choose the right symbol in each case.

miligram
kilolitre
gigajoule
terametre
nanosecond
micronewton

Match each prefix to the corresponding multiplication factor. Look back to Frame 9 to review.

mega
kilo
mili
tera
deca
nano
centi
micro
giga

10³
10^-6
10
10^-3
10⁹
10^-2
10⁶
10^-9
10¹²

For this activity, you will need the list of measurement units you made at home. The list should include some units used in the past or in other parts of the world, as well as their corresponding equivalents in the International System.

You can go as far back in time as you want. If you want, you can find out what standardized units were used in Ancient Rome or Egypt.

Medieval market in the town of Chinchón.

In groups or individually, imagine you are merchants and need to sell your goods or services in a market:

Make your price list in the units chosen, calculate the equivalent in the International System.
Visit other stands in the market, see their goods, the units and how they compare to your offers.
Finally, discuss advantages and disadvantages of using only one units system.

Upload a document with the price list and the units chosen and the advantages and disadvantages of a standardized system of units like the SI.

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Homework

Egyptian cubit

A good deal gone bad

The map shows some of the trade routes in the Roman Empire. Imagine how chaotic trade could be without shared measurement units.

The longest yard

How long is a foot?