The International System of Units

If you travel to the United States, you may find posters like this one, asking to stay 6 feet apart from people to reduce the risk of covid contagion.

Is that more or less than the 2 metres recommended for physical distance in our country?

For some curiosities about the Imperial System of units, watch this video.

Research and discuss

Find out about the ship in the image and how many stadiums it could travel per hour. How does that compare to modern ships?

In the times of the ancient Romans, Greeks and Egyptians, the stadium was used as a sailing distance unit. But what the stadium measured was slightly different for each one of them.

The Roman stadium was 185 metres long, but the Greek one was around 192 metres. For the Egyptians, it was slightly smaller, with around 157 metres.

Greeks, Romans and Egyptians had trade relations, so the difference in their unit systems must have been a problem sometimes.

Using different units makes it difficult to compare values. This is why the International System of Units (SI) was established.

The SI sets the symbol of the units, multiples and submultiples, and establishes rules for writing them:

The symbol of the units is written in lower case unless it refers to the name of a person: m (metre), g (gram), N (newton).
The symbol of the multiples and fractions is written before the unit: km, cL, etc.
Symbols are never written in plural. So, to write eight kilometres, we use 8 km instead of 8 kms.

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

Derived quantities

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

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 $mu$ m.
The distance from the Earth to the Sun is 149.6 Gm.

In mass, length and capacity measurements:

To convert a quantity into the next multiple up, we divide it by 10. For example, 20 hg = 2 kg.

To convert a quantity into the next fraction down, we multiply it by 10. For example, 5 g = 50 dg.

We find the area of a surface by multiplying two lengths. They must be expressed with the same unit. For example:

5.40 m · 6.50 m = 35.1 m²

When we measure area:

To move to the next multiple up, we divide it by 100. For example, 500 cm² = 5 dm².
To move to the next fraction down, we multiply it by 100. For example, 3 m² = 300 dm².

Units of area are equal to the square of the units of length.

	Name	Symbol	Factor	Surface
Multiple	kilo	k	× 10⁶	km²
	hecto	h	× 10⁴	hm²
	deca	da	× 10²	dam²
Unit				m²
Fraction	deci	d	× 10⁻²	dm²
	centi	c	× 10⁻⁴	cm²
	mili	m	× 10⁻⁶	mm²

We find volume by multiplying three lengths. They must be expressed with the same unit. For example:

5.40 m · 6.50 m · 3 m = 105.3 m³

When we measure volume:

To move to the next multiple up, we divide it by 1000. For example, 4000 dm³ = 4 m³.
To move to the next fraction down, we multiply it by 1000. For example, 3 hm³ = 3000 dam³.

Units of volume correspond to the cube of the units of length.

	Name	Symbol	Factor	Surface
Multiple	kilo	k	× 10⁹	km³
	hecto	h	× 10⁶	hm³
	deca	da	× 10³	dam³
Unit				m³
Fraction	deci	d	× 10⁻³	dm³
	centi	c	× 10⁻⁶	cm³
	mili	m	× 10⁻⁹	mm³

Match each magnitude with its corresponding SI unit.

Surface
Temperature
Luminous intensity
Speed
Length
Mass
Current intensity
Force
Time

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

Which of these are SI units?

Choose the right symbol in each case.

miligram		gigajoule		nanosecond
kilolitre		terametre		micronewton

Match each prefix to the corresponding multiplication factor. Look back to Frame 6 to review.

mega
kilo
milli
tera
deca
nano
centi
micro
giga

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

Do the following transformations and select the correct answer for each one.

73 m³ → km³
73 dm² → cm²
0,73 dam² → cm²
73 km² → cm²
73 cm³ → hm³

73 · 10² cm²
73 · 10^-12 hm³
73 · 10^-9 km³
73 · 10⁴ cm²
73 · 10¹⁰ cm²

Put the following amounts in ascending order.

Summary. The International System of Units

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