Expressing Quantities & SI Units Notes

Q: What are SI units?

SI units are the standard units that scientists use so measurements can be compared worldwide. Every physical quantity has an SI unit, and your answer must include it.

Q: How do prefixes change a unit?

A prefix multiplies the unit by a power of ten, so you avoid long strings of zeros. 1 kilometre = 1000 m; 1 millimetre = 0.001 m.

Q: How do you convert between units?

Find the relationship between the two units, then multiply or divide by it. 1 hour = 60 min = 3600 s, so hours to seconds means multiply by 3600; seconds to hours means divide by 3600.

Q: How should numbers be written in physics?

Give answers to a sensible number of significant figures, and use standard form for very large or small numbers. Give answers to the same number of significant figures as the least precise data (usually 2 or 3).

Edexcel GCSE Physics: Revision notes

Key facts

Use SI units: metre (m), kilogram (kg), second (s), newton (N), joule (J), watt (W).
Always give the unit with a number; a correct number with no unit loses a mark.
Prefixes: kilo ×10³, mega ×10⁶, giga ×10⁹; milli ×10⁻³, micro ×10⁻⁶, nano ×10⁻⁹.
Hours to seconds: ×3600; km/h to m/s: ÷3.6.
Standard form is $A\times10^n$ with $1\le A<10$ .

SI units

SI units are the standard units that scientists use so measurements can be compared worldwide.

Every physical quantity has an SI unit, and your answer must include it.

For example: distance in metres (m), mass in kilograms (kg), time in seconds (s), energy in joules (J), power in watts (W).

1
Distance
metre (m)
2
Mass
kilogram (kg)
3
Time
second (s)
4
Force
newton (N)

SI base units used in physics.

Unit Symbol Distance metre m Mass kilogram kg Time second s Force newton N

	Unit	Symbol
Distance	metre	m
Mass	kilogram	kg
Time	second	s
Force	newton	N

Unit

Distance:: metre
Mass:: kilogram
Time:: second
Force:: newton

Symbol

Distance:: m
Mass:: kg
Time:: s
Force:: N

A student writes "the force is 12". What is missing?

Prefixes

A prefix multiplies the unit by a power of ten, so you avoid long strings of zeros.

1 kilometre = 1000 m; 1 millimetre = 0.001 m.

To convert, multiply or divide by the prefix's multiplier, then check the answer is sensible.

1
millimetre (mm)
1 mm = 0.001 m
2
metre (m)
base unit
3
kilometre (km)
1 km = 1000 m

Each step up the length ladder multiplies by 1000.

Symbol Multiplier giga G \times10⁹ mega M \times10⁶ kilo k \times10³ centi c \times10⁻²

	Symbol	Multiplier
giga	G	×10⁹
mega	M	×10⁶
kilo	k	×10³
centi	c	×10⁻²

Symbol

giga:: G
mega:: M
kilo:: k
centi:: c

Multiplier

giga:: ×10⁹
mega:: ×10⁶
kilo:: ×10³
centi:: ×10⁻²

Symbol Multiplier milli m \times10⁻³ micro µ \times10⁻⁶ nano n \times10⁻⁹

	Symbol	Multiplier
milli	m	×10⁻³
micro	µ	×10⁻⁶
nano	n	×10⁻⁹

Symbol

milli:: m
micro:: µ
nano:: n

Multiplier

milli:: ×10⁻³
micro:: ×10⁻⁶
nano:: ×10⁻⁹

Worked example

Convert 4500 mm into metres, and 0.35 MW into watts.

1
4500 × 10⁻³ = 4.5 m.
2
0.35 × 10⁶ = 350 000 W.

What is 5 ms in seconds?

Converting units

Find the relationship between the two units, then multiply or divide by it.

1 hour = 60 min = 3600 s, so hours to seconds means multiply by 3600; seconds to hours means divide by 3600.

For speeds, 1 km/h = $\dfrac{1000}{3600}$ m/s, so divide by 3.6 to go from km/h to m/s.

Converting speed from km/h to m/s: divide by 3.6, so 72 km/h is 20 m/s.

Hours to seconds× 3600
km/h to m/s÷ 3.6

Worked example

Convert 2.5 hours to seconds, and 72 km/h to m/s.

1
2.5 × 3600 = 9000 s.
2
72 ÷ 3.6 = 20.

How many seconds are in 15 minutes?

Standard form and sig figs

Give answers to a sensible number of significant figures, and use standard form for very large or small numbers.

Give answers to the same number of significant figures as the least precise data (usually 2 or 3).

Standard form is $A\times10^n$ with $1\le A<10$ and $n$ a whole number.

The speed of light, 300 000 000 m/s, is $3\times10^8$ m/s.

1
0.00045
start with the decimal
2
Move the decimal point 4 places right
gives 4.5, which is between 1 and 10
3
4.5 × 10⁻⁴
the power is negative because the number was small

Writing 0.00045 s in standard form.

Standard form $A\times10^n$ , with $1\le A<10$

Worked example

Write 0.00045 s in standard form and round 0.004567 m to 2 significant figures.

1
0.00045 = 4.5 × 10⁻⁴.
2
Significant figures start at the first non-zero digit: 0.0046.

Which is in standard form?

Try an exam question

(a) Convert 2.5 MW into watts. (b) Write 0.00032 s in standard form. (c) Convert 36 km/h into m/s.

[4 marks]

That's the notes covered.

Carry on to the next subtopic.