SI Units and Prefixes

Every measurement in physics has two parts: a numerical value and a unit. Saying "the mass is 5" means nothing without stating "5 kg." The international system of units — called SI (from the French Système International d'Unités) — provides a universal set of base units so that scientists everywhere can communicate results unambiguously. At GCSE level you must be confident converting between units and using standard prefixes.

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The Seven SI Base Units

The SI system is built on seven base quantities. Every other unit in physics (called a derived unit) can be expressed as a combination of these base units.

Base Quantity	SI Base Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

For GCSE Combined Science you mainly need the first five. Notice that the kilogram — not the gram — is the base unit for mass. This often catches students out in calculations.

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Derived Units

Derived units are combinations of base units. You should recognise the most common ones and be able to break them down.

Quantity	Derived Unit	Symbol	In Base Units
Force	newton	N	kg m/s²
Energy	joule	J	kg m²/s²
Power	watt	W	kg m²/s³
Pressure	pascal	Pa	kg/(m s²)
Frequency	hertz	Hz	1/s
Charge	coulomb	C	A s
Potential difference	volt	V	kg m²/(A s³)
Resistance	ohm	Ω	kg m²/(A² s³)
Speed	(no special name)	m/s	m/s
Acceleration	(no special name)	m/s²	m/s²

Worked Example 1 — Checking Units

Question: Show that the units of energy (J) are consistent with the equation E = ½mv².

Solution:

• Mass m is in kg
• Velocity v is in m/s
• v² is in m²/s²
• So ½mv² has units: kg × m²/s² = kg m²/s²

A joule is defined as kg m²/s², so the units are consistent. This technique — called dimensional analysis — is a powerful way to check your answers.

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SI Prefixes

Prefixes scale the base unit up or down by powers of ten. You must be able to convert fluently.

Prefix	Symbol	Multiplier	Power of 10
tera	T	1 000 000 000 000	10¹²
giga	G	1 000 000 000	10⁹
mega	M	1 000 000	10⁶
kilo	k	1 000	10³
(none)	—	1	10⁰
centi	c	0.01	10⁻²
milli	m	0.001	10⁻³
micro	μ	0.000 001	10⁻⁶
nano	n	0.000 000 001	10⁻⁹

flowchart LR
    A["nano (n)\n10⁻⁹"] -->|"×1000"| B["micro (μ)\n10⁻⁶"]
    B -->|"×1000"| C["milli (m)\n10⁻³"]
    C -->|"×1000"| D["(base unit)\n10⁰"]
    D -->|"×1000"| E["kilo (k)\n10³"]
    E -->|"×1000"| F["mega (M)\n10⁶"]
    F -->|"×1000"| G["giga (G)\n10⁹"]

Conversion Method

To convert from a prefixed unit to the base unit, multiply by the prefix value.

• 3.5 km = 3.5 × 10³ m = 3500 m
• 250 mA = 250 × 10⁻³ A = 0.25 A
• 47 μF = 47 × 10⁻⁶ F = 0.000047 F

To convert from a base unit to a prefixed unit, divide by the prefix value.

• 0.006 m = 0.006 ÷ 10⁻³ mm = 6 mm
• 4 500 000 J = 4 500 000 ÷ 10⁶ MJ = 4.5 MJ

Worked Example 2 — Multi-Step Conversion

Question: A wire is 2.4 km long and has a cross-sectional area of 0.50 mm². Convert both to SI base units.

Solution:

Length: 2.4 km = 2.4 × 10³ m = 2400 m

Area: 0.50 mm² — be careful here. 1 mm = 10⁻³ m, so 1 mm² = (10⁻³)² = 10⁻⁶ m²

0.50 mm² = 0.50 × 10⁻⁶ m² = 5.0 × 10⁻⁷ m²

Worked Example 3 — Energy Conversion

Question: A household uses 12 kWh of energy per day. Convert this to joules.

Solution:

1 kWh = 1000 W × 3600 s = 3 600 000 J = 3.6 × 10⁶ J

12 kWh = 12 × 3.6 × 10⁶ J = 4.32 × 10⁷ J = 43 200 000 J

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Standard Form (Scientific Notation)

Very large and very small numbers are written in standard form: a × 10ⁿ where 1 ≤ a < 10.

Value	Standard Form
300 000 000 m/s (speed of light)	3.0 × 10⁸ m/s
0.000 000 001 6 m (radius of atom)	1.6 × 10⁻⁹ m
6 400 000 m (radius of Earth)	6.4 × 10⁶ m
0.000 25 A	2.5 × 10⁻⁴ A

Calculating in Standard Form

When multiplying: multiply the numbers and add the powers.

(3.0 × 10⁸) × (2.0 × 10⁻³) = 6.0 × 10⁵

When dividing: divide the numbers and subtract the powers.

(8.0 × 10⁶) ÷ (4.0 × 10²) = 2.0 × 10⁴

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Worked Example 4 — Checking Units in an Equation

Question: The equation for pressure is P = F/A. Verify that the units of pressure (Pa) are consistent.

Solution:

Force F is in N = kg m/s². Area A is in m².

P = F/A has units: (kg m/s²) / m² = kg/(m s²) = kg m⁻¹ s⁻²

This matches the definition of a pascal (Pa). If your final answer does not have the correct units, there is an error in your working.

Worked Example 5 — Converting Between Prefixed Units

Question: A signal has a frequency of 2.4 GHz. Express this in (a) Hz, (b) MHz.

Solution:

(a) 2.4 GHz = 2.4 × 10⁹ Hz = 2 400 000 000 Hz

(b) 2.4 GHz = 2.4 × 10⁹ Hz ÷ 10⁶ = 2400 MHz

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Significant Figures and Rounding

At GCSE you are expected to give answers to an appropriate number of significant figures (s.f.) — usually the same as the least precise value given in the question.

Given Values	Appropriate s.f. for Answer
3.5 m, 2.1 s	2 s.f.
12.0 kg, 9.8 N/kg	2 or 3 s.f.
250 m, 60 s	2 s.f.

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Common GCSE Exam Mistakes

Mistake	Why It Happens	How to Avoid It
Using grams instead of kg in F = ma	Forgetting kg is the base unit	Always convert mass to kg first
Converting mm² or cm³ incorrectly	Squaring/cubing the conversion only once	Square or cube the linear conversion factor
Writing 3.5 × 10³ as 3500 then making arithmetic errors	Not staying in standard form	Keep numbers in standard form during calculations
Confusing M (mega, 10⁶) with m (milli, 10⁻³)	Both use the letter M	Capital M = mega; lowercase m = milli
Giving kWh when asked for joules	Not reading the question carefully	Check what unit the question demands
Rounding too early in multi-step calculations	Losing precision at intermediate steps	Keep full calculator display until the final answer, then round
Forgetting units in the final answer	Rushing	Always write the unit after your numerical answer

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Key Points

• The SI system has seven base units; length (m), mass (kg), time (s), current (A), and temperature (K) are the most important at GCSE.
• Derived units are combinations of base units — e.g., 1 N = 1 kg m/s².
• Prefixes allow you to write very large or very small numbers concisely — know them from nano (10⁻⁹) to giga (10⁹).
• When converting squared or cubed units, square or cube the conversion factor.
• Always convert to SI base units before substituting into equations.
• Use standard form for very large and very small numbers: a × 10ⁿ where 1 ≤ a < 10.
• Dimensional analysis (checking units) is a powerful way to verify your equations and answers.