SI Units and Prefixes

This lesson covers the International System of Units (SI) and how to use unit prefixes and standard form — as required by the Edexcel GCSE Physics specification (1PH0), Topic 1: Key Concepts of Physics. You need to know the SI base units, common derived units, unit prefixes, and how to convert between them confidently.

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The SI Base Units

The SI system is the internationally agreed system of measurement used in science. There are seven base units from which all other units are derived. At GCSE level you need to be aware of these and use several of them regularly.

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

Key Points

• The kilogram (kg) is the SI unit of mass — not the gram. This is unusual because it already contains a prefix (kilo).
• The second (s) is the SI unit of time — not the minute or hour.
• The kelvin (K) is the SI unit of temperature — not degrees Celsius. However, at GCSE you will often use degrees Celsius (°C) in practice. To convert: K = °C + 273.

Exam Tip: You do not need to memorise all seven base units for the Edexcel GCSE exam, but you must be comfortable using metres, kilograms, seconds, amperes and kelvins in calculations.

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Derived Units

Derived units are combinations of base units used to measure other physical quantities. You will encounter these throughout your GCSE Physics course.

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 (= J/s)
Pressure	pascal	Pa	kg/(m s²) (= N/m²)
Frequency	hertz	Hz	1/s (= s⁻¹)
Charge	coulomb	C	A s
Potential difference	volt	V	kg m²/(A s³) (= J/C)
Resistance	ohm	Ω	kg m²/(A² s³) (= V/A)

Understanding Derived Units

Each derived unit can be broken down into base units. For example:

• 1 newton (N) is the force needed to accelerate a mass of 1 kg at 1 m/s². So 1 N = 1 kg m/s².
• 1 joule (J) is the energy transferred when a force of 1 N moves an object 1 m. So 1 J = 1 N m = 1 kg m²/s².
• 1 watt (W) is the rate of energy transfer of 1 joule per second. So 1 W = 1 J/s.

Exam Tip: You are not required to derive these units from scratch in the exam, but you must know what each unit measures and be able to use the correct unit in your answers. Losing a mark for an incorrect or missing unit is one of the most common errors.

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Unit Prefixes

Prefixes are placed before a unit to indicate a multiple or fraction of that unit. You must know the following prefixes and be able to convert between them.

Prefix	Symbol	Multiplier	Example
nano	n	10⁻⁹ (0.000 000 001)	1 nm = 1 × 10⁻⁹ m
micro	μ	10⁻⁶ (0.000 001)	1 μs = 1 × 10⁻⁶ s
milli	m	10⁻³ (0.001)	1 mm = 1 × 10⁻³ m
centi	c	10⁻² (0.01)	1 cm = 1 × 10⁻² m
kilo	k	10³ (1 000)	1 km = 1 × 10³ m
mega	M	10⁶ (1 000 000)	1 MHz = 1 × 10⁶ Hz
giga	G	10⁹ (1 000 000 000)	1 GW = 1 × 10⁹ W

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Converting Between Units

When performing physics calculations, you must convert all values to SI base units before substituting into an equation. Here is how to convert:

Converting to Larger or Smaller Units

• To convert from a smaller unit to a larger unit, divide.
• To convert from a larger unit to a smaller unit, multiply.

Worked Examples

Example 1: Convert 4.5 km to metres.

• 1 km = 1000 m
• 4.5 km = 4.5 × 1000 = 4500 m

Example 2: Convert 250 g to kilograms.

• 1 kg = 1000 g
• 250 g = 250 ÷ 1000 = 0.25 kg

Example 3: Convert 0.035 A to milliamps (mA).

• 1 A = 1000 mA
• 0.035 A = 0.035 × 1000 = 35 mA

Example 4: Convert 6700 mm to metres.

• 1 m = 1000 mm
• 6700 mm = 6700 ÷ 1000 = 6.7 m

Example 5: Convert 2.4 MJ to joules.

• 1 MJ = 1 × 10⁶ J
• 2.4 MJ = 2.4 × 10⁶ = 2 400 000 J

Exam Tip: The most common unit conversion error in GCSE Physics exams is forgetting to convert grams to kilograms, centimetres to metres, or milliamps to amps before using an equation. Always check your units before calculating.

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Standard Form

Standard form (also called scientific notation) is a way of writing very large or very small numbers. A number in standard form is written as:

A × 10ⁿ

where 1 ≤ A < 10 and n is an integer.

Examples of Standard Form

Ordinary Number	Standard Form
300 000 000 (speed of light in m/s)	3 × 10⁸
6 400 000 (radius of Earth in m)	6.4 × 10⁶
0.000 001 (1 micrometre in m)	1 × 10⁻⁶
0.000 000 000 1 (radius of an atom in m)	1 × 10⁻¹⁰
0.000 000 001 6 (charge on an electron in C)	1.6 × 10⁻¹⁹

How to Convert to Standard Form

1. Move the decimal point so that there is one non-zero digit before the decimal point.
2. Count how many places you moved the decimal point — this gives the power of 10.
3. If you moved the decimal point to the left, the power is positive.
4. If you moved the decimal point to the right, the power is negative.

Worked Example

Convert 0.000 045 m to standard form.

1. Move the decimal point 5 places to the right: 4.5
2. The power is negative (we moved right): −5
3. Answer: 4.5 × 10⁻⁵ m

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Using Standard Form in Calculations

When multiplying or dividing numbers in standard form:

• Multiplying: Multiply the numbers and add the powers.
  • (3 × 10⁴) × (2 × 10³) = 6 × 10⁷
• Dividing: Divide the numbers and subtract the powers.
  • (8 × 10⁶) ÷ (4 × 10²) = 2 × 10⁴

Worked Example

A wire has a cross-sectional area of 2.5 × 10⁻⁶ m² and a length of 3.0 × 10² m. Calculate the volume of the wire.

Volume = area × length Volume = (2.5 × 10⁻⁶) × (3.0 × 10²) Volume = (2.5 × 3.0) × 10⁻⁶⁺² = 7.5 × 10⁻⁴ m³

Exam Tip: Make sure you can use your calculator to enter numbers in standard form. On most scientific calculators, use the EXP or ×10ˣ button. Practise this so you do not make errors in the exam.

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Summary

• The SI system has seven base units — the most important for GCSE Physics are the metre (m), kilogram (kg), second (s), ampere (A), and kelvin (K).
• Derived units (N, J, W, Pa, Hz, C, V, Ω) are combinations of base units.
• Prefixes (nano, micro, milli, centi, kilo, mega, giga) multiply or divide a unit by powers of 10.
• Always convert to SI base units before substituting values into equations.
• Standard form writes numbers as A × 10ⁿ where 1 ≤ A < 10 — essential for very large or very small quantities in physics.
• Practise unit conversions and standard form calculations until they are automatic — these skills are tested across every topic in the course.

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Extended Worked Examples

Worked Example 1 — Converting a mass into SI base units

A pupil records the mass of a metal block as 450 g. They need to substitute this into the kinetic energy equation KE = ½mv².

1. Identify the SI base unit for mass — this is the kilogram (kg), not the gram.
2. Recall the prefix relationship: 1 g = 10⁻³ kg, so 450 g = 450 × 10⁻³ kg.
3. Convert to a single power of ten: 450 × 10⁻³ kg = 4.50 × 10⁻¹ kg = 0.45 kg.

Common mistake: Forgetting to convert before substitution. Using 450 in KE = ½ × 450 × v² gives an answer 1,000 times too large. Always convert to SI base units first.

Worked Example 2 — Combining prefixes and standard form

A radio wave has a frequency of 2.4 GHz. Express this in hertz using standard form.

• Recall: 1 GHz = 1 × 10⁹ Hz (giga = 10⁹).
• So 2.4 GHz = 2.4 × 10⁹ Hz.
• In standard form, the coefficient must satisfy 1 ≤ A < 10, and 2.4 does, so the answer is 2.4 × 10⁹ Hz.

Worked Example 3 — Converting between derived units

A light bulb is rated at 60 W. How much energy does it transfer in 5 minutes?

1. Use the correct derived unit relationship: 1 W = 1 J/s, so energy = power × time.
2. Convert time into SI base units: 5 minutes = 5 × 60 s = 300 s.
3. Calculate: E = 60 × 300 = 18,000 J = 1.8 × 10⁴ J.

Worked Example 4 — Converting a very small length

A virus has a diameter of 120 nm. Express this in metres in standard form, and give the answer to 2 significant figures.

• 1 nm = 1 × 10⁻⁹ m, so 120 nm = 120 × 10⁻⁹ m.
• Rewrite so 1 ≤ A < 10: 120 × 10⁻⁹ m = 1.20 × 10⁻⁷ m.
• To 2 sig. fig.: 1.2 × 10⁻⁷ m.

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Significant Figures and Precision

Physics answers should be given to an appropriate number of significant figures. As a rule of thumb, give your final answer to the same number of significant figures as the least precise value in the question — usually 2 or 3 at GCSE.

Raw value	2 sig. fig.	3 sig. fig.
0.003748	0.0037	0.00375
12,340	12,000	12,300
9.806	9.8	9.81

Exam Tip: Never quote a calculator display of 8 digits. Round sensibly. Writing 4.7619047 m/s loses marks; writing 4.76 m/s (or 4.8 m/s) gains them.

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Dimensional Analysis (a Useful Check)

Even at GCSE you can use dimensional analysis to check whether an equation is sensible. Both sides of any physics equation must have the same units.

• F = ma → units of F: kg × m/s² = kg m/s² = N ✓
• E = ½mv² → units: kg × (m/s)² = kg m²/s² = J ✓
• P = E/t → units: J/s = W ✓

If your calculation produces "kg/s²" for energy, you know something has gone wrong.

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Common-Mistake Callouts

Mistake 1: Writing "m" for mass when the unit is kilograms (kg). Physicists use m for the quantity mass and kg for the unit.

Mistake 2: Confusing the prefix milli (m = 10⁻³) with the base unit metre (m). Context matters — "mm" means millimetre, not "metre metre".

Mistake 3: Treating temperature conversion as a prefix. Kelvin and Celsius are offset (K = °C + 273), not multiplied.

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graph TD
    A[Quantity given] --> B{In SI base units?}
    B -->|Yes| C[Substitute into equation]
    B -->|No| D[Identify prefix]
    D --> E[Convert using power of ten]
    E --> C
    C --> F[Calculate]
    F --> G[Round to appropriate sig. figs.]
    G --> H[State answer with unit]
    style A fill:#2c3e50,color:#fff
    style B fill:#e67e22,color:#fff
    style C fill:#2980b9,color:#fff
    style D fill:#c0392b,color:#fff
    style E fill:#c0392b,color:#fff
    style F fill:#2980b9,color:#fff
    style G fill:#27ae60,color:#fff
    style H fill:#27ae60,color:#fff

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Answering at different grade levels

Grade 3–4 answer: "A kilogram is a unit of mass. Kilo means a thousand, so 1 kilogram is 1,000 grams. Milli means a thousandth."

Grade 5–6 answer: "Mass is measured in the SI base unit kilogram (kg). The prefix kilo represents 10³, so 1 kg = 10³ g. The prefix milli represents 10⁻³. To convert 450 g to kg, divide by 1,000 to get 0.45 kg."

Grade 7–9 answer: "Mass has the SI base unit kilogram (kg); the gram is a decimal sub-multiple formed using the prefix milli (10⁻³). To substitute a mass into a physics equation we must convert to the SI base unit. 450 g = 450 × 10⁻³ kg = 4.50 × 10⁻¹ kg in standard form to three significant figures. Using the wrong derived unit or missing a prefix conversion typically produces an answer out by a factor of a thousand, so dimensional analysis (checking that both sides of the equation balance after rearrangement) is a useful final check."

Edexcel alignment: This content is aligned with Edexcel GCSE Physics (1PH0) specification Topic 1 Key concepts of physics — specifically 1.1 Units and unit prefixes, 1.2 Equations and standard form, and 1.3 Converting quantities. Assessed on Paper 1 and Paper 2.