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 Combined Science specification (1SC0). Being confident with units and conversions is essential for every physics calculation you will meet in your exams.

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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, but at GCSE Combined Science level you need to work comfortably with five of them.

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.
• The second (s) is the SI unit of time — not the minute or hour.
• The kelvin (K) is the SI unit of temperature. To convert: $$K = °C + 273$$

Exam Tip: In the Combined Science exam you will most often use metres, kilograms, seconds and amperes. Always check the units given in the question and convert to SI base units before substituting into an equation.

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Derived Units

Derived units are built from combinations of base units. You will use these throughout the physics papers.

Quantity	Derived Unit	Symbol	In Base Units
Force	newton	N	kg m/s²
Energy	joule	J	kg m²/s²
Power	watt	W	J/s = kg m²/s³
Pressure	pascal	Pa	N/m² = kg/(m s²)
Frequency	hertz	Hz	s⁻¹
Charge	coulomb	C	A s
Potential difference	volt	V	J/C
Resistance	ohm	Ω	V/A

Understanding Derived Units

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

Exam Tip: One of the most common errors in GCSE exams is giving an answer with the wrong unit or no unit at all. Always write the unit alongside your numerical answer.

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Unit Prefixes

Prefixes are placed before a unit to indicate a multiple or fraction of that unit.

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

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Converting Between Units

When performing calculations you must convert all values to SI base units before substituting into an equation.

• 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 × 1000 = 4500 m

Example 2: Convert 250 g to kilograms.

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

Example 3: Convert 0.035 A to milliamps.

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

Example 4: Convert 2.4 MJ to joules.

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

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

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Standard Form

Standard form (scientific notation) is used to write very large or very small numbers:

$$A \times 10^n$$

where 1 ≤ A < 10 and n is an integer.

Ordinary Number	Standard Form
300 000 000 m/s	3.0 × 10⁸ m/s
0.000 001 m	1.0 × 10⁻⁶ m
6 400 000 m	6.4 × 10⁶ m
0.000 000 32 s	3.2 × 10⁻⁷ s

Worked Examples

Example 5: Write 47 000 in standard form.

• Move the decimal point so the number is between 1 and 10: 4.7
• Count how many places you moved it: 4 places to the left
• Answer: 4.7 × 10⁴

Example 6: Write 0.000 056 in standard form.

• Move the decimal: 5.6
• Count places moved: 5 places to the right (negative index)
• Answer: 5.6 × 10⁻⁵

Calculating with Standard Form

Example 7: Calculate (3 × 10⁴) × (2 × 10³).

• Multiply the numbers: 3 × 2 = 6
• Add the powers: 4 + 3 = 7
• Answer: 6 × 10⁷

Example 8: Calculate (8 × 10⁶) ÷ (4 × 10²).

• Divide the numbers: 8 ÷ 4 = 2
• Subtract the powers: 6 − 2 = 4
• Answer: 2 × 10⁴

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Significant Figures and Rounding

In physics calculations, you should give your answer to the same number of significant figures as the data in the question, or to 2–3 significant figures as a general rule.

Rules for Significant Figures

• All non-zero digits are significant: 345 has 3 s.f.
• Zeros between non-zero digits are significant: 3045 has 4 s.f.
• Leading zeros are not significant: 0.0045 has 2 s.f.
• Trailing zeros after a decimal point are significant: 3.40 has 3 s.f.

Example 9: Round 0.04567 to 2 significant figures.

• The first significant figure is 4, the second is 5.
• Answer: 0.046 (round up because the next digit is 6).

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Summary

• The SI system provides the standard units for scientific measurement.
• The five base units you use most at GCSE are: 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) scale units up or down by powers of 10.
• Always convert to SI base units before substituting into equations.
• Use standard form for very large or very small numbers: A × 10ⁿ where 1 ≤ A < 10.
• Give answers to an appropriate number of significant figures.