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: $K = °C + 273$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:

$A \times 10^n$A×10n

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.

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Extended Worked Examples and Rearrangement Practice

Most GCSE Combined Science marks are lost through poor unit handling rather than conceptual misunderstanding. The following worked examples build fluency with conversions, equation rearrangement and standard form arithmetic.

Example 10: Multi-step unit conversion

A wire has a diameter of 0.45 mm. Give its diameter in metres in standard form to 2 significant figures.

• Step 1 — convert: 1 mm = 1 × 10⁻³ m, so 0.45 mm = 0.45 × 10⁻³ m.
• Step 2 — convert to standard form: 0.45 × 10⁻³ = 4.5 × 10⁻⁴ m.
• Step 3 — check s.f.: 4.5 has 2 s.f., which matches the data.

Answer: 4.5 × 10⁻⁴ m.

Example 11: Rearranging W = mg

A satellite has a weight of 2.4 kN on Earth. Find its mass (g = 9.8 N/kg).

• Step 1 — convert: 2.4 kN = 2.4 × 10³ N = 2400 N.
• Step 2 — rearrange: $m = W / g$m=W/g.
• Step 3 — substitute: $m = 2400 / 9.8 = 244.9$m=2400/9.8=244.9 kg.
• Step 4 — round: 240 kg to 2 s.f.

Example 12: Combined prefixes and standard form

A current of 4.7 μA flows for 2.5 ms. Find the charge transferred (Q = It).

• Convert: I = 4.7 × 10⁻⁶ A; t = 2.5 × 10⁻³ s.
• Multiply: Q = (4.7 × 2.5) × 10⁻⁶⁻³ = 11.75 × 10⁻⁹ C.
• Re-express in standard form: 1.175 × 10⁻⁸ C.
• Round to 2 s.f.: 1.2 × 10⁻⁸ C (or 12 nC).

Common-mistake callout: Students often leave answers like 11.75 × 10⁻⁹. Although numerically correct, this is not standard form because the coefficient is not between 1 and 10. Always tidy up the mantissa.

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Comparison Table: Unit Conversions at a Glance

Given	To convert to SI base unit	Multiply by	Example
cm	m	10⁻²	45 cm = 0.45 m
mm	m	10⁻³	18 mm = 0.018 m
km	m	10³	3.2 km = 3200 m
g	kg	10⁻³	750 g = 0.75 kg
t (tonne)	kg	10³	1.5 t = 1500 kg
min	s	60	4 min = 240 s
h	s	3600	2 h = 7200 s
mA	A	10⁻³	350 mA = 0.35 A
kJ	J	10³	4.5 kJ = 4500 J
MJ	J	10⁶	2 MJ = 2 × 10⁶ J

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Mermaid Map: Choosing the Right Prefix

graph TD
    A[Is the number very large or very small?] --> B[Very large]
    A --> C[Very small]
    B --> D[Use kilo, mega or giga]
    C --> E[Use milli, micro or nano]
    D --> F[Then convert to standard form if a calculation follows]
    E --> F
    F --> G[Always end in SI base units before substituting]

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Significant Figures — Edge Cases

Number	Significant figures	Reason
0.0060	2	Leading zeros not significant; trailing zero after decimal is
1200	Ambiguous (2-4)	Write as 1.2 × 10³ or 1.20 × 10³ to make it clear
3.00 × 10⁴	3	All digits in mantissa count
0.700	3	Trailing zeros after decimal point are significant

Exam tip: If the question gives data to 3 s.f., your final answer should also be to 3 s.f. — not 2 and not 5. Carry extra digits through intermediate steps and round only at the end.

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Common-Mistake Callouts

• Forgetting to convert grams to kilograms before using $E_k = \tfrac{1}{2}mv^2$Ek​=21​mv2 or $F = ma$F=ma. A car mass written as 1200 must be in kg not g.
• Mixing prefixes: writing "kJ" when you meant "J", or treating kW and W as the same.
• Capital vs lowercase symbols: M (mega) ≠ m (milli). A 5 MΩ resistor is a million times larger than a 5 mΩ resistor.
• Standard form mantissa must satisfy 1 ≤ A < 10. "10 × 10⁵" should be rewritten as "1 × 10⁶".
• Giving an answer without a unit is worth zero marks in a "calculate" question.

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Answering at different grade levels

A grade 3–4 response identifies the quantity and picks a unit, often writing "the SI unit of force is newtons" without specifying that N is a derived unit built from the base units kg, m and s.

A grade 5–6 response uses correct prefixes and converts consistently to SI base units before substituting into an equation, and expresses very large or very small numbers in standard form with a mantissa between 1 and 10.

A grade 7–9 response explains that the kilogram is the SI base unit of mass (unusually containing a prefix), derives units such as the pascal (N/m² = kg m⁻¹ s⁻²) from base units, uses equation rearrangement fluently, reports answers to an appropriate number of significant figures, and distinguishes clearly between mass (a scalar in kg) and weight (a vector in N). Top-band students also justify the precision of the final answer in terms of the input data.

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Edexcel alignment: This content is aligned with Edexcel GCSE Combined Science (1SC0) Physics Topic 1 Key concepts of physics — specifically CP1 Units and unit prefixes, CP2 Equations and standard form, and CP3 Significant figures. Assessed on Physics Papers 1 and 2.