Unit Prefixes and Conversions

Physics deals with quantities of extraordinary range. The radius of a proton is of the order 10⁻¹⁵ m. The radius of the observable universe is about 10²⁶ m. That is forty-one orders of magnitude between the smallest and largest lengths an A-Level physicist must be comfortable with. To avoid writing strings of zeros — and to avoid losing track of powers of ten — physicists use SI prefixes.

This lesson covers every prefix on the OCR A-Level specification (from pico through tera), shows you how to convert between prefixed units reliably, and trains you to avoid the most common slips that cost students marks in calculation questions.

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Why Prefixes Matter

Consider the statement: "A typical capacitor in a radio tuner has a capacitance of 0.000000000047 farads." It is almost impossible to parse without counting zeros. With a prefix:

C = 47 pF (picofarads)

This is immediately understandable and much harder to miscopy. Prefixes make physics readable and robust.

The crucial skill, though, is not just recognising prefixes but converting them to base units before doing any algebra. Almost every calculation mistake in A-Level Physics involves either forgetting to convert a prefix or mis-converting one.

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The SI Prefix Table

You must memorise the following prefixes. OCR may ask you directly to state a prefix, its symbol and its multiplier — and you will use them in every calculation paper.

Prefix	Symbol	Multiplier	Decimal
tera	T	10¹²	1 000 000 000 000
giga	G	10⁹	1 000 000 000
mega	M	10⁶	1 000 000
kilo	k	10³	1 000
(none)	—	10⁰	1
centi	c	10⁻²	0.01
milli	m	10⁻³	0.001
micro	μ	10⁻⁶	0.000 001
nano	n	10⁻⁹	0.000 000 001
pico	p	10⁻¹²	0.000 000 000 001

Notation Notes

• kilo uses lower-case k (to distinguish from kelvin K).
• mega uses capital M (to distinguish from milli m).
• micro uses the Greek letter μ (lower-case mu). In ASCII typing it is sometimes written as "u": "uF" for microfarad. In written exam answers, use μ.
• giga is pronounced with a hard "g" in physics (GHz = "gig-a-hertz"), though you occasionally hear a soft "g".
• centi is not strictly part of the preferred SI prefixes but is ubiquitous in everyday life (centimetre, centilitre).

Worked Example 1 — Reading a Prefix

What does each of the following represent as a pure number in base units?

(a) 2.5 km (b) 47 μF (c) 3.2 nm (d) 8.0 MΩ (e) 650 nm (the wavelength of red light)

Solutions:

(a) 2.5 km = 2.5 × 10³ m = 2500 m (b) 47 μF = 47 × 10⁻⁶ F = 4.7 × 10⁻⁵ F (c) 3.2 nm = 3.2 × 10⁻⁹ m (d) 8.0 MΩ = 8.0 × 10⁶ Ω (e) 650 nm = 650 × 10⁻⁹ m = 6.5 × 10⁻⁷ m

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Rules for Converting Between Prefixed Units

When converting, ask yourself: "Am I going to a smaller unit or a bigger one?" If you are going to a smaller unit, the number gets bigger. If you are going to a bigger unit, the number gets smaller.

Rule 1 — Going from prefixed unit to base unit

Multiply by the prefix multiplier.

5.0 km → 5.0 × 10³ m → 5000 m 7.0 mA → 7.0 × 10⁻³ A → 0.007 A

Rule 2 — Going from base unit to prefixed unit

Divide by the prefix multiplier (equivalently, multiply by the reciprocal).

2 × 10⁻⁶ s → 2 × 10⁻⁶ / 10⁻⁶ μs → 2 μs 4.5 × 10⁹ Hz → 4.5 × 10⁹ / 10⁹ GHz → 4.5 GHz

Rule 3 — Converting directly between two prefixed units

Go via the base unit. Never try to convert directly — it nearly always introduces an error.

350 mm → ? μm

350 mm = 350 × 10⁻³ m = 0.350 m 0.350 m = 0.350 × 10⁶ μm = 3.5 × 10⁵ μm

Exam Tip: When in doubt, always convert to base units first, do the calculation, then convert back to the prefix the question asks for. This is slightly slower but dramatically safer.

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Worked Example 2 — Prefix Conversion in a Current Calculation

A capacitor of capacitance 220 μF is charged to a potential difference of 12 V. Calculate the charge stored.

Solution:

Q = CV

Convert C to base units:

C = 220 μF = 220 × 10⁻⁶ F = 2.2 × 10⁻⁴ F

Substitute:

Q = 2.2 × 10⁻⁴ × 12 = 2.64 × 10⁻³ C = 2.6 mC (2 s.f.)

If you had used "220" instead of "220 × 10⁻⁶", you would have found Q = 2640 C — equivalent to a household lightning strike. Always convert prefixes before substitution.

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Worked Example 3 — Area and Volume with Prefixes