You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
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.
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.
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 |
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
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.
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
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
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.
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.
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.