SI prefix
Physical Quantities & Units - OCR A-Level Physics
Key Definition
SI prefix
A symbol placed in front of a unit that multiplies the unit by a fixed power of ten. Prefixes turn unwieldy numbers like $0.000\,000\,001 \text{ s}$ into $1 \text{ ns}$. The prefix tells you the factor of ten by which the unit is multiplied.
A symbol placed in front of a unit that multiplies the unit by a fixed power of ten. Prefixes turn unwieldy numbers like $0.000\,000\,001 \text{ s}$ into $1 \text{ ns}$. The prefix tells you the factor of ten by which the unit is multiplied.
$$1 \text{ km} = 1 \times 10^{3} \text{ m} \qquad 1 \text{ ms} = 1 \times 10^{-3} \text{ s}$$
Diagram pending
A vertical SI prefix ladder from tera (top) down to femto (bottom). Each rung shows: prefix name, symbol, multiplying factor. Bigger-than-one prefixes (T, G, M, k) shaded purple; less-than-one prefixes (c, m, $\mu$, n, p, f) shaded teal. An arrow on the right labelled "$\times 10^{3}$ per step" between adjacent SI-standard rungs.
Will be replaced with a styled SVG ladder in stream 2.
- teraSI prefix meaning $10^{12}$. Symbol: T. ($\text{T}$) $= 10^{12}$. Example: $1 \text{ TJ}$ of energy released by a small earthquake.
- gigaSI prefix meaning $10^{9}$. Symbol: G. ($\text{G}$) $= 10^{9}$. Example: a $2 \text{ GHz}$ processor clock.
- megaSI prefix meaning $10^{6}$. Symbol: M. ($\text{M}$) $= 10^{6}$. Example: a $1 \text{ M}\Omega$ resistor.
- kiloSI prefix meaning $10^{3}$. Symbol: k. ($\text{k}$) $= 10^{3}$. Example: $1 \text{ kg}$, $1 \text{ km}$.
- centiSI prefix meaning $10^{-2}$. Symbol: c. ($\text{c}$) $= 10^{-2}$. Example: $1 \text{ cm}$. Not on Ofqual's strict SI list, but in everyday use.
- milliSI prefix meaning $10^{-3}$. Symbol: m. ($\text{m}$) $= 10^{-3}$. Example: $1 \text{ mA}$ of current.
- microSI prefix meaning $10^{-6}$. Symbol: $\mu$. ($\mu$) $= 10^{-6}$. Example: $470 \, \mu\text{F}$ capacitor.
- nanoSI prefix meaning $10^{-9}$. Symbol: n. ($\text{n}$) $= 10^{-9}$. Example: $500 \text{ nm}$ wavelength of green light.
- picoSI prefix meaning $10^{-12}$. Symbol: p. ($\text{p}$) $= 10^{-12}$. Example: $1 \text{ pF}$ stray capacitance.
- femto ($\text{f}$) $= 10^{-15}$. Example: $1 \text{ fm}$, the size of a proton.
Common Mistake
HIGH
Wrong: Using $\text{mm}^{2}$ or $\text{cm}^{2}$ directly in equations without squaring the conversion factor. For example, treating $5 \text{ mm}^{2}$ as $5 \times 10^{-3} \text{ m}^{2}$.
Right: The prefix sits inside the unit, so it gets squared too. $1 \text{ mm} = 10^{-3} \text{ m}$, therefore $1 \text{ mm}^{2} = (10^{-3})^{2} \text{ m}^{2} = 10^{-6} \text{ m}^{2}$. Always square (or cube) the conversion factor when the unit carries a power.
Right: The prefix sits inside the unit, so it gets squared too. $1 \text{ mm} = 10^{-3} \text{ m}$, therefore $1 \text{ mm}^{2} = (10^{-3})^{2} \text{ m}^{2} = 10^{-6} \text{ m}^{2}$. Always square (or cube) the conversion factor when the unit carries a power.
Examiner Tips and Tricks
- OCR expects you to recall every prefix from tera to femto. Learn the symbol, the name, and the factor of ten.
- Capital $\text{M}$ is mega ($10^{6}$); lower-case $\text{m}$ is milli ($10^{-3}$). They differ by a factor of $10^{9}$, so a slip costs the whole question.
- Convert every prefix to a plain power of ten before substituting into an equation. Do not leave $\text{kJ}$ inside $E_{k} = \tfrac{1}{2}mv^{2}$.