Physics: SI Units

1 Base units:

• There are seven base units:
• Mass: kilograms, $\mathrm{kg}$$\mathrm{kg}$
• Time: seconds, $\mathrm{s}$$\mathrm{s}$
• Length: metres, $\mathrm{m}$$\mathrm{m}$
• Electrical current: amperes, $\mathrm{A}$$\mathrm{A}$
• Temperature: kelvin, $\mathrm{K}$$\mathrm{K}$ ($0$$0$ °C = $273\ \mathrm{K}$$273\ \mathrm{K}$)
• Luminous intensity: candela, $\mathrm{cd}$$\mathrm{cd}$
• Amount of substance: mole, $\mathrm{mol}$$\mathrm{mol}$

Derived quantities:

• The seven base units can be combined to give units of any quantity
- For example, electrical charge is $\mathrm{A}\ \mathrm{s}$$\mathrm{A}\ \mathrm{s}$ (because $Q = It$$Q = It$)
- frequency is $\mathrm{s}^{-1}$$\mathrm{s}^{-1}$ (because $f =$$f =$ $\frac{1}{T}$$\frac{1}{T}$)
• These are called derived quantities

Conventions:

• Units should be upright, not italicised
• There should be a space or dot multiplication symbol (·) between each base unit (e.g. velocity should be written as $\mathrm{m}\ \mathrm{s}^{-1}$$\mathrm{m}\ \mathrm{s}^{-1}$ or $\mathrm{m}$$\mathrm{m}$·$\mathrm{s}^{-1}$$\mathrm{s}^{-1}$, not $\mathrm{ms}^{-1}$$\mathrm{ms}^{-1}$)
• There should always be a space between the number and the unit
• Symbols (like $I$$I$ for amperes) should be italicised, and those that are multiplied together should be written with no space between them (e.g. $It$$It$)

C.0.1 SI Prefixes:

• Prefixes can be put directly in front of a quantity to make it easier to read and remove the need to use standard form
• For example, you can write $5.3 \times 10^{7}$$5.3 \times 10^{7}$ $\mathrm{m}$$\mathrm{m}$ as $53\ \mathrm{Mm}$$53\ \mathrm{Mm}$

 Tera $\mathrm{T}$$\mathrm{T}$ $10^{12}$$10^{12}$ Giga $\mathrm{G}$$\mathrm{G}$ $10^{9}$$10^{9}$ Mega $\mathrm{M}$$\mathrm{M}$ $10^{6}$$10^{6}$ Kilo $\mathrm{k}$$\mathrm{k}$ $10^{3}$$10^{3}$ Deci $\mathrm{d}$$\mathrm{d}$ $10^{-1}$$10^{-1}$ Centi $\mathrm{c}$$\mathrm{c}$ $10^{-2}$$10^{-2}$ Milli $\mathrm{m}$$\mathrm{m}$ $10^{-3}$$10^{-3}$ Micro $\mathrm{µ}$$\mathrm{µ}$ $10^{-6}$$10^{-6}$ Nano $\mathrm{n}$$\mathrm{n}$ $10^{-9}$$10^{-9}$ Pico $\mathrm{p}$$\mathrm{p}$ $10^{-12}$$10^{-12}$ Femto $\mathrm{f}$$\mathrm{f}$ $10^{-15}$$10^{-15}$

C.0.2 Converting from a prefixed quantity to standard form:

• Multiply the quantity by the power in the above table
• For example, to convert $53\ \mathrm{Mm}$$53\ \mathrm{Mm}$ to standard form, multiply the quantity ($53$$53$) by the power of 10 listed above ($10^6$$10^6$)
• So $53\ \mathrm{Mm}$$53\ \mathrm{Mm}$ $= 53 \times 10^{6} = 5.3 \times 10^7$$= 53 \times 10^{6} = 5.3 \times 10^7$ $\mathrm{m}$$\mathrm{m}$
• If you have a CASIO fx-991EX calculator, enter the quantity ($53$$53$), press OPTN, press 3 for Engineer Symbol and enter the prefix. Now press =

Converting from standard form to a prefixed quantity:

• Pick the closest multiple of 3 to the power of your standard form quantity
• Divide your standard form value by 10 to the power of your chosen multiple of 3
• For example, we have $5.3 \times 10^7$$5.3 \times 10^7$. 6 is the closest power of 3 to our power (7), so we do $5.3 \times 10^7 \div 10^6$$5.3 \times 10^7 \div 10^6$, which gives us $53$$53$. Now look up the value of $10^6$$10^6$ in the above table, which is $\mathrm{M}$$\mathrm{M}$. So our value is $53\ \mathrm{Mm}$$53\ \mathrm{Mm}$
• If you have a CASIO fx-991 series calculator (ES, ES PLUS, EX, etc), enter your value in standard form and press the ENG button to convert it to the nearest power of 3