Physics: SI Units

    1 Base units:

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    • There are seven base units:
    • Mass: kilograms, kg\mathrm{kg}
    • Time: seconds, s\mathrm{s}
    • Length: metres, m\mathrm{m}
    • Electrical current: amperes, A\mathrm{A}
    • Temperature: kelvin, K\mathrm{K} (00 °C = 273 K273\ \mathrm{K})
    • Luminous intensity: candela, cd\mathrm{cd}
    • Amount of substance: mole, mol\mathrm{mol}

    Derived quantities:

    • The seven base units can be combined to give units of any quantity
      - For example, electrical charge is A s\mathrm{A}\ \mathrm{s} (because Q=ItQ = It)
      - frequency is s−1\mathrm{s}^{-1} (because f=f = 1T\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 m s−1\mathrm{m}\ \mathrm{s}^{-1} or m\mathrm{m}·s−1\mathrm{s}^{-1}, not ms−1\mathrm{ms}^{-1})
    • There should always be a space between the number and the unit
    • Symbols (like II for amperes) should be italicised, and those that are multiplied together should be written with no space between them (e.g. ItIt)

    C.0.1 SI Prefixes:

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    • 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 5.3×1075.3 \times 10^{7} m\mathrm{m} as 53 Mm53\ \mathrm{Mm}

      TeraT\mathrm{T}101210^{12}
      GigaG\mathrm{G}10910^{9}
      MegaM\mathrm{M}10610^{6}
      Kilok\mathrm{k}10310^{3}
      Decid\mathrm{d}10−110^{-1}
      Centic\mathrm{c}10−210^{-2}
      Millim\mathrm{m}10−310^{-3}
      Microµ\mathrm{µ}10−610^{-6}
      Nanon\mathrm{n}10−910^{-9}
      Picop\mathrm{p}10−1210^{-12}
      Femtof\mathrm{f}10−1510^{-15}

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

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    • Multiply the quantity by the power in the above table
    • For example, to convert 53 Mm53\ \mathrm{Mm} to standard form, multiply the quantity (5353) by the power of 10 listed above (10610^6)
    • So 53 Mm53\ \mathrm{Mm} =53×106=5.3×107= 53 \times 10^{6} = 5.3 \times 10^7 m\mathrm{m}
    • If you have a CASIO fx-991EX calculator, enter the quantity (5353), 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 5.3×1075.3 \times 10^7. 6 is the closest power of 3 to our power (7), so we do 5.3×107÷1065.3 \times 10^7 \div 10^6, which gives us 5353. Now look up the value of 10610^6 in the above table, which is M\mathrm{M}. So our value is 53 Mm53\ \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