SI Prefixes, Standard Form & Converting Units

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Prefixes of Units

Using prefixes before a unit indicates the scale of the value.
For example, 1 nanometre (nm) = 10-9m. 3nm = 3×10-9m.

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Nano (n)

  • Multiplies the unit by 10-9.
  • This is equivalent to multiplying by 0.000000001.
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Micro (μ)

  • Multiplies the unit by 10-6.
  • This is equivalent to multiplying by 0.000001.
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Milli (m)

  • Multiplies the unit by 10-3.
  • This is equivalent to multiplying by 0.001.
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Centi (c)

  • Multiplies the unit by 10-2.
  • This is equivalent to multiplying by 0.01.
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Kilo (k)

  • Multiplies the unit by 103.
  • This is equivalent to multiplying by 1000.
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Mega (M)

  • Multiplies the unit by 106.
  • This is equivalent to multiplying by 1000000.
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Giga (G)

  • Multiplies the unit by 109.
  • This is equivalent to multiplying by 1000000000.

Standard Form

Standard form is used to represent very large or very small numbers. In standard form numbers are written in the format: A x 10n where A is a number between 0 and 10 and n is how many places to move the decimal point.

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Standard form examples

  • To write 1,000,000 as standard form 1 x 106.
  • To write 0.0004 as standard form 4 x 10-4.

Converting Units

Consider a simple example of how to convert units. Let us say that we want to convert 80 metres (m) to kilometres (km).

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Step one

  • The first thing to do is to list the units that you have and the units that you want to convert to.
  • In this case, we have units in metres and we want to convert to kilometres.
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Step two

  • Next, we need to determine a conversion factor relating metres to kilometres.
    • A conversion factor is a ratio expressing how many of one unit are equal to another unit.
    • For example, there are 12 inches in one foot, 100 centimetres in one metre, 60 seconds in one minute, and so on.
  • In this case, we know that there are 1,000 metres in one kilometre.
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Step three

  • Now we can set up our unit conversion.
  • We write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown in the image.
  • Note that the unwanted m unit cancels, leaving only the desired km unit.
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Other examples

  • You can use this method to convert between any types of unit.
  • For example between J and eV or between J and kW/h.

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