When we want to know how long something is we often get a numerical answer, like 10 m, with a unit after the number showing us the type and size of the measurement. In this case it is metres so we know it is about distance, and we have an idea about how big 1 metre is. If we were to ask about the length of a river it might be 9000 m long. In this case it might be easier to talk about it as being 9 km long. Similarly , if we are measuring an insect its size might be 0.002 m in length. So we might write this as 2 mm instead.
\begin{aligned} 9000 \text{ m} &= 9 \times 10^3 \text{ m} &= &\,\,9 \text{ km} \\ 0.002 \text{ m} &=2 \times 10^{-3} \text{ m} &=&\,\,2\text{ mm} \end{aligned}
All of these units are related to the metre (m). We added prefixes ("k" and "m") to this unit ("m") to make the unit bigger or smaller by a certain amount. This makes it easier to talk about values that are very large or very small.
Prefix | Letter | Size |
---|---|---|
\text{yotta} | \text{Y} | {10}^{24} |
\text{zetta} | \text{Z} | {10}^{21} |
\text{exa} | \text{E} | {10}^{18} |
\text{peta} | \text{P} | {10}^{15} |
\text{tera} | \text{T} | {10}^{12} |
\text{giga} | \text{G} | {10}^{9} |
\text{mega} | \text{M} | {10}^{6} |
\text{kilo} | \text{k} | {10}^{3} |
\text{hecto} | \text{h} | {10}^{2} |
\text{deca} | \text{da} | {10}^{1} |
{10}^{0} | ||
\text{deci} | \text{d} | {10}^{-1} |
\text{centi} | \text{c} | {10}^{-2} |
\text{milli} | \text{m} | {10}^{-3} |
\text{micro} | \mu | {10}^{-6} |
\text{nano} | \text{n} | {10}^{-9} |
\text{pico} | \text{p} | {10}^{-12} |
\text{femto} | \text{f} | {10}^{-15} |
\text{atto} | \text{a} | {10}^{-18} |
\text{zepto} | \text{z} | {10}^{-21} |
\text{yocto} | \text{y} | {10}^{-24} |
To convert between units with a different prefix it is easiest to reduce it to the original unit.
Which of the following is the same wattage as 1\,000\,000 W?
Write 52 ms in ns.
Write 5\times {10}^{5} dL in hL.
Units can have prefixes added to make them larger or smaller. Below is a table of the most common prefixes:
Prefix | Letter | Size |
---|---|---|
\text{giga} | \text{G} | {10}^{9} |
\text{mega} | \text{M} | {10}^{6} |
\text{kilo} | \text{k} | {10}^{3} |
\text{hecto} | \text{h} | {10}^{2} |
\text{deca} | \text{da} | {10}^{1} |
{10}^{0} | ||
\text{deci} | \text{d} | {10}^{-1} |
\text{centi} | \text{c} | {10}^{-2} |
\text{milli} | \text{m} | {10}^{-3} |
\text{micro} | \mu | {10}^{-6} |
\text{nano} | \text{n} | {10}^{-9} |