# What Are the Prefixes for SI Units?

In math, you often use prefixes to write large and small numbers in a simpler way. For example, 2 million byte is much easier to write as 2 megabyte or $2$ MB, where M means “mega” and mega $=1{0}^{6}=1\phantom{\rule{0.17em}{0ex}}000\phantom{\rule{0.17em}{0ex}}000$.

Theory

### Prefixes

 giga G billion $1{0}^{9}$ mega M million $1{0}^{6}$ kilo k thousand $1{0}^{3}$ hecto h hundred $1{0}^{2}$ deka da ten $10$ deci d one tenth $1{0}^{-1}$ centi c one hundredth $1{0}^{-2}$ milli m one thousandth $1{0}^{-3}$ micro μ one millionth $1{0}^{-6}$ nano n one billionth $1{0}^{-9}$

Example 1

Uncle Sam bought $\text{}2.3\text{}$ hectograms (hg) of candy when he was at the store. How many grams does that correspond to?

Hecto (h) means “hundred”. That means Uncle Sam bought

 $2.3\phantom{\rule{0.17em}{0ex}}\text{hg}=\left(2.3\cdot 100\right)\phantom{\rule{0.33em}{0ex}}\text{g}=230\phantom{\rule{0.17em}{0ex}}\text{g}$

of candy.

Example 2

One stage of the cycling race Tour de France can be 192 kilometers (km) long. How many meters is that?

Kilo (k) means “1000”. Thus, the boys ride

 $192\phantom{\rule{0.17em}{0ex}}\text{km}=\left(192\cdot 1000\right)\phantom{\rule{0.33em}{0ex}}\text{m}=192\phantom{\rule{0.17em}{0ex}}000\phantom{\rule{0.17em}{0ex}}\text{m}.$

The stage is $192\phantom{\rule{0.17em}{0ex}}000$ meters.

Example 3

Albert Einstein was in the laboratory playing with a microscope. While playing, he saw an organism weighing 521 micrograms. How many grams is that?

Micro (μ) means millionth. Thus, the organism weighed

$\begin{array}{llll}\hfill 521\phantom{\rule{0.17em}{0ex}}\text{μg}& =521\cdot \frac{1}{1\phantom{\rule{0.17em}{0ex}}000\phantom{\rule{0.17em}{0ex}}000}\phantom{\rule{0.17em}{0ex}}\text{g}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =0.000\phantom{\rule{0.17em}{0ex}}521\phantom{\rule{0.17em}{0ex}}\text{g}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $521\phantom{\rule{0.17em}{0ex}}\text{μg}=521\cdot \frac{1}{1\phantom{\rule{0.17em}{0ex}}000\phantom{\rule{0.17em}{0ex}}000}\phantom{\rule{0.17em}{0ex}}\text{g}=0.000\phantom{\rule{0.17em}{0ex}}521\phantom{\rule{0.17em}{0ex}}\text{g}$

Note! You switch the prefix with the numeric value of the prefix.