Multiples and submultiples
Table of multiples and submultiples
The International System of Units (SI) defines the following multiples and submultiples for physical quantities.
| Multiples | Submultiples | ||||
|---|---|---|---|---|---|
| deca | da | 101 | deci | d | 10-1 |
| hecto | h | 102 | centi | c | 10-2 |
| kilo | k | 103 | milli | m | 10-3 |
| mega | M | 106 | micro | μ | 10-6 |
| giga | G | 109 | nano | n | 10-9 |
| tera | T | 1012 | pico | p | 10-12 |
| peta | P | 1015 | femto | f | 10-15 |
| exa | E | 1018 | atto | a | 10-18 |
| zetta | Z | 1021 | zepto | z | 10-21 |
| yotta | Y | 1024 | yocto | y | 10-24 |
The prefixes for multiples greater than 1 are derived from Greek, while those for submultiples smaller than 1 come from Latin.
Examples in practice
By convention, the symbol for the multiple or submultiple always precedes the symbol of the unit of the physical quantity.
kg (kilogram)
Mb (Megabyte)
cm (centimeter)
hl (hectoliter)
μs (microsecond)
How to convert multiples and submultiples
To convert from X to Y, calculate the ratio $ \frac{X}{Y}, $ based on their powers of 10. $$ \frac{10_X^a}{10_Y^b} $$
Example
How many attoseconds are in a nanosecond?
In this case, the starting unit X is nanoseconds, which corresponds to $ 10^{-9} $ (nano).
The target unit Y is attoseconds, which corresponds to $ 10^{-18} $.
Now, calculate the ratio of the powers of 10:
$$ \frac{10_X^a}{10_Y^b} = \frac{10^{-9}}{10^{-18}} $$
Then apply the properties of exponents:
$$ \frac{10^{-9}}{10^{-18}} $$
$$ 10^{-9-(-18)} $$
$$ 10^{-9+18} $$
$$ 10^{9} $$
So, there are $ 10^9 $ attoseconds in one nanosecond, which equals one billion attoseconds, since $ 10^9 = 1,000,000,000 $.
And so forth.
