In the spring of 2020, on my NC State sabbatical, during the initial lock-down for the worst pandemic of my lifetime, I stayed busy in part by writing a text called g = 2: A Gentle Introduction to Relativistic Quantum Mechanics. In the text, I tried using SI prefixes to simply express small quantities but was disappointed that they were inadequate. Not until recently did I notice that six new extreme prefixes were added to the Système international d’unités in 2022, as included in the table below.
| quecto | q | 10-30 | quetta | Q | 1030 |
| ronto | r | 10-27 | ronna | R | 1027 |
| yocto | y | 10-24 | yotta | Y | 1024 |
| zepto | z | 10-21 | zetta | Z | 1021 |
| atto | a | 10-18 | exa | E | 1018 |
| femto | f | 10-15 | peta | P | 1015 |
| pico | p | 10-12 | tera | T | 1012 |
| nano | n | 10-9 | giga | G | 109 |
| micro | μ | 10-6 | mega | M | 106 |
| milli | m | 10-3 | kilo | k | 103 |
| centi | c | 10-2 | hecto | h | 102 |
| deci | d | 10-1 | deca | d | 101 |
I am now pleased to report the following data, to 3 significant figures.
Earth’s mass is 5.97 ronnagrams,
M_E = 5.97~\text{Rg} = 5.97\times 10^{24}~\text{kg}.An electron’s mass is 911 quectograms,
m_e = 911~\text{qg} = 9.11\times 10^{-31}~\text{kg}.An elementary charge is 160 zeptocoulombs,
e = 160~\text{zC} = 1.60\times 10^{-19}~\text{C}.Light speed is 300 meters per microsecond,
c = 300~\text{m}/\text{μs} = 3.00\times 10^{8}~\text{m}/\text{s}.The quantum of action is 105 yoctojoules per terahertz,
\hbar = 105~\text{yJ}/\text{THz} =1.05\times 10^{-34}~\text{J}/\text{Hz}.Vacuum permittivity is 8.85 microcoulombs squared per joule per meter,
\epsilon_0 = 8.85~\text{μC}^2/(\text{J}~\text{m} )= 8.85\times 10^{-12}~\text{C}^2/(\text{J}~\text{m}).Thus, the fine structure constant
\alpha = \frac{e^2}{4\pi\epsilon_0 \hbar c} = \frac{(160\,\text{zC})^2}{4\pi\, 8.85\frac{\text{μC}^2}{\text{J}\,\text{m} } 105\frac{\text{yJ}}{\text{THz}} 300\frac{\text{m}}{\text{μs}} } = \frac{1}{137}.