What is the best way to write something like 6.22E-21 in LaTeX, given that I don't want the numerals to be \tt? I do want the E to be small, and I may want the exponent to be negative (without the huge LaTeX minus sign)?
I'm sure this is a duplicate of another question that I just can't find.
Example here: 
For a one-off implementation of your typesetting needs, you could try
6.22\mbox{\textsc{e-}}21 This will work in both text and math mode. If you use the amsmath package, you should type
6.22\text{\textsc{e-}}21 as this is slightly more general than the first solution. Specifically, it'll work better if the expression ever occurs in scriptstyle (first-level sub- and superscripts) or scriptscriptstyle (second-level sub- and superscripts) material.
Conversely, if you have a lot of numbers that you wish to typeset in this way, you should implement a solution along the lines provided in @AlfC's answer. Otherwise, sooner or later some inconsistencies in the way you typeset these numbers will creep in.
By far the most elegant way to do it is using the siunitx package:
\documentclass{article} \usepackage{siunitx} \sisetup{output-exponent-marker=\textsc{e}} \begin{document} \num{6.02e23} \end{document} 
EDIT 1: If you want a short minus sign, a not so elegant solution (but still within siunitx) is to replace this more complicated sisetup line:
\sisetup{output-exponent-marker=\textsc{e}, bracket-negative-numbers, open-bracket={\text{-}}, close-bracket={}} 
This will in general affect also negative numbers (even without exponents) used within \num. For other hacks regarding the minus sign look at this question Making a shorter minus or Typesetting of negative versus minus?, no answer on this was really satisfactory to me.
EDIT 2 (2014): If you make XeLaTeX use Écran Font (for example) and some TikZ shadows you can give it a complete look
(note the use of the unicode chacaracter "ᴇ", I needed to use this particular font because it was the only one with this character)
\documentclass{article} \usepackage{xcolor} \usepackage{siunitx} \usepackage{fontspec} \setmainfont[ExternalLocation={./}]{ecran-monochrome---monochrome-display.ttf} % Écran Monochrome \usepackage{tikz} \newcommand\calcshadow[1]{ \tikz[baseline]{ \node[black!50!white] at (0.02,-0.02) {\num[output-exponent-marker=\text{ᴇ}, output-decimal-marker=\text{.}, bracket-negative-numbers, open-bracket={\text{-}}, close-bracket={}]{#1}}; \node[] at (0.,0.) {\num[output-exponent-marker=\text{ᴇ}, output-decimal-marker=\text{.}, bracket-negative-numbers, open-bracket={\text{-}}, close-bracket={}]{#1}}; } } \begin{document} \colorbox{gray!70}{ \calcshadow{6.02e-23} } \end{document} EDIT 3: Alternative style using unicode block character "█":
... \newcommand\calcshadow[1]{ \tikz[baseline]{ \node[black!20!white] at (0.,0.) {████████}; \node[black!80!white,opacity=0.5] at (0.02,-0.02) {\num[output-exponent-marker=\text{ᴇ}, output-decimal-marker=\text{.}, bracket-negative-numbers, open-bracket={\text{-}}, close-bracket={}]{#1}}; \node[] at (0.,0.) {\num[output-exponent-marker=\text{ᴇ}, output-decimal-marker=\text{.}, bracket-negative-numbers, open-bracket={\text{-}}, close-bracket={}]{#1}}; } } ... 
siunitx: the question seems to be after what you see with a calculator, which is much more hyphen-like. It is working in LaTeX, http://www.ctan.org/pkg/lcd .
For 10,
\DefineLCDchar{10}{00000000000000010111101011010110111} For small caps shape {E},
\DefineLCDchar{12}{00000000000111101000011100100001111} It may be necessary, http://latexcolor.com/
Thanks a lot, Mike Kaufmann.
You could try this code:
% this has to go in the preamble of the document. \DeclareMathSymbol{\minus}{\mathord}{operators}{"2D} % unary minus \newcommand{\scinot}[2]{#1\,\textrm{\scriptsize E}{#2}} % scientific notation $\scinot{10}{\minus2}$ 
$6.22\mbox{\textsc{e}}-21$. I'm assuming this number will be typeset on math mode, right? If you don't want a (typographically correct) math minus sign but a simple dash, be sure to include it in the argument of the\mboxcommand.$6.22\mbox{\sc{e}-}21$is definitely the correct answer, it looks exactly how I'd like it to! You should post that so I can checkmark it.