fontsmath-mode
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: 
When a formula with base and exponent is being typeset in "textstyle" mode, TeX sets the base in textstyle size and the exponent in "cramped scriptsize". On the other hand, when the same formula is typeset in "displaystyle" mode, TeX sets the base in textstyle but the exponent in "non-cramped scriptsize". The "cramped" vs "non-cramped" mode doesn't affect the size of the exponents (they're both in "scriptsize") but, rather, their vertical placement. As the name suggests, "cramped" means in the present case that a superscript isn't raised as much as it is in non-cramped mode. See chapter 17 of the TeXbook for an exhaustive listing of the ways in which decides to be in cramped vs non-cramped mode.
The following MWE illustrates the effects of being in textstyle math vs is displaystyle math for the relative positioning of the exponents: the first two expressions are typeset in textstyle, the next two are in displaystyle.
\documentclass{standalone}
\usepackage{amssymb}
\begin{document}
$R^n \ \mathbb{R}^n \ \displaystyle R^n \ \mathbb{R}^n $
\end{document}
I am not a fan of typing numbers in the text in mathmode. It's fine if you use a complete font, but what if you decide to change the math font later? I prefer to use the textminus from the textcomp package. If your editor is unicode capable you can enter the proper minus symbol directly.
Edit: siunitx is able to handle numbers correctly as well.
Edit 2: To respond a bit more to the question asked, there is no typographical difference between a 'minus' and 'negative' sign. The difference is the kerning: With $-12$ the sign is close to the number, with $10-12$ the minus has appropriate kerning between the numbers. In short, there should be no need to resize the minus sign for negative numbers as a good font should have a minus sign so that its length blends in well with text.
\documentclass{scrartcl}
\usepackage{textcomp}
\usepackage{mathpazo}
\usepackage{eulervm}
\usepackage[utf8]{inputenc}
\DeclareUnicodeCharacter{2212}{\textminus}% requires a unicode capable editor
\usepackage{siunitx}
\sisetup{
detect-mode,
detect-family,
detect-inline-family=math,
}
\begin{document}
\noindent
Number \textminus10 (textcomp minus)\\
Number −10 (unicode minus)\\% requires a unicode capable editor
Number -10 (normal text minus)\\
Number $-10$ (all math mode)\\
\vspace{1ex}
\noindent
Number \num{-16} (siunitx textmode. No bug, my bad. Sorry Joseph)\\
Number $\num{-16}$ (siunitx mathmode)
\end{document}
Best Answer
For a one-off implementation of your typesetting needs, you could try
This will work in both text and math mode. If you use the
amsmathpackage, you should typeas 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.