Truncating floating point numbers for display while maintaining full accuracy for computations

Question

The MWE below suggests that truncating an fp type number is not just for cosmetics but actually changes the number's value. Is there a way to reduce the number of decimals displayed without affecting the number's full accuracy in computations? I browsed through siunitx but nothing jumped at me.

\documentclass{article}
% RN. 6 April 2017
% TOPIC:
%  Truncating floating point numbers 
%=======================
\usepackage[check-declarations]{expl3}
\usepackage{xparse}
%-----------------------
\ExplSyntaxOn
\NewDocumentCommand\myTruncatingFloatingPoints{mO{3.11998}O{3.0198}}
  {
    \fp_eval:n {trunc(#2,#1)*trunc(#3,#1)}
  }  %  \myTruncatingFloatingPoints

\ExplSyntaxOff
%-----------------------
\begin{document}
    1. Full complement of digits:~\myTruncatingFloatingPoints{5}

    2. Truncated to 2 decimal digits:~  \myTruncatingFloatingPoints{2}
\end{document}

Answer 1

Taken from How to set the precision in numbers (there are more versions, have a look):

\documentclass{article}
\usepackage{siunitx}
\begin{document}
\num{0.12368455}

\num[round-mode=places,round-precision=4]{0.12368455}
\end{document}

Is that what you are looking for?

Answer 2

Here I use \num just for pretty printing.

\documentclass{article}
\usepackage{siunitx,xfp}

\begin{document}

\begin{tabular}{ll}
No truncation  & \num{\fpeval{3.11998*3.0198}} \\
Truncation     & \num{\fpeval{trunc(3.11998*3.0198,2)}} \\
Bad truncation & \num{\fpeval{trunc(3.11998,2)*trunc(3.0198,2)}}
\end{tabular}

\end{document}

Answer 3

Because I felt like reinventing the wheel...(again)

EDITED so that truncating to 0 places does not present the decimal.

RE-EDITED to handle negative numbers.

\documentclass{article}
\newcounter{digits}
\newcommand\myTruncatingFloatingPoints[2]{%
  \whole{#1}#2..\relax%
}
\def\whole#1#2.#3.#4\relax{%
    \presentwhole#2\relax\relax%
    \ifx\relax#3\relax.\trunc{#1}00\relax\else%
      \ifnum#1>0\relax.\trunc{#1}#3\relax\fi%
    \fi%
}
\def\presentwhole#1#2\relax{%
  \ifx-#1\ensuremath{-}\the\numexpr0#2\else\the\numexpr0#1#2\fi%
}
\def\trunc#1#2#3#4\relax{%
  \setcounter{digits}{#1}%
  \addtocounter{digits}{-1}%
  \ifnum\thedigits>0\relax%
    #2%
    \trunc{\thedigits}#3#40\relax%
  \else%
    \ifnum#3<5\relax#2\else\the\numexpr#2+1\relax\fi% ROUNDED
%    #2% TRUNCATED
  \fi%%  \fi%
}
\begin{document}
1. \makebox[.8in][r]{9.421715604} to 5 digits: \myTruncatingFloatingPoints{5}{9.421715604}

2. \makebox[.8in][r]{9.421715604} to 3 digits: \myTruncatingFloatingPoints{3}{9.421715604}

3. \makebox[.8in][r]{9.421715604} to 1 digits: \myTruncatingFloatingPoints{1}{9.421715604}

4. \makebox[.8in][r]{9.421715604} to 0 digits: \myTruncatingFloatingPoints{0}{9.421715604}

5. \makebox[.8in][r]{29} to 2 digits: \myTruncatingFloatingPoints{2}{29}

6. \makebox[.8in][r]{.1275} to 3 digits: \myTruncatingFloatingPoints{3}{.1275}

7. \makebox[.8in][r]{.1275} to 4 digits: \myTruncatingFloatingPoints{4}{.1275}

8. \makebox[.8in][r]{$-$.12} to 6 digits: \myTruncatingFloatingPoints{6}{-.12}
\end{document}