Convert hours (as decimals) to fractions for billable-time invoice

Question

I'm creating an invoice in LaTeX and I've entered the hours I've worked as decimals (for example, 1, 1.5, 0.75, 2.25), but I want to display those decimals as fractions (1, 1½, ¾, 2¼).

(The reason I've entered the hours worked as a decimal is so I can perform simple invoice math with the fp package along the lines of this answer)

For a little context, here's the synopsis of the macro I created that includes the number of hours worked:

\lineitem{DATE}{HOURS}{RATE}{PROJECT}{DESCRIPTION}

The conversions I have in mind are pretty simple:

\documentclass{article}
\usepackage{xfrac}
\begin{document}
\begin{tabular}{r @{} l | r @{\hspace{0.1em}} l}
\multicolumn{2}{c}{Given...} & \multicolumn{2}{c}{Output} \\
\hline
1 & & 1 & \\
1 & .5 & 1 & \sfrac{1}{2} \\
0 & .75 & \sfrac{3}{4} & \\
2 & .25 & 2 & \sfrac{1}{4} \\
\end{tabular}
\end{document}

(I'm not married to \sfrac for displaying fractions, it's just the first package I reached for)

Is there an off-the-shelf package that will do what I want? If not, can anyone give me a few pointers how I might go about implementing my own conversion/display logic?

Answer 1

Adapting the solution from Automatically add fractions and reduce the result (if neccessary) yields:

Notes:

• The \hphantom line should be commented out in your actual use case. It was added to produce a nicer output for posting on TeX.SE.
• This may not yield ideal results for all possible decimals but does work for the ones requested.
• For the HH:MM format, I used the xstring package for string comparison as I prefer its format, but probably can be done without this package if desired.

Code:

\documentclass{article}
\usepackage{tikz}
\usepackage{xfrac}
\usepackage{xstring}
\makeatletter
\newcommand*{@PositionOfColon}{}%
\newcommand{\IfStrContains}[4]{%
    \StrPosition{#1}{#2}[@PositionOfColon]% Record position in @PositionOfColon
    \IfEq{@PositionOfColon}{0}%
    {#4}% StrPosition=0 => Did not find the target string
    {#3}% StrPosition>0 => Found the target string
}%
% Use Euclid's Algorithm to find the greatest 
% common divisor of two integers.
\def\gcd#1#2{{% #1 = a, #2 = b
    \ifnum#2=0 \edef\next{#1}\else
        @tempcnta=#1 @tempcntb=#2 \divide@tempcnta by@tempcntb
        \multiply@tempcnta by@tempcntb  % q*b
        @tempcntb=#1
        \advance@tempcntb by-@tempcnta % remainder in @tempcntb
        \ifnum@tempcntb=0
            @tempcnta=#2
            \ifnum@tempcnta < 0 @tempcnta=-@tempcnta\fi
            \xdef\gcd@next{\noexpand%
                \def\noexpand\thegcd{\the@tempcnta}}%
        \else
            \xdef\gcd@next{\noexpand\gcd{#2}{\the@tempcntb}}%
        \fi
    \fi}\gcd@next
}
%% Adapted from https://tex.stackexchange.com/questions/28628/automatically-add-fractions-and-reduce-the-result-if-neccessary
\newcommand{\rfNumer}{}%
\newcommand{\rfDenom}{}%
\newcommand\reduceFrac[2]{%
   \gcd{#1}{#2}{@tempcnta=#1 \divide@tempcnta by\thegcd
   @tempcntb=#2 \divide@tempcntb by\thegcd
   \ifnum@tempcntb<0\relax
      @tempcntb=-@tempcntb
      @tempcnta=-@tempcnta
    \fi
    \xdef\rfNumer{\the@tempcnta}
    \xdef\rfDenom{\the@tempcntb}}%
}
\makeatother
\newcommand*{\fracReduced}[2]{\reduceFrac{#1}{#2}\ensuremath{\sfrac{\rfNumer}{\rfDenom}}}%
\newcommand{\TempNumerator}{}%
\newcommand{\TempDenominator}{}%
\newcommand{\DecimalToFrac}[1]{%
    \IfStrContains{#1}{:}{%
        \StrBefore{#1}{:}[\WholePortion]%
        \StrBehind{#1}{:}[\TempNumerator]%
        \def\TempDenominator{60}%
    }{%
        \pgfmathtruncatemacro{\WholePortion}{int(#1)}%
        \pgfmathtruncatemacro{\TempNumerator}{100(#1-\WholePortion)}%
        \def\TempDenominator{100}%
    }%
    #1 =
    \ifnum\WholePortion > 0\relax%
        \WholePortion%
    \else
        \hphantom{0}% Just for nicer output of MWE. Should be deleted in actual use
    \fi
    \fracReduced{\TempNumerator}{\TempDenominator}%
}%
\begin{document}
Using decimals:
\DecimalToFrac{0.75},
\quad
\DecimalToFrac{0.50},
\quad
\DecimalToFrac{0.25}.
\DecimalToFrac{2.75},
\quad
\DecimalToFrac{1.50},
\quad
\DecimalToFrac{3.25}.
\bigskip
Using \texttt{HH:MM} format:
\DecimalToFrac{0:45},
\quad
\DecimalToFrac{0:30},
\quad
\DecimalToFrac{0:15},
\DecimalToFrac{0:20},
\quad
\DecimalToFrac{0:10},
\quad
\DecimalToFrac{0:05}.
\medskip
\DecimalToFrac{2:45},
\quad
\DecimalToFrac{1:15},
\quad
\DecimalToFrac{3:10}.
\DecimalToFrac{2:20},
\quad
\DecimalToFrac{1:10},
\quad
\DecimalToFrac{3:05}.
\end{document}

Answer 2

tikz provides this type of formatting:

\documentclass{article}
\usepackage{tikz,xfrac}
\usetikzlibrary{fpu}
\newcommand{\dectofrac}[1]{\begingroup%
  \pgfkeys{/pgf/number format/frac}% Format as fraction
  \let\frac\sfrac% Let \frac act like \sfrac
  \pgfmathprintnumber{#1}\endgroup}
\pagestyle{empty}
\begin{document}

\begin{tabular}{r @{} l | r @{\hspace{0.1em}} l}
  \multicolumn{2}{c}{Given...} & \multicolumn{2}{c}{Output} \\
  \hline
  1&    & 1& \\
  1&.5  & 1&\dectofrac{0.5} \\
  0&.75 &  &\dectofrac{0.75} \\
  2&.25 & 2&\dectofrac{0.25}
\end{tabular}
\end{document}​