How do I write a recurring decimal in LaTeX?

Question

Title says it all. Since I am a newbie, I don't know how to do this.

Any help?

Answer 1

If you're thinking of using a horizontal bar over a recurring group of decimals, you could use the \overline command:

\documentclass{article}
\begin{document}
$\frac{1}{7}=0.\overline{142857}$
\end{document}

Answer 2

There are at least four representations; here is a way to produce all of them, take your pick (the macro names can of course be modified). I strongly suggest to use a special macro name, even if you decide to use the overline, so you can change your mind later and choose another realization.

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn

%% Dots on the first and last digit
\NewDocumentCommand{\periodfl}{m}
 {
  \repdec_initial_final_dots:n { #1 }
 }

\seq_new:N \l__repdec_digits_seq
\tl_new:N \l__repdec_first_tl
\tl_new:N \l__repdec_last_tl

\cs_new_protected:Npn \repdec_initial_final_dots:n #1
 {
  \seq_set_split:Nnn \l__repdec_digits_seq {} { #1 }
  \seq_pop_left:NN \l__repdec_digits_seq \l__repdec_first_tl
  \seq_pop_right:NN \l__repdec_digits_seq \l__repdec_last_tl
  \quark_if_no_value:VF \l__repdec_first_tl { \dot{\l__repdec_first_tl} }
  \seq_use:Nnnn \l__repdec_digits_seq {}{}{}
  \quark_if_no_value:VF \l__repdec_last_tl { \dot{\l__repdec_last_tl} }
 }
\cs_generate_variant:Nn \quark_if_no_value:nF { V }

%% Dots on all digits
\NewDocumentCommand{\periodalldots}{m}
 {
  \repdec_initial_all_dots:n { #1 }
 }

\cs_new_protected:Npn \repdec_initial_all_dots:n #1
 {
  \tl_map_inline:nn { #1 } { \dot{##1} }
 }

%% Bar over period
\NewDocumentCommand{\periodbar}{m}
 {
  \overline{ #1 }
 }

%% Parentheses around period
\NewDocumentCommand{\periodparens}{m}
 {
  (#1)
 }

%% Dot on unique digit, bar on several digits
\NewDocumentCommand{\periodmixed}{m}
 {
  \repdec_mixed:n { #1 }
 }
\cs_new_protected:Npn \repdec_mixed:n #1
 {
  \int_case:nnn { \tl_count:n { #1 } }
   {
    { 0 } { }
    { 1 } { \dot{#1} }
   }
   {
    \overline{#1}
   } 
 }

\ExplSyntaxOff

\begin{document}
$1.2\periodfl{3}$ --- $1.2\periodfl{34}$ --- $1.2\periodfl{345}$ --- 
$1.2\periodfl{3456}$ --- $1.2\periodfl{34567}$

\medskip
$1.2\periodalldots{3}$ --- $1.2\periodalldots{34}$ --- $1.2\periodalldots{345}$ --- 
$1.2\periodalldots{3456}$ --- $1.2\periodalldots{34567}$

\medskip
$1.2\periodbar{3}$ --- $1.2\periodbar{34}$ --- $1.2\periodbar{345}$ --- 
$1.2\periodbar{3456}$ --- $1.2\periodbar{34567}$

\medskip
$1.2\periodparens{3}$ --- $1.2\periodparens{34}$ --- $1.2\periodparens{345}$ --- 
$1.2\periodparens{3456}$ --- $1.2\periodparens{34567}$


\medskip
$1.2\periodmixed{3}$ --- $1.2\periodmixed{34}$ --- $1.2\periodmixed{345}$ ---
$1.2\periodmixed{3456}$ --- $1.2\periodmixed{34567}$

\end{document}

For \periodbar and \periodparens the overhead of xparse is not necessary and they can be realized with the standard

\newcommand{\periodbar}[1]{\overline{#1}}
\newcommand{\periodparens}[1]{(#1)}

---

A different definition of \repdec_initial_final_dots:n can be as follows

\int_new:N \l__repdec_digits_int
\int_new:N \l__repdec_count_int
\cs_new_protected:Npn \repdec_initial_final_dots:n #1
 {
  \int_set:Nn \l__repdec_digits_int { \tl_count:n { #1 } }
  \int_zero:N \l__repdec_count_int
  \tl_map_inline:nn { #1 } { \__repdec_add_dot:n { ##1 } }
 }
\cs_new_protected:Npn \__repdec_add_dot:n #1
 {
  \int_incr:N \l__repdec_count_int
  \int_case:nnn { \l__repdec_count_int }
   {
    { 1 } { \dot{#1} }
    { \l__repdec_digits_int } { \dot{#1} }
   }
   {
    #1
   }
 }

However, the sequence method seems more general.

---

Just for completeness, here is a possible approach for this macro in the traditional LaTeX programming:

\makeatletter
\DeclareRobustCommand{\periodfl}[1]{\@periodflold#1\@nil\relax}
\def\@periodflold#1#2{%
  \ifx#2\relax
    \expandafter\@gobble
  \else
    \expandafter\@firstofone
  \fi
  {\@periodflold@i#1#2}%
}
\def\@periodflold@i#1#2{%
  \dot{#1}%
  \ifx#2\@nil
    \expandafter\@gobble
  \else
    \expandafter\@firstofone
  \fi
  {\@periodflold@ii#2}%
}
\def\@periodflold@ii#1#2{%
  \ifx#2\@nil
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi
  {\dot{#1}}{#1\@periodflold@ii#2}%
}
\makeatother