Can I write a rule for table containing tens, ones, tenths, hundredths and thousands

Question

I am wondering if I can write a rule for this? Is a rule even a good idea for this or is it better if I keep doing the table. Happy to hear any thoughts.

Also trying to create that red arrow and the label of x10 over it but not really sure how to do this.

I am happy to just keep doing the table if better.

Thank you

Warning- very messy...

\documentclass[
  a5paper,
  % pagesize,11pt,% both are default and therefore not needed
  bibliography=totoc,% bibtotoc is deprecated and therefore replaced according
                     % to the warning message
  numbers=noenddot,% pointlessnumbers is deprecated and therefore replaced
                   % according to the warning message
  headings=normal,% normalheadings is deprecated and therefore replaced
                  % according to the warning message
  DIV=9,twoside=false,
  headsepline,footsepline,footinclude=false,% see the KOMA-Script manual
headheight=87pt,% not used, to not lower the header, but this results in a warning
footheight=52pt, % no longer needed, because the lines are not part of the footer
]{scrbook}
\KOMAoptions{DIV=last}
\usepackage{trajan}
\usepackage{setspace}
\linespread{1.05}
\KOMAoptions{DIV=last}% moved according to the KOMA-Script manual, because it
                      % makes no sense before changing font an linespread.
\usepackage{graphicx}
\usepackage[%
  autoenlargeheadfoot=false,% only warn but don't change height reserved for header or footer

  manualmark,% or maybe automark, this is not clear due to missing information
             % in the question.
  plainheadsepline,plainfootsepline,% See the KOMA-Script manual for more information
  ]{scrlayer-scrpage}
\usepackage{geometry}
 \geometry{
 a5paper,
 total={100mm,200mm}, %not sue what this line is either.
 left=15mm,
 right=15mm,
 top=30mm,
 bottom=35mm,
 headsep=2mm,
 }
\usepackage[dvipsnames]{xcolor}
\definecolor{ssblue}{rgb}{0.22,0.714,1}
\definecolor{red}{RGB}{214,39,41}
\definecolor{Lgreen}{RGB}{125,173,62}
\definecolor{Dgreen}{RGB}{74,108,47}
\definecolor{O}{RGB}{252,133,0}
\usepackage[framemethod=tikz]{mdframed}
\usepackage{lipsum}
\usetikzlibrary{shadows}
\newmdenv[tikzsetting={fill=white},
          roundcorner=0pt,shadow=false,]{myshadowbox}
%%%Highlightbox
\usepackage[framemethod=tikz]{mdframed}
\usepackage{lipsum}
\usetikzlibrary{shadows}
\newmdenv[tikzsetting={fill=ssblue!50},
          roundcorner=0pt,shadow=false,]{highlight}
\newtheorem{example}{Example}
\let\oldexample\example
\renewcommand{\example}{\oldexample\normalfont}
%%%%%%%%%%%%%%%%%Packagaes%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{enumitem}
\usepackage{tikz}
\usepackage{multicol,amsmath,amsfonts}
\usepackage{enumitem}
\usepackage{tasks}
\usepackage{cancel}
%%%%%%%%%table
\usepackage{pbox}
\usepackage{tabularray}
\UseTblrLibrary{booktabs}
\usepackage{xcolor,colortbl}
%%%%%%%%%table
\begin{document}
\begin{enumerate}[labelwidth=1.5em, labelsep=0.5em, wide=0pt]\everymath{\displaystyle}
    \item Fill in the blanks.
        \begin{tasks}label=\alph*), label-width=1.5em, after-item-skip=10pt
            \task Multiply 0.3 by 10.
            \begin{tblr}{colspec = {|X[2,c]|X[0.1,c]|X[2,c]|X[2.3,c]| X[2.4,c]|},
        column{2} = {gray!40},
        cell{1}{1} = {ssblue!40},
        cell{1}{3} = {red!40},
        cell{1}{4} = {yellow!40},
        cell{1}{5} = {Lgreen!40},}
            \hline
             \textbf{Ones} &  & \textbf{Tenths} & \textbf{Hundredths} & \textbf{Thousandths} \\
            \hline
            & $\cdot$ & 3\\
            \hline
            3 & $\cdot$& \\
            \hline
            \end{tblr}

            \begin{align*}
                \text{3 tenths} \times 10 &= \rule{2cm}{0.1mm} \; \text{tenths} \\
                &= \rule{2cm}{0.1mm} \; \text{ones} \\
            \end{align*}
            So, $0.3 \times 10$ = \rule{2cm}{0.1mm}
    \end{tasks}

\end{enumerate}
\end{document}

Answer 1

Something like this? You could automate the task as a whole, probably, if they are similar enough, but I don't know how much variation there is so I've only tried to handle the table.

\tsktens[<key-value list>]{<comma-separated list>} takes an optional and a mandatory argument.

• If specified, the optional argument may be used to change the colours of the column headers for a particular table. The colours are specified as colones={<colour>},coltenths={<colour>} and so on, with coldot=<colour> for the dot column.
• The mandatory argument is a list of entries for the cells of the table from top left to top right and then bottom left to bottom right, with no entry for the second column. Empty cells are specified by empty entries, except these may be omitted if all further values are to be empty. For example, \tsktens{1,2,3,4,5,6,7,8} would create a row for 1.234 above a row for 5.678, while \tsktens{,,1,3} would create a row for __13 above an entirely empty row.
  • To name the contents of cells in order to draw arrows between them, enter the cell value in the form <content>|<name>. <name> should be both unique and simple. (Letters and numbers should be OK. At least some punctuation is not e.g. n.3 doesn't work but a is OK.) For example, ,,3|a,,,3|b will name the node in the first row a and that in the second b. These may then be used in tikzpictures to draw the arrows as shown below.
  • Theoretically, the arrows could be automated, too, but I doubt this makes sense. The labels over the arrows need to be placed in different places to ensure readability. Of course, you can create arguments and key-value interfaces etc., but I doubt the effort would be worth it given that (1) the names need to be unique, (2) the number of arrows may differ, (3) the position and content of labels needs to vary and (4) the colour is probably best varied, too, in case of multiple arrows. However, if you're doing something more restricted, you could always create some form of shortcut.
    • Note that the use of tikzmark to enable arrows with a tabularray environment means at least two compilations are required. If the basic table was created as a matrix of nodes this would be avoidable.
    • If you externalise images, you may need to disable externalisation (external library) or find it is automatically disabled (memoize), depending on the method you use.

If it were not for the use of tabularray, this could be done more concisely, but tabularray needs to parse the rows and columns before typesetting so we can't automate it in ways which would hide the structure from the parser. (Standard tabular etc. don't do this, but they don't have the bells and whistles of tabularray, I guess.)

\documentclass{article}
% ateb: https://tex.stackexchange.com/a/714449/ addaswyd o gwestiwn user292225: https://tex.stackexchange.com/q/714446/
\usepackage{tabularray}
\usepackage{mathtools}
\usepackage{tikz}
\usetikzlibrary{tikzmark,arrows.meta}
\usepackage{enumitem}
\usepackage{tasks}
\definecolor{ssblue}{rgb}{0.22,0.714,1}
\definecolor{myred}{RGB}{214,39,41}
\definecolor{Lgreen}{RGB}{125,173,62}
\newlist{tenumerate}{enumerate}{1}
\setlist[tenumerate]{label=\arabic*.,labelwidth=1.5em,labelsep=0.5em,wide=0pt,before={\everymath{\displaystyle}}}
\ExplSyntaxOn
\seq_new:N \l__tsktens_cells_seq
\seq_new:N \l__tsktens_tmpa_seq
\keys_define:nn { tsktens }
{
  colones .code:n = {\colorlet{colones}{#1}},
  colones .initial:n = {ssblue!40},
  coltenths .code:n = {\colorlet{coltenths}{#1}},
  coltenths .initial:n = {myred!40},
  colhundredths .code:n = {\colorlet{colhundredths}{#1}},
  colhundredths .initial:n = {yellow!40},
  colthousandths .code:n = {\colorlet{colthousandths}{#1}},
  colthousandths .initial:n = {Lgreen!40},
  coldot .code:n = {\colorlet{coldot}{#1}},
  coldot .initial:n = {gray!40},
}
\NewDocumentCommand \tsktens { o m }
{
  \group_begin:
    \IfValueT { #1 }
    {
      \keys_set:nn { tsktens } { #1 }
    }
    \seq_set_split:Nnn \l__tsktens_cells_seq {,} { #2 }
    \seq_map_indexed_inline:Nn \l__tsktens_cells_seq
    {
      \seq_set_split:Nnn \l__tsktens_tmpa_seq { | } { ##2 }
      \int_compare:nNnT { \seq_count:N \l__tsktens_tmpa_seq } = { 2 }
      {
        \exp_args:NNNe \seq_set_item:Nnn \l__tsktens_cells_seq { ##1 } 
        {
          \exp_not:N \tikzmarknode { \seq_item:Nn \l__tsktens_tmpa_seq { 2 } } 
          { \seq_item:Nn \l__tsktens_tmpa_seq { 1 } }
        }
      }
    }
    \begin{tblr}{colspec = {|X[2,c]|X[0.1,c]|X[2,c]|X[2.3,c]| X[2.4,c]|},
        column{2} = {coldot},
        cell{1}{1} = {colones},
        cell{1}{3} = {coltenths},
        cell{1}{4} = {colhundredths},
        cell{1}{5} = {colthousandths},}
      \hline
      \textbf{Ones} &  & \textbf{Tenths} & \textbf{Hundredths} & \textbf{Thousandths} \\
      \hline
      \seq_item:Nn \l__tsktens_cells_seq {1} & $\cdot$ & \seq_item:Nn \l__tsktens_cells_seq {2} & \seq_item:Nn \l__tsktens_cells_seq {3} & \seq_item:Nn \l__tsktens_cells_seq {4} \\
      \hline
      \seq_item:Nn \l__tsktens_cells_seq {5} & $\cdot$ & \seq_item:Nn \l__tsktens_cells_seq {6} & \seq_item:Nn \l__tsktens_cells_seq {7} & \seq_item:Nn \l__tsktens_cells_seq {8} \\
      \hline
    \end{tblr}
  \group_end:
}
\ExplSyntaxOff
\tikzset{%
  >/.tip=Latex,
}
\begin{document}
\begin{tenumerate}
  \item Fill in the blanks.
  \begin{tasks}[label=\alph*), label-width=1.5em, after-item-skip=10pt](1)
    \task Multiply 0.3 by 10.
\tsktens {,3|a,,,3|b}
\begin{tikzpicture}[remember picture,overlay]
  \draw [myred,->] (a) -- node [pos=.75,above,sloped,myred] {$\times 10$} (b);
\end{tikzpicture}

\begin{align*}
  \text{3 tenths} \times 10 &= \rule{2cm}{0.1mm} \; \text{tenths} \\
  &= \rule{2cm}{0.1mm} \; \text{ones} \\
\end{align*}
So, $0.3 \times 10$ = \rule{2cm}{0.1mm}
\task Multiply 0.042 by 100.

\tsktens [colhundredths=magenta!40] {,,4|c,2|d,4|e,2|f}
\begin{tikzpicture}[remember picture,overlay]
  \draw [ssblue,->] (c) -- node [pos=.5,above,sloped,ssblue] {$\times 100$} (e);
  \draw [myred,->] (d) -- node [pos=.65,below,sloped,myred] {$\times 100$} (f);
\end{tikzpicture}


\end{tasks}
\end{tenumerate}
\end{document}