\documentclass[a4paper,11pt]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[french]{babel}
\usepackage[a4paper,top=3.2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\usepackage{fancyhdr}
\usepackage{qrcode}
\usepackage[table]{xcolor}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
% Puces nettes (babel-french remplace sinon la puce par un tiret « – » peu pro).
% Vaut pour TOUTES les fiches qui importent ce module. AtBeginDocument pour
% passer après la personnalisation des listes faite par babel-french.
\AtBeginDocument{%
  \setlist[itemize]{leftmargin=1.8em,itemsep=0.5ex,topsep=0.4ex,parsep=0pt}%
  \setlist[itemize,1]{label=\textcolor{red!75!black}{\small\textbullet}}%
  \setlist[itemize,2]{label=\textcolor{red!75!black}{\scriptsize\textbullet}}%
}
% Titres compacts (gain de place vertical, fiches plus denses) — vaut pour tous.
\usepackage{titlesec}
\titlespacing*{\section}{0pt}{1.4ex}{0.6ex}
\titlespacing*{\subsection}{0pt}{1.0ex}{0.3ex}
% multicol : listes denses (calcul mental) sur 2 colonnes — neutre tant qu'il
% n'est pas utilisé, dispo pour tous les générateurs.
\usepackage{multicol}
\setlength{\columnsep}{1.5em}
% needspace : empêche un titre d'exercice de rester orphelin en bas de page
% (réserve quelques lignes ; sinon le titre passe à la page suivante avec sa
% liste). Neutre tant qu'il n'est pas appelé — dispo pour tous les générateurs.
\usepackage{needspace}
\usepackage{tikz}
\usetikzlibrary{decorations.text}

\usepackage{tgheros}
\pagestyle{fancy}
\fancyhf{}
\setlength{\headheight}{75pt}
\setlength{\headsep}{10pt}

\newcommand{\logowouf}{%
\begin{tikzpicture}[baseline={(current bounding box.center)},scale=0.55,
                    line cap=round,line join=round]
    \path[use as bounding box] (-2.20,-1.45) rectangle (2.20,2.20);
    \path[
        postaction={decorate},
        decoration={
            text along path,
            text={|\fontfamily{qhv}\bfseries\fontsize{9}{9}\selectfont|site2wouf.fr},
            text align={center},
            raise=0.03ex
        }
    ] (-1.29,0.48) arc[start angle=160,end angle=20,radius=1.29];
    \begin{scope}[xshift=-0.06cm]
        \fill[black] (-0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] ( 0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] (-0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black] ( 0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black]
            (0,-0.10)
            .. controls (-0.36,-0.02) and (-0.63,-0.24) .. (-0.58,-0.58)
            .. controls (-0.52,-0.93) and (-0.16,-1.12) .. (0,-0.90)
            .. controls (0.16,-1.12) and (0.52,-0.93) .. (0.58,-0.58)
            .. controls (0.63,-0.24) and (0.36,-0.02) .. (0,-0.10)
            -- cycle;
    \end{scope}
\end{tikzpicture}%
}

\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 72}

\fancyhead[C]{%
\raisebox{4pt}{%
\begin{minipage}[c]{0.15\textwidth}
    \centering
    \logowouf
\end{minipage}
\begin{minipage}[c]{0.62\textwidth}
    \centering
    {\Large\bfseries \titre\par}
    {\small\color{gray} \soustitre}
\end{minipage}
\begin{minipage}[c]{0.21\textwidth}
    \centering
    \qrcode[height=1.5cm]{https://site2wouf.fr/exercices_conversions_cycle3.php?x=72}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0072}
\end{minipage}%
}
}

\begin{document}

\begin{center}
    \small Fractions décimales, multiplication/division par 10, 100, 1 000, conversions d'unités.
\end{center}
\vspace{0.5em}
\sloppy

\needspace{5\baselineskip}
\section*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,032  ~ \(\times\)  ~ 10
\item   7,28  ~ \(\times\)  ~ 10
\item   39,8  ~ \(\times\)  ~ 1 000
\item   3,6  ~ \(\times\)  ~ 100
\item   837  ~ \(\times\)  ~ 100
\item   0,79  ~ \(\times\)  ~ 10
\item   5,26  ~ \(\times\)  ~ 1 000
\item   0,027  ~ \(\times\)  ~ 100
\item   2,84  ~ \(\times\)  ~ 100
\item   2,34  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   41,76  ~ : ~ 1 000
\item   825,1  ~ : ~ 100
\item   67,88  ~ : ~ 10
\item   753  ~ : ~ 10
\item   10,01  ~ : ~ 100
\item   1,104  ~ : ~ 10
\item   25,01  ~ : ~ 10
\item   7,334  ~ : ~ 10
\item   8,958  ~ : ~ 1 000
\item   652,7  ~ : ~ 10
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   0,814  ~ \(\times\)  ~ ... ~ = ~ 814
\item   982  ~ \(\times\)  ~ ... ~ = ~ 98 200
\item   4,76  ~ \(\times\)  ~ ... ~ = ~ 476
\item   66  ~ \(\times\)  ~ ... ~ = ~ 6 600
\item   6,73  ~ \(\times\)  ~ ... ~ = ~ 6 730
\item   37,9  ~ \(\times\)  ~ ... ~ = ~ 379
\item   0,081  ~ \(\times\)  ~ ... ~ = ~ 8,1
\item   92  ~ \(\times\)  ~ ... ~ = ~ 920
\item   439  ~ \(\times\)  ~ ... ~ = ~ 4 390
\item   0,666  ~ \(\times\)  ~ ... ~ = ~ 6,66
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   9 581  ~ \(\times\)  ~ 0,01
\item   339,6  ~ \(\times\)  ~ 0,1
\item   5,385  ~ \(\times\)  ~ 0,1
\item   589,6  ~ \(\times\)  ~ 0,1
\item   8,795  ~ \(\times\)  ~ 0,1
\item   6 352  ~ \(\times\)  ~ 0,001
\item   55,93  ~ \(\times\)  ~ 0,01
\item   939,4  ~ \(\times\)  ~ 0,01
\item   0,575  ~ \(\times\)  ~ 0,1
\item   8,647  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   5,98  ~ \(\times\)  ~ ... ~ = ~  0,598
\item   3,183  ~ \(\times\)  ~ ... ~ = ~  0,031 83
\item   7 629  ~ \(\times\)  ~ ... ~ = ~  7,629
\item   36,58  ~ \(\times\)  ~ ... ~ = ~  0,036 58
\item   5,96  ~ \(\times\)  ~ ... ~ = ~  0,005 96
\item   9 699  ~ \(\times\)  ~ ... ~ = ~  969,9
\item   1,855  ~ \(\times\)  ~ ... ~ = ~  0,185 5
\item   2 047  ~ \(\times\)  ~ ... ~ = ~  20,47
\item   89,13  ~ \(\times\)  ~ ... ~ = ~  0,891 3
\item   291  ~ \(\times\)  ~ ... ~ = ~  0,291
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~cm~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   1 641,2 ~kL~ = ...~daL
\item   307,44 ~daL~ = ...~mL
\item   664,27 ~hL~ = ...~cL
\item   9 019 ~mL~ = ...~cL
\item   257,16 ~kg~ = ...~dag
\item   286,66 ~km~ = ...~cm
\item   327,44 ~kL~ = ...~mL
\item   556,81 ~km~ = ...~hm
\item   514,94 ~hm~ = ...~dm
\item   6 609,2 ~mm~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{5500}{100}\) = \(\dfrac{550}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{900}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{580}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,032  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,32}
\item   7,28  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 72,8}
\item   39,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 39 800}
\item   3,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 360}
\item   837  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 83 700}
\item   0,79  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,9}
\item   5,26  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 260}
\item   0,027  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,7}
\item   2,84  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 284}
\item   2,34  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 234}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   41,76 ~ : ~ 1 000 ~ = ~{\color{red} 0,041 76}
\item   825,1 ~ : ~ 100 ~ = ~{\color{red} 8,251}
\item   67,88 ~ : ~ 10 ~ = ~{\color{red} 6,788}
\item   753 ~ : ~ 10 ~ = ~{\color{red} 75,3}
\item   10,01 ~ : ~ 100 ~ = ~{\color{red} 0,100 1}
\item   1,104 ~ : ~ 10 ~ = ~{\color{red} 0,110 4}
\item   25,01 ~ : ~ 10 ~ = ~{\color{red} 2,501}
\item   7,334 ~ : ~ 10 ~ = ~{\color{red} 0,733 4}
\item   8,958 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 958}
\item   652,7 ~ : ~ 10 ~ = ~{\color{red} 65,27}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   0,814 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~814
\item   982 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~98 200
\item   4,76 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~476
\item   66 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 600
\item   6,73 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 730
\item   37,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~379
\item   0,081 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,1
\item   92 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~920
\item   439 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 390
\item   0,666 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,66
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   9 581 ~ \(\times\)  0,01 ~ = ~{\color{red} 95,81
}\item   339,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 33,96
}\item   5,385 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,538 5
}\item   589,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 58,96
}\item   8,795 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,879 5
}\item   6 352 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,352
}\item   55,93 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,559 3
}\item   939,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,394
}\item   0,575 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,057 5
}\item   8,647 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,086 47
}\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   5,98 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,598
\item   3,183 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,031 83
\item   7 629 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,629
\item   36,58 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,036 58
\item   5,96 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 96
\item   9 699 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 969,9
\item   1,855 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,185 5
\item   2 047 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 20,47
\item   89,13 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,891 3
\item   291 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,291
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   1 641,2 ~kL~ = {\color{red}  164 120 }~daL
\item   307,44 ~daL~ = {\color{red}  3 074 400 }~mL
\item   664,27 ~hL~ = {\color{red}  6 642 700 }~cL
\item   9 019 ~mL~ = {\color{red}  901,9 }~cL
\item   257,16 ~kg~ = {\color{red}  25 716 }~dag
\item   286,66 ~km~ = {\color{red}  28 666 000 }~cm
\item   327,44 ~kL~ = {\color{red}  327 440 000 }~mL
\item   556,81 ~km~ = {\color{red}  5 568,1 }~hm
\item   514,94 ~hm~ = {\color{red}  514 940 }~dm
\item   6 609,2 ~mm~ = {\color{red}  66,092 }~dm
\end{itemize}
\end{multicols}
\end{document}
