\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 278}

\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=278}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0278}
\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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{72}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,706  ~ \(\times\)  ~ 100
\item   0,237  ~ \(\times\)  ~ 1 000
\item   2,59  ~ \(\times\)  ~ 100
\item   7,99  ~ \(\times\)  ~ 10
\item   0,041  ~ \(\times\)  ~ 10
\item   0,626  ~ \(\times\)  ~ 1 000
\item   882  ~ \(\times\)  ~ 10
\item   0,669  ~ \(\times\)  ~ 1 000
\item   0,063  ~ \(\times\)  ~ 100
\item   684  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   29,22  ~ : ~ 1 000
\item   74,32  ~ : ~ 100
\item   64,6  ~ : ~ 1 000
\item   1,186  ~ : ~ 100
\item   334,1  ~ : ~ 100
\item   2 774  ~ : ~ 10
\item   715,3  ~ : ~ 1 000
\item   13,62  ~ : ~ 10
\item   572,7  ~ : ~ 1 000
\item   394,9  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,19  ~ \(\times\)  ~ ... ~ = ~ 419
\item   1,34  ~ \(\times\)  ~ ... ~ = ~ 1 340
\item   35,6  ~ \(\times\)  ~ ... ~ = ~ 356
\item   41  ~ \(\times\)  ~ ... ~ = ~ 41 000
\item   41,6  ~ \(\times\)  ~ ... ~ = ~ 41 600
\item   0,606  ~ \(\times\)  ~ ... ~ = ~ 6,06
\item   0,087  ~ \(\times\)  ~ ... ~ = ~ 87
\item   0,337  ~ \(\times\)  ~ ... ~ = ~ 3,37
\item   6  ~ \(\times\)  ~ ... ~ = ~ 6 000
\item   0,88  ~ \(\times\)  ~ ... ~ = ~ 88
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   12,91  ~ \(\times\)  ~ 0,1
\item   49,01  ~ \(\times\)  ~ 0,1
\item   1 119  ~ \(\times\)  ~ 0,01
\item   463,2  ~ \(\times\)  ~ 0,01
\item   378  ~ \(\times\)  ~ 0,01
\item   6 902  ~ \(\times\)  ~ 0,01
\item   66,9  ~ \(\times\)  ~ 0,01
\item   3 853  ~ \(\times\)  ~ 0,1
\item   8 907  ~ \(\times\)  ~ 0,001
\item   7 620  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   62,73  ~ \(\times\)  ~ ... ~ = ~  0,627 3
\item   312,5  ~ \(\times\)  ~ ... ~ = ~  31,25
\item   3,418  ~ \(\times\)  ~ ... ~ = ~  0,003 418
\item   57,88  ~ \(\times\)  ~ ... ~ = ~  5,788
\item   7,838  ~ \(\times\)  ~ ... ~ = ~  0,783 8
\item   4,7  ~ \(\times\)  ~ ... ~ = ~  0,004 7
\item   1 841  ~ \(\times\)  ~ ... ~ = ~  184,1
\item   2,638  ~ \(\times\)  ~ ... ~ = ~  0,002 638
\item   5 791  ~ \(\times\)  ~ ... ~ = ~  579,1
\item   4 951  ~ \(\times\)  ~ ... ~ = ~  49,51
\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 ~dm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   906,36 ~dag~ = ...~cg
\item   6 776,4 ~cL~ = ...~mL
\item   6 899,4 ~hg~ = ...~g
\item   551,1 ~mL~ = ...~kL
\item   861,05 ~hL~ = ...~cL
\item   6 873,9 ~hm~ = ...~m
\item   6 438,8 ~dL~ = ...~L
\item   8 535,4 ~hm~ = ...~km
\item   5 011,9 ~dg~ = ...~g
\item   145,08 ~dm~ = ...~km
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{460}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{72}{10}\) = \(\dfrac{720}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{920}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,706  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 70,6}
\item   0,237  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 237}
\item   2,59  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 259}
\item   7,99  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 79,9}
\item   0,041  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,41}
\item   0,626  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 626}
\item   882  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 820}
\item   0,669  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 669}
\item   0,063  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,3}
\item   684  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 684 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   29,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,029 22}
\item   74,32 ~ : ~ 100 ~ = ~{\color{red} 0,743 2}
\item   64,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,064 6}
\item   1,186 ~ : ~ 100 ~ = ~{\color{red} 0,011 86}
\item   334,1 ~ : ~ 100 ~ = ~{\color{red} 3,341}
\item   2 774 ~ : ~ 10 ~ = ~{\color{red} 277,4}
\item   715,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,715 3}
\item   13,62 ~ : ~ 10 ~ = ~{\color{red} 1,362}
\item   572,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,572 7}
\item   394,9 ~ : ~ 100 ~ = ~{\color{red} 3,949}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,19 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~419
\item   1,34 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 340
\item   35,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~356
\item   41 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~41 000
\item   41,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~41 600
\item   0,606 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,06
\item   0,087 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~87
\item   0,337 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,37
\item   6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 000
\item   0,88 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   12,91 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,291
}\item   49,01 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,901
}\item   1 119 ~ \(\times\)  0,01 ~ = ~{\color{red} 11,19
}\item   463,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,632
}\item   378 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,78
}\item   6 902 ~ \(\times\)  0,01 ~ = ~{\color{red} 69,02
}\item   66,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,669
}\item   3 853 ~ \(\times\)  0,1 ~ = ~{\color{red} 385,3
}\item   8 907 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,907
}\item   7 620 ~ \(\times\)  0,1 ~ = ~{\color{red} 762
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   62,73 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,627 3
\item   312,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 31,25
\item   3,418 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 418
\item   57,88 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,788
\item   7,838 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,783 8
\item   4,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 7
\item   1 841 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 184,1
\item   2,638 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 638
\item   5 791 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 579,1
\item   4 951 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 49,51
\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 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   906,36 ~dag~ = {\color{red}  906 360 }~cg
\item   6 776,4 ~cL~ = {\color{red}  67 764 }~mL
\item   6 899,4 ~hg~ = {\color{red}  689 940 }~g
\item   551,1 ~mL~ = {\color{red}  0,000 551 1 }~kL
\item   861,05 ~hL~ = {\color{red}  8 610 500 }~cL
\item   6 873,9 ~hm~ = {\color{red}  687 390 }~m
\item   6 438,8 ~dL~ = {\color{red}  643,88 }~L
\item   8 535,4 ~hm~ = {\color{red}  853,54 }~km
\item   5 011,9 ~dg~ = {\color{red}  501,19 }~g
\item   145,08 ~dm~ = {\color{red}  0,014 508 }~km
\end{itemize}
\end{multicols}
\end{document}
