\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 144}

\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=144}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0144}
\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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{61}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,099  ~ \(\times\)  ~ 100
\item   61  ~ \(\times\)  ~ 100
\item   71  ~ \(\times\)  ~ 10
\item   438  ~ \(\times\)  ~ 100
\item   13,3  ~ \(\times\)  ~ 1 000
\item   27,1  ~ \(\times\)  ~ 1 000
\item   274  ~ \(\times\)  ~ 100
\item   705  ~ \(\times\)  ~ 1 000
\item   36,4  ~ \(\times\)  ~ 1 000
\item   0,025  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,509  ~ : ~ 100
\item   325,3  ~ : ~ 1 000
\item   65,83  ~ : ~ 10
\item   4 337  ~ : ~ 1 000
\item   7,446  ~ : ~ 1 000
\item   10,02  ~ : ~ 100
\item   42,48  ~ : ~ 10
\item   3,559  ~ : ~ 10
\item   5,27  ~ : ~ 10
\item   3,337  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,6  ~ \(\times\)  ~ ... ~ = ~ 20 600
\item   462  ~ \(\times\)  ~ ... ~ = ~ 4 620
\item   57,1  ~ \(\times\)  ~ ... ~ = ~ 57 100
\item   0,053  ~ \(\times\)  ~ ... ~ = ~ 53
\item   0,048  ~ \(\times\)  ~ ... ~ = ~ 4,8
\item   659  ~ \(\times\)  ~ ... ~ = ~ 659 000
\item   0,098  ~ \(\times\)  ~ ... ~ = ~ 0,98
\item   0,362  ~ \(\times\)  ~ ... ~ = ~ 36,2
\item   823  ~ \(\times\)  ~ ... ~ = ~ 823 000
\item   6,62  ~ \(\times\)  ~ ... ~ = ~ 6 620
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   252,2  ~ \(\times\)  ~ 0,001
\item   579,6  ~ \(\times\)  ~ 0,1
\item   4,279  ~ \(\times\)  ~ 0,01
\item   1 455  ~ \(\times\)  ~ 0,01
\item   5,718  ~ \(\times\)  ~ 0,001
\item   3 066  ~ \(\times\)  ~ 0,01
\item   8,989  ~ \(\times\)  ~ 0,01
\item   502,1  ~ \(\times\)  ~ 0,1
\item   3 877  ~ \(\times\)  ~ 0,1
\item   11,99  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   834  ~ \(\times\)  ~ ... ~ = ~  83,4
\item   5 109  ~ \(\times\)  ~ ... ~ = ~  510,9
\item   73,46  ~ \(\times\)  ~ ... ~ = ~  0,734 6
\item   2 789  ~ \(\times\)  ~ ... ~ = ~  2,789
\item   661,6  ~ \(\times\)  ~ ... ~ = ~  6,616
\item   5 837  ~ \(\times\)  ~ ... ~ = ~  583,7
\item   3,674  ~ \(\times\)  ~ ... ~ = ~  0,036 74
\item   522,4  ~ \(\times\)  ~ ... ~ = ~  52,24
\item   332,9  ~ \(\times\)  ~ ... ~ = ~  3,329
\item   737,3  ~ \(\times\)  ~ ... ~ = ~  73,73
\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~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~km
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 731,8 ~daL~ = ...~cL
\item   4 381,2 ~cm~ = ...~dm
\item   192,38 ~cL~ = ...~kL
\item   470,27 ~mm~ = ...~dam
\item   7 533,1 ~hL~ = ...~dL
\item   5 882,4 ~dag~ = ...~cg
\item   8 847,2 ~dam~ = ...~m
\item   9 870,7 ~dam~ = ...~mm
\item   522,01 ~m~ = ...~mm
\item   798,71 ~daL~ = ...~mL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{6900}{100}\) = \(\dfrac{690}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{320}{100}\)
\item   \(\dfrac{61}{100}\) = \(\dfrac{610}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,099  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,9}
\item   61  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 100}
\item   71  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 710}
\item   438  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 43 800}
\item   13,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 13 300}
\item   27,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 27 100}
\item   274  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 27 400}
\item   705  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 705 000}
\item   36,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 36 400}
\item   0,025  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,509 ~ : ~ 100 ~ = ~{\color{red} 0,015 09}
\item   325,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,325 3}
\item   65,83 ~ : ~ 10 ~ = ~{\color{red} 6,583}
\item   4 337 ~ : ~ 1 000 ~ = ~{\color{red} 4,337}
\item   7,446 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 446}
\item   10,02 ~ : ~ 100 ~ = ~{\color{red} 0,100 2}
\item   42,48 ~ : ~ 10 ~ = ~{\color{red} 4,248}
\item   3,559 ~ : ~ 10 ~ = ~{\color{red} 0,355 9}
\item   5,27 ~ : ~ 10 ~ = ~{\color{red} 0,527}
\item   3,337 ~ : ~ 100 ~ = ~{\color{red} 0,033 37}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~20 600
\item   462 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 620
\item   57,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~57 100
\item   0,053 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~53
\item   0,048 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4,8
\item   659 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~659 000
\item   0,098 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,98
\item   0,362 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~36,2
\item   823 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~823 000
\item   6,62 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 620
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   252,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,252 2
}\item   579,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 57,96
}\item   4,279 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,042 79
}\item   1 455 ~ \(\times\)  0,01 ~ = ~{\color{red} 14,55
}\item   5,718 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 718
}\item   3 066 ~ \(\times\)  0,01 ~ = ~{\color{red} 30,66
}\item   8,989 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,089 89
}\item   502,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 50,21
}\item   3 877 ~ \(\times\)  0,1 ~ = ~{\color{red} 387,7
}\item   11,99 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,011 99
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   834 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 83,4
\item   5 109 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 510,9
\item   73,46 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,734 6
\item   2 789 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,789
\item   661,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,616
\item   5 837 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 583,7
\item   3,674 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,036 74
\item   522,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 52,24
\item   332,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,329
\item   737,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 73,73
\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~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 731,8 ~daL~ = {\color{red}  6 731 800 }~cL
\item   4 381,2 ~cm~ = {\color{red}  438,12 }~dm
\item   192,38 ~cL~ = {\color{red}  0,001 923 8 }~kL
\item   470,27 ~mm~ = {\color{red}  0,047 027 }~dam
\item   7 533,1 ~hL~ = {\color{red}  7 533 100 }~dL
\item   5 882,4 ~dag~ = {\color{red}  5 882 400 }~cg
\item   8 847,2 ~dam~ = {\color{red}  88 472 }~m
\item   9 870,7 ~dam~ = {\color{red}  98 707 000 }~mm
\item   522,01 ~m~ = {\color{red}  522 010 }~mm
\item   798,71 ~daL~ = {\color{red}  7 987 100 }~mL
\end{itemize}
\end{multicols}
\end{document}
