\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 287}

\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=287}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0287}
\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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{26}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{32}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,044  ~ \(\times\)  ~ 1 000
\item   53,5  ~ \(\times\)  ~ 10
\item   1,58  ~ \(\times\)  ~ 100
\item   0,2  ~ \(\times\)  ~ 1 000
\item   118  ~ \(\times\)  ~ 1 000
\item   5,6  ~ \(\times\)  ~ 1 000
\item   0,822  ~ \(\times\)  ~ 1 000
\item   20,5  ~ \(\times\)  ~ 1 000
\item   0,697  ~ \(\times\)  ~ 10
\item   0,099  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   72,79  ~ : ~ 1 000
\item   7 839  ~ : ~ 10
\item   18,13  ~ : ~ 1 000
\item   8,744  ~ : ~ 10
\item   60,6  ~ : ~ 1 000
\item   5 411  ~ : ~ 1 000
\item   63,7  ~ : ~ 1 000
\item   9,489  ~ : ~ 100
\item   43,53  ~ : ~ 1 000
\item   836,5  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,72  ~ \(\times\)  ~ ... ~ = ~ 47,2
\item   149  ~ \(\times\)  ~ ... ~ = ~ 14 900
\item   320  ~ \(\times\)  ~ ... ~ = ~ 3 200
\item   0,012  ~ \(\times\)  ~ ... ~ = ~ 1,2
\item   2,52  ~ \(\times\)  ~ ... ~ = ~ 2 520
\item   73,4  ~ \(\times\)  ~ ... ~ = ~ 73 400
\item   0,582  ~ \(\times\)  ~ ... ~ = ~ 58,2
\item   0,016  ~ \(\times\)  ~ ... ~ = ~ 16
\item   4,95  ~ \(\times\)  ~ ... ~ = ~ 4 950
\item   14,8  ~ \(\times\)  ~ ... ~ = ~ 14 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   570,7  ~ \(\times\)  ~ 0,1
\item   64,03  ~ \(\times\)  ~ 0,1
\item   65,58  ~ \(\times\)  ~ 0,1
\item   6 000  ~ \(\times\)  ~ 0,001
\item   8 506  ~ \(\times\)  ~ 0,1
\item   90,3  ~ \(\times\)  ~ 0,001
\item   7 693  ~ \(\times\)  ~ 0,1
\item   519,2  ~ \(\times\)  ~ 0,01
\item   235,7  ~ \(\times\)  ~ 0,01
\item   1,206  ~ \(\times\)  ~ 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   6,835  ~ \(\times\)  ~ ... ~ = ~  0,006 835
\item   92,46  ~ \(\times\)  ~ ... ~ = ~  0,092 46
\item   8,975  ~ \(\times\)  ~ ... ~ = ~  0,089 75
\item   708,4  ~ \(\times\)  ~ ... ~ = ~  70,84
\item   74,3  ~ \(\times\)  ~ ... ~ = ~  0,074 3
\item   7 499  ~ \(\times\)  ~ ... ~ = ~  749,9
\item   672,8  ~ \(\times\)  ~ ... ~ = ~  67,28
\item   5,81  ~ \(\times\)  ~ ... ~ = ~  0,005 81
\item   940,9  ~ \(\times\)  ~ ... ~ = ~  0,940 9
\item   4 994  ~ \(\times\)  ~ ... ~ = ~  49,94
\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 ~dam~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   272,57 ~daL~ = ...~hL
\item   376,21 ~mg~ = ...~g
\item   3 862,7 ~cL~ = ...~dL
\item   355,05 ~L~ = ...~daL
\item   1 398,2 ~dam~ = ...~mm
\item   629,1 ~hL~ = ...~dL
\item   531,59 ~kL~ = ...~dL
\item   218,16 ~mm~ = ...~hm
\item   4 706,8 ~cg~ = ...~kg
\item   8 113,5 ~mm~ = ...~cm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{510}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{26}{10}\) = \(\dfrac{260}{100}\)
\item   \(\dfrac{32}{100}\) = \(\dfrac{320}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,044  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 44}
\item   53,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 535}
\item   1,58  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 158}
\item   0,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 200}
\item   118  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 118 000}
\item   5,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 600}
\item   0,822  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 822}
\item   20,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 20 500}
\item   0,697  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,97}
\item   0,099  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 99}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   72,79 ~ : ~ 1 000 ~ = ~{\color{red} 0,072 79}
\item   7 839 ~ : ~ 10 ~ = ~{\color{red} 783,9}
\item   18,13 ~ : ~ 1 000 ~ = ~{\color{red} 0,018 13}
\item   8,744 ~ : ~ 10 ~ = ~{\color{red} 0,874 4}
\item   60,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,060 6}
\item   5 411 ~ : ~ 1 000 ~ = ~{\color{red} 5,411}
\item   63,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,063 7}
\item   9,489 ~ : ~ 100 ~ = ~{\color{red} 0,094 89}
\item   43,53 ~ : ~ 1 000 ~ = ~{\color{red} 0,043 53}
\item   836,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,836 5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,72 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~47,2
\item   149 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~14 900
\item   320 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 200
\item   0,012 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,2
\item   2,52 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 520
\item   73,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~73 400
\item   0,582 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~58,2
\item   0,016 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~16
\item   4,95 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 950
\item   14,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   570,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 57,07
}\item   64,03 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,403
}\item   65,58 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,558
}\item   6 000 ~ \(\times\)  0,001 ~ = ~{\color{red} 6
}\item   8 506 ~ \(\times\)  0,1 ~ = ~{\color{red} 850,6
}\item   90,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,090 3
}\item   7 693 ~ \(\times\)  0,1 ~ = ~{\color{red} 769,3
}\item   519,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,192
}\item   235,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,357
}\item   1,206 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,120 6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,835 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 835
\item   92,46 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,092 46
\item   8,975 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,089 75
\item   708,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 70,84
\item   74,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,074 3
\item   7 499 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 749,9
\item   672,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 67,28
\item   5,81 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 81
\item   940,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,940 9
\item   4 994 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 49,94
\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 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   272,57 ~daL~ = {\color{red}  27,257 }~hL
\item   376,21 ~mg~ = {\color{red}  0,376 21 }~g
\item   3 862,7 ~cL~ = {\color{red}  386,27 }~dL
\item   355,05 ~L~ = {\color{red}  35,505 }~daL
\item   1 398,2 ~dam~ = {\color{red}  13 982 000 }~mm
\item   629,1 ~hL~ = {\color{red}  629 100 }~dL
\item   531,59 ~kL~ = {\color{red}  5 315 900 }~dL
\item   218,16 ~mm~ = {\color{red}  0,002 181 6 }~hm
\item   4 706,8 ~cg~ = {\color{red}  0,047 068 }~kg
\item   8 113,5 ~mm~ = {\color{red}  811,35 }~cm
\end{itemize}
\end{multicols}
\end{document}
