\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 73}

\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=73}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0073}
\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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,81  ~ \(\times\)  ~ 1 000
\item   0,084  ~ \(\times\)  ~ 100
\item   0,054  ~ \(\times\)  ~ 10
\item   470  ~ \(\times\)  ~ 10
\item   0,27  ~ \(\times\)  ~ 10
\item   4,34  ~ \(\times\)  ~ 1 000
\item   0,441  ~ \(\times\)  ~ 1 000
\item   45,2  ~ \(\times\)  ~ 10
\item   9,68  ~ \(\times\)  ~ 1 000
\item   61,8  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,588  ~ : ~ 1 000
\item   58,28  ~ : ~ 10
\item   3 852  ~ : ~ 10
\item   45,39  ~ : ~ 1 000
\item   90,2  ~ : ~ 1 000
\item   2,887  ~ : ~ 10
\item   1 456  ~ : ~ 1 000
\item   323,1  ~ : ~ 1 000
\item   2,436  ~ : ~ 100
\item   808,1  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,87  ~ \(\times\)  ~ ... ~ = ~ 88,7
\item   0,066  ~ \(\times\)  ~ ... ~ = ~ 0,66
\item   0,831  ~ \(\times\)  ~ ... ~ = ~ 83,1
\item   872  ~ \(\times\)  ~ ... ~ = ~ 872 000
\item   745  ~ \(\times\)  ~ ... ~ = ~ 74 500
\item   42,9  ~ \(\times\)  ~ ... ~ = ~ 4 290
\item   0,807  ~ \(\times\)  ~ ... ~ = ~ 8,07
\item   14,8  ~ \(\times\)  ~ ... ~ = ~ 148
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 8,4
\item   0,885  ~ \(\times\)  ~ ... ~ = ~ 88,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,343  ~ \(\times\)  ~ 0,1
\item   8 105  ~ \(\times\)  ~ 0,001
\item   1 664  ~ \(\times\)  ~ 0,001
\item   4,388  ~ \(\times\)  ~ 0,001
\item   158,2  ~ \(\times\)  ~ 0,01
\item   83,8  ~ \(\times\)  ~ 0,1
\item   8,79  ~ \(\times\)  ~ 0,1
\item   2,334  ~ \(\times\)  ~ 0,1
\item   9,772  ~ \(\times\)  ~ 0,001
\item   2 646  ~ \(\times\)  ~ 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   229,5  ~ \(\times\)  ~ ... ~ = ~  0,229 5
\item   638,2  ~ \(\times\)  ~ ... ~ = ~  6,382
\item   1 278  ~ \(\times\)  ~ ... ~ = ~  1,278
\item   68,55  ~ \(\times\)  ~ ... ~ = ~  0,068 55
\item   62,85  ~ \(\times\)  ~ ... ~ = ~  6,285
\item   5,006  ~ \(\times\)  ~ ... ~ = ~  0,050 06
\item   2,302  ~ \(\times\)  ~ ... ~ = ~  0,023 02
\item   7,814  ~ \(\times\)  ~ ... ~ = ~  0,781 4
\item   82,21  ~ \(\times\)  ~ ... ~ = ~  0,822 1
\item   8 707  ~ \(\times\)  ~ ... ~ = ~  87,07
\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~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   278,78 ~cm~ = ...~dam
\item   884,2 ~hg~ = ...~kg
\item   140,24 ~hm~ = ...~mm
\item   2 069,2 ~hm~ = ...~dam
\item   752,19 ~dL~ = ...~mL
\item   118,54 ~hg~ = ...~g
\item   808,37 ~L~ = ...~cL
\item   139,24 ~km~ = ...~hm
\item   510,03 ~km~ = ...~cm
\item   5 288,5 ~dL~ = ...~hL
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{750}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{340}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,81  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 810}
\item   0,084  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,4}
\item   0,054  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,54}
\item   470  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 700}
\item   0,27  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,7}
\item   4,34  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 340}
\item   0,441  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 441}
\item   45,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 452}
\item   9,68  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 680}
\item   61,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 61 800}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,588 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 588}
\item   58,28 ~ : ~ 10 ~ = ~{\color{red} 5,828}
\item   3 852 ~ : ~ 10 ~ = ~{\color{red} 385,2}
\item   45,39 ~ : ~ 1 000 ~ = ~{\color{red} 0,045 39}
\item   90,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,090 2}
\item   2,887 ~ : ~ 10 ~ = ~{\color{red} 0,288 7}
\item   1 456 ~ : ~ 1 000 ~ = ~{\color{red} 1,456}
\item   323,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,323 1}
\item   2,436 ~ : ~ 100 ~ = ~{\color{red} 0,024 36}
\item   808,1 ~ : ~ 100 ~ = ~{\color{red} 8,081}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,87 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~88,7
\item   0,066 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,66
\item   0,831 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~83,1
\item   872 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~872 000
\item   745 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74 500
\item   42,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 290
\item   0,807 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,07
\item   14,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~148
\item   0,084 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,4
\item   0,885 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,343 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,434 3
}\item   8 105 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,105
}\item   1 664 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,664
}\item   4,388 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 388
}\item   158,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,582
}\item   83,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,38
}\item   8,79 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,879
}\item   2,334 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,233 4
}\item   9,772 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 772
}\item   2 646 ~ \(\times\)  0,1 ~ = ~{\color{red} 264,6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   229,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,229 5
\item   638,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,382
\item   1 278 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,278
\item   68,55 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,068 55
\item   62,85 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,285
\item   5,006 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,050 06
\item   2,302 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,023 02
\item   7,814 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,781 4
\item   82,21 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,822 1
\item   8 707 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 87,07
\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~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   278,78 ~cm~ = {\color{red}  0,278 78 }~dam
\item   884,2 ~hg~ = {\color{red}  88,42 }~kg
\item   140,24 ~hm~ = {\color{red}  14 024 000 }~mm
\item   2 069,2 ~hm~ = {\color{red}  20 692 }~dam
\item   752,19 ~dL~ = {\color{red}  75 219 }~mL
\item   118,54 ~hg~ = {\color{red}  11 854 }~g
\item   808,37 ~L~ = {\color{red}  80 837 }~cL
\item   139,24 ~km~ = {\color{red}  1 392,4 }~hm
\item   510,03 ~km~ = {\color{red}  51 003 000 }~cm
\item   5 288,5 ~dL~ = {\color{red}  5,288 5 }~hL
\end{itemize}
\end{multicols}
\end{document}
