\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 87}

\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=87}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0087}
\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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,067  ~ \(\times\)  ~ 1 000
\item   344  ~ \(\times\)  ~ 100
\item   0,24  ~ \(\times\)  ~ 100
\item   781  ~ \(\times\)  ~ 100
\item   0,054  ~ \(\times\)  ~ 1 000
\item   8  ~ \(\times\)  ~ 100
\item   97,4  ~ \(\times\)  ~ 1 000
\item   578  ~ \(\times\)  ~ 100
\item   0,38  ~ \(\times\)  ~ 100
\item   0,618  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   748,7  ~ : ~ 1 000
\item   578,7  ~ : ~ 1 000
\item   79,65  ~ : ~ 10
\item   5 030  ~ : ~ 100
\item   5 726  ~ : ~ 1 000
\item   96,5  ~ : ~ 100
\item   9 851  ~ : ~ 10
\item   8 840  ~ : ~ 1 000
\item   10,99  ~ : ~ 100
\item   3,367  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,003  ~ \(\times\)  ~ ... ~ = ~ 0,3
\item   79,8  ~ \(\times\)  ~ ... ~ = ~ 7 980
\item   3,02  ~ \(\times\)  ~ ... ~ = ~ 302
\item   85,5  ~ \(\times\)  ~ ... ~ = ~ 85 500
\item   2,45  ~ \(\times\)  ~ ... ~ = ~ 24,5
\item   6,78  ~ \(\times\)  ~ ... ~ = ~ 67,8
\item   124  ~ \(\times\)  ~ ... ~ = ~ 12 400
\item   3,1  ~ \(\times\)  ~ ... ~ = ~ 31
\item   0,024  ~ \(\times\)  ~ ... ~ = ~ 2,4
\item   8,09  ~ \(\times\)  ~ ... ~ = ~ 80,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   688,2  ~ \(\times\)  ~ 0,001
\item   5 487  ~ \(\times\)  ~ 0,001
\item   35,21  ~ \(\times\)  ~ 0,1
\item   592  ~ \(\times\)  ~ 0,1
\item   8 625  ~ \(\times\)  ~ 0,1
\item   825,1  ~ \(\times\)  ~ 0,01
\item   519  ~ \(\times\)  ~ 0,001
\item   6 017  ~ \(\times\)  ~ 0,01
\item   72,46  ~ \(\times\)  ~ 0,1
\item   31,62  ~ \(\times\)  ~ 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   2,851  ~ \(\times\)  ~ ... ~ = ~  0,285 1
\item   70,38  ~ \(\times\)  ~ ... ~ = ~  0,703 8
\item   784,7  ~ \(\times\)  ~ ... ~ = ~  0,784 7
\item   26,2  ~ \(\times\)  ~ ... ~ = ~  0,262
\item   454,2  ~ \(\times\)  ~ ... ~ = ~  0,454 2
\item   82,12  ~ \(\times\)  ~ ... ~ = ~  0,082 12
\item   2 990  ~ \(\times\)  ~ ... ~ = ~  29,9
\item   1,959  ~ \(\times\)  ~ ... ~ = ~  0,195 9
\item   96,21  ~ \(\times\)  ~ ... ~ = ~  0,962 1
\item   17,74  ~ \(\times\)  ~ ... ~ = ~  1,774
\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 ~km~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 235,1 ~km~ = ...~dm
\item   9 218,3 ~kL~ = ...~hL
\item   2 786,5 ~hL~ = ...~dL
\item   4 393,4 ~g~ = ...~dag
\item   517,7 ~km~ = ...~hm
\item   116,3 ~cL~ = ...~mL
\item   9 508,6 ~dg~ = ...~kg
\item   8 371,7 ~hm~ = ...~dam
\item   238,09 ~cg~ = ...~mg
\item   399,08 ~dam~ = ...~mm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{8000}{100}\) = \(\dfrac{800}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{460}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{530}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,067  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 67}
\item   344  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 34 400}
\item   0,24  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 24}
\item   781  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 78 100}
\item   0,054  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 54}
\item   8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 800}
\item   97,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 97 400}
\item   578  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 57 800}
\item   0,38  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 38}
\item   0,618  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 61,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   748,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,748 7}
\item   578,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,578 7}
\item   79,65 ~ : ~ 10 ~ = ~{\color{red} 7,965}
\item   5 030 ~ : ~ 100 ~ = ~{\color{red} 50,3}
\item   5 726 ~ : ~ 1 000 ~ = ~{\color{red} 5,726}
\item   96,5 ~ : ~ 100 ~ = ~{\color{red} 0,965}
\item   9 851 ~ : ~ 10 ~ = ~{\color{red} 985,1}
\item   8 840 ~ : ~ 1 000 ~ = ~{\color{red} 8,84}
\item   10,99 ~ : ~ 100 ~ = ~{\color{red} 0,109 9}
\item   3,367 ~ : ~ 100 ~ = ~{\color{red} 0,033 67}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,003 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,3
\item   79,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 980
\item   3,02 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~302
\item   85,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~85 500
\item   2,45 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~24,5
\item   6,78 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~67,8
\item   124 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~12 400
\item   3,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~31
\item   0,024 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,4
\item   8,09 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~80,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   688,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,688 2
}\item   5 487 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,487
}\item   35,21 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,521
}\item   592 ~ \(\times\)  0,1 ~ = ~{\color{red} 59,2
}\item   8 625 ~ \(\times\)  0,1 ~ = ~{\color{red} 862,5
}\item   825,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,251
}\item   519 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,519
}\item   6 017 ~ \(\times\)  0,01 ~ = ~{\color{red} 60,17
}\item   72,46 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,246
}\item   31,62 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,031 62
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,851 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,285 1
\item   70,38 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,703 8
\item   784,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,784 7
\item   26,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,262
\item   454,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,454 2
\item   82,12 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,082 12
\item   2 990 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 29,9
\item   1,959 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,195 9
\item   96,21 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,962 1
\item   17,74 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,774
\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 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 235,1 ~km~ = {\color{red}  52 351 000 }~dm
\item   9 218,3 ~kL~ = {\color{red}  92 183 }~hL
\item   2 786,5 ~hL~ = {\color{red}  2 786 500 }~dL
\item   4 393,4 ~g~ = {\color{red}  439,34 }~dag
\item   517,7 ~km~ = {\color{red}  5 177 }~hm
\item   116,3 ~cL~ = {\color{red}  1 163 }~mL
\item   9 508,6 ~dg~ = {\color{red}  0,950 86 }~kg
\item   8 371,7 ~hm~ = {\color{red}  83 717 }~dam
\item   238,09 ~cg~ = {\color{red}  2 380,9 }~mg
\item   399,08 ~dam~ = {\color{red}  3 990 800 }~mm
\end{itemize}
\end{multicols}
\end{document}
