\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 238}

\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=238}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0238}
\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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   83,8  ~ \(\times\)  ~ 10
\item   0,056  ~ \(\times\)  ~ 1 000
\item   592  ~ \(\times\)  ~ 10
\item   1,82  ~ \(\times\)  ~ 100
\item   426  ~ \(\times\)  ~ 100
\item   3,08  ~ \(\times\)  ~ 10
\item   90,3  ~ \(\times\)  ~ 100
\item   11  ~ \(\times\)  ~ 100
\item   968  ~ \(\times\)  ~ 10
\item   0,068  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 770  ~ : ~ 10
\item   5 907  ~ : ~ 10
\item   6,078  ~ : ~ 1 000
\item   95  ~ : ~ 100
\item   5,543  ~ : ~ 100
\item   461,3  ~ : ~ 1 000
\item   671,3  ~ : ~ 10
\item   7 915  ~ : ~ 1 000
\item   72,53  ~ : ~ 100
\item   2 019  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,1  ~ \(\times\)  ~ ... ~ = ~ 8 010
\item   70,3  ~ \(\times\)  ~ ... ~ = ~ 7 030
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 8,8
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 6,8
\item   4,17  ~ \(\times\)  ~ ... ~ = ~ 4 170
\item   960  ~ \(\times\)  ~ ... ~ = ~ 96 000
\item   80,9  ~ \(\times\)  ~ ... ~ = ~ 8 090
\item   7,37  ~ \(\times\)  ~ ... ~ = ~ 737
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 0,22
\item   26,8  ~ \(\times\)  ~ ... ~ = ~ 2 680
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 750  ~ \(\times\)  ~ 0,1
\item   89,87  ~ \(\times\)  ~ 0,01
\item   88,8  ~ \(\times\)  ~ 0,1
\item   16,41  ~ \(\times\)  ~ 0,001
\item   25,56  ~ \(\times\)  ~ 0,1
\item   6,596  ~ \(\times\)  ~ 0,001
\item   3 002  ~ \(\times\)  ~ 0,01
\item   8 142  ~ \(\times\)  ~ 0,01
\item   971,6  ~ \(\times\)  ~ 0,01
\item   3,786  ~ \(\times\)  ~ 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   671,9  ~ \(\times\)  ~ ... ~ = ~  0,671 9
\item   521,5  ~ \(\times\)  ~ ... ~ = ~  5,215
\item   905,3  ~ \(\times\)  ~ ... ~ = ~  90,53
\item   65,23  ~ \(\times\)  ~ ... ~ = ~  6,523
\item   37,3  ~ \(\times\)  ~ ... ~ = ~  0,037 3
\item   1,175  ~ \(\times\)  ~ ... ~ = ~  0,117 5
\item   1 843  ~ \(\times\)  ~ ... ~ = ~  18,43
\item   1 263  ~ \(\times\)  ~ ... ~ = ~  12,63
\item   354  ~ \(\times\)  ~ ... ~ = ~  3,54
\item   0,898  ~ \(\times\)  ~ ... ~ = ~  0,089 8
\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 ~cm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   870,52 ~hL~ = ...~mL
\item   476,98 ~daL~ = ...~kL
\item   279,8 ~L~ = ...~mL
\item   6 652,2 ~cL~ = ...~mL
\item   510,66 ~m~ = ...~km
\item   387,34 ~m~ = ...~cm
\item   5 200,2 ~g~ = ...~mg
\item   735,45 ~dag~ = ...~g
\item   8 927,5 ~cg~ = ...~g
\item   6 364,4 ~cL~ = ...~daL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{220}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{290}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   83,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 838}
\item   0,056  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 56}
\item   592  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 920}
\item   1,82  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 182}
\item   426  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 42 600}
\item   3,08  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 30,8}
\item   90,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 030}
\item   11  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 100}
\item   968  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9 680}
\item   0,068  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 68}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 770 ~ : ~ 10 ~ = ~{\color{red} 977}
\item   5 907 ~ : ~ 10 ~ = ~{\color{red} 590,7}
\item   6,078 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 078}
\item   95 ~ : ~ 100 ~ = ~{\color{red} 0,95}
\item   5,543 ~ : ~ 100 ~ = ~{\color{red} 0,055 43}
\item   461,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,461 3}
\item   671,3 ~ : ~ 10 ~ = ~{\color{red} 67,13}
\item   7 915 ~ : ~ 1 000 ~ = ~{\color{red} 7,915}
\item   72,53 ~ : ~ 100 ~ = ~{\color{red} 0,725 3}
\item   2 019 ~ : ~ 1 000 ~ = ~{\color{red} 2,019}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 010
\item   70,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 030
\item   0,088 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,8
\item   0,068 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,8
\item   4,17 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 170
\item   960 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96 000
\item   80,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 090
\item   7,37 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~737
\item   0,022 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,22
\item   26,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 680
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 750 ~ \(\times\)  0,1 ~ = ~{\color{red} 975
}\item   89,87 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,898 7
}\item   88,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,88
}\item   16,41 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,016 41
}\item   25,56 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,556
}\item   6,596 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 596
}\item   3 002 ~ \(\times\)  0,01 ~ = ~{\color{red} 30,02
}\item   8 142 ~ \(\times\)  0,01 ~ = ~{\color{red} 81,42
}\item   971,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,716
}\item   3,786 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 786
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   671,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,671 9
\item   521,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,215
\item   905,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 90,53
\item   65,23 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,523
\item   37,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,037 3
\item   1,175 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,117 5
\item   1 843 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 18,43
\item   1 263 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 12,63
\item   354 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,54
\item   0,898 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,089 8
\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 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   870,52 ~hL~ = {\color{red}  87 052 000 }~mL
\item   476,98 ~daL~ = {\color{red}  4,769 8 }~kL
\item   279,8 ~L~ = {\color{red}  279 800 }~mL
\item   6 652,2 ~cL~ = {\color{red}  66 522 }~mL
\item   510,66 ~m~ = {\color{red}  0,510 66 }~km
\item   387,34 ~m~ = {\color{red}  38 734 }~cm
\item   5 200,2 ~g~ = {\color{red}  5 200 200 }~mg
\item   735,45 ~dag~ = {\color{red}  7 354,5 }~g
\item   8 927,5 ~cg~ = {\color{red}  89,275 }~g
\item   6 364,4 ~cL~ = {\color{red}  6,364 4 }~daL
\end{itemize}
\end{multicols}
\end{document}
