\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 70}

\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=70}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0070}
\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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{28}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{52}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,8  ~ \(\times\)  ~ 1 000
\item   0,07  ~ \(\times\)  ~ 10
\item   0,74  ~ \(\times\)  ~ 100
\item   0,249  ~ \(\times\)  ~ 1 000
\item   0,008  ~ \(\times\)  ~ 100
\item   7,99  ~ \(\times\)  ~ 100
\item   0,808  ~ \(\times\)  ~ 10
\item   104  ~ \(\times\)  ~ 100
\item   3,63  ~ \(\times\)  ~ 10
\item   0,35  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,083  ~ : ~ 1 000
\item   116,4  ~ : ~ 100
\item   888,8  ~ : ~ 1 000
\item   1 421  ~ : ~ 1 000
\item   6 552  ~ : ~ 1 000
\item   517,1  ~ : ~ 1 000
\item   5 944  ~ : ~ 10
\item   2 622  ~ : ~ 1 000
\item   4,918  ~ : ~ 10
\item   2,569  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8  ~ \(\times\)  ~ ... ~ = ~ 8 000
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 0,63
\item   753  ~ \(\times\)  ~ ... ~ = ~ 75 300
\item   7,9  ~ \(\times\)  ~ ... ~ = ~ 79
\item   76,8  ~ \(\times\)  ~ ... ~ = ~ 76 800
\item   128  ~ \(\times\)  ~ ... ~ = ~ 12 800
\item   817  ~ \(\times\)  ~ ... ~ = ~ 8 170
\item   69,2  ~ \(\times\)  ~ ... ~ = ~ 6 920
\item   882  ~ \(\times\)  ~ ... ~ = ~ 88 200
\item   776  ~ \(\times\)  ~ ... ~ = ~ 776 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   707,9  ~ \(\times\)  ~ 0,1
\item   77,51  ~ \(\times\)  ~ 0,001
\item   129,4  ~ \(\times\)  ~ 0,01
\item   529,8  ~ \(\times\)  ~ 0,001
\item   43,33  ~ \(\times\)  ~ 0,1
\item   86,11  ~ \(\times\)  ~ 0,001
\item   888  ~ \(\times\)  ~ 0,001
\item   735  ~ \(\times\)  ~ 0,01
\item   39,91  ~ \(\times\)  ~ 0,01
\item   4,185  ~ \(\times\)  ~ 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   1,382  ~ \(\times\)  ~ ... ~ = ~  0,013 82
\item   4 357  ~ \(\times\)  ~ ... ~ = ~  4,357
\item   839,1  ~ \(\times\)  ~ ... ~ = ~  0,839 1
\item   319  ~ \(\times\)  ~ ... ~ = ~  31,9
\item   7,823  ~ \(\times\)  ~ ... ~ = ~  0,782 3
\item   853,8  ~ \(\times\)  ~ ... ~ = ~  8,538
\item   8,291  ~ \(\times\)  ~ ... ~ = ~  0,082 91
\item   38,33  ~ \(\times\)  ~ ... ~ = ~  0,383 3
\item   24,21  ~ \(\times\)  ~ ... ~ = ~  0,242 1
\item   2,721  ~ \(\times\)  ~ ... ~ = ~  0,027 21
\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~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 572,1 ~km~ = ...~dam
\item   651,08 ~hL~ = ...~kL
\item   314,41 ~daL~ = ...~dL
\item   6 616,7 ~dm~ = ...~hm
\item   3 499,3 ~dam~ = ...~mm
\item   7 859 ~dg~ = ...~cg
\item   986,7 ~mm~ = ...~cm
\item   1 824,1 ~m~ = ...~cm
\item   6 960,9 ~cm~ = ...~km
\item   567,55 ~dg~ = ...~dag
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{6900}{100}\) = \(\dfrac{690}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{28}{10}\) = \(\dfrac{280}{100}\)
\item   \(\dfrac{52}{100}\) = \(\dfrac{520}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 11 800}
\item   0,07  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,7}
\item   0,74  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 74}
\item   0,249  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 249}
\item   0,008  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,8}
\item   7,99  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 799}
\item   0,808  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,08}
\item   104  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 10 400}
\item   3,63  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 36,3}
\item   0,35  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 35}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,083 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 083}
\item   116,4 ~ : ~ 100 ~ = ~{\color{red} 1,164}
\item   888,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,888 8}
\item   1 421 ~ : ~ 1 000 ~ = ~{\color{red} 1,421}
\item   6 552 ~ : ~ 1 000 ~ = ~{\color{red} 6,552}
\item   517,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,517 1}
\item   5 944 ~ : ~ 10 ~ = ~{\color{red} 594,4}
\item   2 622 ~ : ~ 1 000 ~ = ~{\color{red} 2,622}
\item   4,918 ~ : ~ 10 ~ = ~{\color{red} 0,491 8}
\item   2,569 ~ : ~ 100 ~ = ~{\color{red} 0,025 69}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 000
\item   0,063 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,63
\item   753 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~75 300
\item   7,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~79
\item   76,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~76 800
\item   128 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~12 800
\item   817 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 170
\item   69,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 920
\item   882 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88 200
\item   776 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~776 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   707,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 70,79
}\item   77,51 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,077 51
}\item   129,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,294
}\item   529,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,529 8
}\item   43,33 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,333
}\item   86,11 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,086 11
}\item   888 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,888
}\item   735 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,35
}\item   39,91 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,399 1
}\item   4,185 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,418 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,382 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,013 82
\item   4 357 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,357
\item   839,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,839 1
\item   319 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 31,9
\item   7,823 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,782 3
\item   853,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,538
\item   8,291 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,082 91
\item   38,33 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,383 3
\item   24,21 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,242 1
\item   2,721 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,027 21
\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}  100 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 572,1 ~km~ = {\color{red}  957 210 }~dam
\item   651,08 ~hL~ = {\color{red}  65,108 }~kL
\item   314,41 ~daL~ = {\color{red}  31 441 }~dL
\item   6 616,7 ~dm~ = {\color{red}  6,616 7 }~hm
\item   3 499,3 ~dam~ = {\color{red}  34 993 000 }~mm
\item   7 859 ~dg~ = {\color{red}  78 590 }~cg
\item   986,7 ~mm~ = {\color{red}  98,67 }~cm
\item   1 824,1 ~m~ = {\color{red}  182 410 }~cm
\item   6 960,9 ~cm~ = {\color{red}  0,069 609 }~km
\item   567,55 ~dg~ = {\color{red}  5,675 5 }~dag
\end{itemize}
\end{multicols}
\end{document}
