\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 320}

\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=320}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0320}
\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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{52}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{24}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,37  ~ \(\times\)  ~ 10
\item   0,077  ~ \(\times\)  ~ 1 000
\item   8,14  ~ \(\times\)  ~ 1 000
\item   64,7  ~ \(\times\)  ~ 1 000
\item   0,783  ~ \(\times\)  ~ 10
\item   0,517  ~ \(\times\)  ~ 10
\item   51,8  ~ \(\times\)  ~ 10
\item   49,4  ~ \(\times\)  ~ 1 000
\item   2,16  ~ \(\times\)  ~ 1 000
\item   6,56  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,9  ~ : ~ 10
\item   6 821  ~ : ~ 1 000
\item   7,338  ~ : ~ 100
\item   8,666  ~ : ~ 1 000
\item   32,92  ~ : ~ 10
\item   6 288  ~ : ~ 100
\item   2,922  ~ : ~ 100
\item   19,07  ~ : ~ 10
\item   2,424  ~ : ~ 10
\item   7,108  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,722  ~ \(\times\)  ~ ... ~ = ~ 7,22
\item   1,2  ~ \(\times\)  ~ ... ~ = ~ 1 200
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 7
\item   0,602  ~ \(\times\)  ~ ... ~ = ~ 60,2
\item   746  ~ \(\times\)  ~ ... ~ = ~ 74 600
\item   61  ~ \(\times\)  ~ ... ~ = ~ 610
\item   0,087  ~ \(\times\)  ~ ... ~ = ~ 87
\item   29,1  ~ \(\times\)  ~ ... ~ = ~ 29 100
\item   158  ~ \(\times\)  ~ ... ~ = ~ 158 000
\item   0,082  ~ \(\times\)  ~ ... ~ = ~ 8,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,22  ~ \(\times\)  ~ 0,001
\item   7,015  ~ \(\times\)  ~ 0,01
\item   2,933  ~ \(\times\)  ~ 0,001
\item   713  ~ \(\times\)  ~ 0,001
\item   6,21  ~ \(\times\)  ~ 0,001
\item   939,1  ~ \(\times\)  ~ 0,01
\item   59,8  ~ \(\times\)  ~ 0,1
\item   4 262  ~ \(\times\)  ~ 0,01
\item   64,49  ~ \(\times\)  ~ 0,1
\item   33,49  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   35,07  ~ \(\times\)  ~ ... ~ = ~  0,350 7
\item   8 007  ~ \(\times\)  ~ ... ~ = ~  8,007
\item   6,268  ~ \(\times\)  ~ ... ~ = ~  0,626 8
\item   1 265  ~ \(\times\)  ~ ... ~ = ~  1,265
\item   0,338  ~ \(\times\)  ~ ... ~ = ~  0,000 338
\item   9 031  ~ \(\times\)  ~ ... ~ = ~  9,031
\item   3 568  ~ \(\times\)  ~ ... ~ = ~  356,8
\item   56,99  ~ \(\times\)  ~ ... ~ = ~  0,569 9
\item   72,8  ~ \(\times\)  ~ ... ~ = ~  7,28
\item   704,3  ~ \(\times\)  ~ ... ~ = ~  7,043
\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 ~cm~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   665,21 ~dg~ = ...~kg
\item   6 300,9 ~dL~ = ...~daL
\item   8 307,8 ~mg~ = ...~kg
\item   3 356,4 ~dm~ = ...~mm
\item   482,26 ~daL~ = ...~kL
\item   2 596,3 ~kL~ = ...~L
\item   7 036,1 ~kg~ = ...~g
\item   1 666,1 ~m~ = ...~km
\item   606,39 ~dg~ = ...~hg
\item   596,01 ~m~ = ...~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   8 = \(\dfrac{80}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{6700}{100}\) = \(\dfrac{670}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{52}{10}\) = \(\dfrac{520}{100}\)
\item   \(\dfrac{24}{100}\) = \(\dfrac{240}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,37  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 43,7}
\item   0,077  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 77}
\item   8,14  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 140}
\item   64,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 64 700}
\item   0,783  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,83}
\item   0,517  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,17}
\item   51,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 518}
\item   49,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 49 400}
\item   2,16  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 160}
\item   6,56  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 656}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,9 ~ : ~ 10 ~ = ~{\color{red} 7,89}
\item   6 821 ~ : ~ 1 000 ~ = ~{\color{red} 6,821}
\item   7,338 ~ : ~ 100 ~ = ~{\color{red} 0,073 38}
\item   8,666 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 666}
\item   32,92 ~ : ~ 10 ~ = ~{\color{red} 3,292}
\item   6 288 ~ : ~ 100 ~ = ~{\color{red} 62,88}
\item   2,922 ~ : ~ 100 ~ = ~{\color{red} 0,029 22}
\item   19,07 ~ : ~ 10 ~ = ~{\color{red} 1,907}
\item   2,424 ~ : ~ 10 ~ = ~{\color{red} 0,242 4}
\item   7,108 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 108}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,722 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,22
\item   1,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 200
\item   0,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7
\item   0,602 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~60,2
\item   746 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74 600
\item   61 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~610
\item   0,087 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~87
\item   29,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~29 100
\item   158 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~158 000
\item   0,082 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,22 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,089 22
}\item   7,015 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,070 15
}\item   2,933 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 933
}\item   713 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,713
}\item   6,21 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 21
}\item   939,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,391
}\item   59,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,98
}\item   4 262 ~ \(\times\)  0,01 ~ = ~{\color{red} 42,62
}\item   64,49 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,449
}\item   33,49 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,334 9
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   35,07 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,350 7
\item   8 007 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,007
\item   6,268 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,626 8
\item   1 265 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,265
\item   0,338 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 338
\item   9 031 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,031
\item   3 568 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 356,8
\item   56,99 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,569 9
\item   72,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,28
\item   704,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,043
\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 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   665,21 ~dg~ = {\color{red}  0,066 521 }~kg
\item   6 300,9 ~dL~ = {\color{red}  63,009 }~daL
\item   8 307,8 ~mg~ = {\color{red}  0,008 307 8 }~kg
\item   3 356,4 ~dm~ = {\color{red}  335 640 }~mm
\item   482,26 ~daL~ = {\color{red}  4,822 6 }~kL
\item   2 596,3 ~kL~ = {\color{red}  2 596 300 }~L
\item   7 036,1 ~kg~ = {\color{red}  7 036 100 }~g
\item   1 666,1 ~m~ = {\color{red}  1,666 1 }~km
\item   606,39 ~dg~ = {\color{red}  0,606 39 }~hg
\item   596,01 ~m~ = {\color{red}  59 601 }~cm
\end{itemize}
\end{multicols}
\end{document}
