\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 68}

\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=68}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0068}
\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   \(\dfrac{8800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{66}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,8  ~ \(\times\)  ~ 100
\item   5,75  ~ \(\times\)  ~ 10
\item   575  ~ \(\times\)  ~ 10
\item   0,567  ~ \(\times\)  ~ 10
\item   8,97  ~ \(\times\)  ~ 10
\item   0,01  ~ \(\times\)  ~ 10
\item   20,8  ~ \(\times\)  ~ 10
\item   0,549  ~ \(\times\)  ~ 100
\item   0,557  ~ \(\times\)  ~ 1 000
\item   0,014  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   975,7  ~ : ~ 1 000
\item   93,87  ~ : ~ 10
\item   2 127  ~ : ~ 100
\item   63,5  ~ : ~ 10
\item   3,379  ~ : ~ 100
\item   6,386  ~ : ~ 10
\item   4,276  ~ : ~ 10
\item   785  ~ : ~ 100
\item   641,3  ~ : ~ 10
\item   15,92  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,69  ~ \(\times\)  ~ ... ~ = ~ 3 690
\item   0,09  ~ \(\times\)  ~ ... ~ = ~ 0,9
\item   0,503  ~ \(\times\)  ~ ... ~ = ~ 50,3
\item   0,048  ~ \(\times\)  ~ ... ~ = ~ 48
\item   0,786  ~ \(\times\)  ~ ... ~ = ~ 78,6
\item   9,07  ~ \(\times\)  ~ ... ~ = ~ 90,7
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,04
\item   46,4  ~ \(\times\)  ~ ... ~ = ~ 46 400
\item   8,58  ~ \(\times\)  ~ ... ~ = ~ 8 580
\item   83,3  ~ \(\times\)  ~ ... ~ = ~ 8 330
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,26  ~ \(\times\)  ~ 0,001
\item   1 934  ~ \(\times\)  ~ 0,1
\item   95,28  ~ \(\times\)  ~ 0,001
\item   30,88  ~ \(\times\)  ~ 0,1
\item   485,4  ~ \(\times\)  ~ 0,001
\item   7,684  ~ \(\times\)  ~ 0,001
\item   54,94  ~ \(\times\)  ~ 0,1
\item   4,238  ~ \(\times\)  ~ 0,01
\item   129,7  ~ \(\times\)  ~ 0,1
\item   67,77  ~ \(\times\)  ~ 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   3,944  ~ \(\times\)  ~ ... ~ = ~  0,039 44
\item   93,62  ~ \(\times\)  ~ ... ~ = ~  0,936 2
\item   2,056  ~ \(\times\)  ~ ... ~ = ~  0,020 56
\item   7 800  ~ \(\times\)  ~ ... ~ = ~  780
\item   20,4  ~ \(\times\)  ~ ... ~ = ~  0,020 4
\item   55,63  ~ \(\times\)  ~ ... ~ = ~  0,055 63
\item   181,6  ~ \(\times\)  ~ ... ~ = ~  18,16
\item   9,328  ~ \(\times\)  ~ ... ~ = ~  0,009 328
\item   871,7  ~ \(\times\)  ~ ... ~ = ~  87,17
\item   44,37  ~ \(\times\)  ~ ... ~ = ~  0,044 37
\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 ~m~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   118,54 ~dL~ = ...~daL
\item   9 932,1 ~km~ = ...~hm
\item   826,39 ~mL~ = ...~daL
\item   6 938,3 ~dag~ = ...~mg
\item   915,62 ~mg~ = ...~dg
\item   299,42 ~dg~ = ...~dag
\item   724,66 ~mm~ = ...~cm
\item   2 710,8 ~daL~ = ...~L
\item   417,07 ~L~ = ...~daL
\item   3 006,8 ~cm~ = ...~km
\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   \(\dfrac{8800}{100}\) = \(\dfrac{880}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{66}{10}\) = \(\dfrac{660}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 280}
\item   5,75  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 57,5}
\item   575  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 750}
\item   0,567  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,67}
\item   8,97  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 89,7}
\item   0,01  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,1}
\item   20,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 208}
\item   0,549  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 54,9}
\item   0,557  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 557}
\item   0,014  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,14}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   975,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,975 7}
\item   93,87 ~ : ~ 10 ~ = ~{\color{red} 9,387}
\item   2 127 ~ : ~ 100 ~ = ~{\color{red} 21,27}
\item   63,5 ~ : ~ 10 ~ = ~{\color{red} 6,35}
\item   3,379 ~ : ~ 100 ~ = ~{\color{red} 0,033 79}
\item   6,386 ~ : ~ 10 ~ = ~{\color{red} 0,638 6}
\item   4,276 ~ : ~ 10 ~ = ~{\color{red} 0,427 6}
\item   785 ~ : ~ 100 ~ = ~{\color{red} 7,85}
\item   641,3 ~ : ~ 10 ~ = ~{\color{red} 64,13}
\item   15,92 ~ : ~ 1 000 ~ = ~{\color{red} 0,015 92}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,69 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 690
\item   0,09 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,9
\item   0,503 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~50,3
\item   0,048 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~48
\item   0,786 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~78,6
\item   9,07 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~90,7
\item   0,004 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,04
\item   46,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~46 400
\item   8,58 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 580
\item   83,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 330
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,26 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,078 26
}\item   1 934 ~ \(\times\)  0,1 ~ = ~{\color{red} 193,4
}\item   95,28 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,095 28
}\item   30,88 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,088
}\item   485,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,485 4
}\item   7,684 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 684
}\item   54,94 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,494
}\item   4,238 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,042 38
}\item   129,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 12,97
}\item   67,77 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,067 77
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,944 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,039 44
\item   93,62 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,936 2
\item   2,056 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,020 56
\item   7 800 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 780
\item   20,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,020 4
\item   55,63 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,055 63
\item   181,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 18,16
\item   9,328 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 328
\item   871,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 87,17
\item   44,37 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,044 37
\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 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\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   118,54 ~dL~ = {\color{red}  1,185 4 }~daL
\item   9 932,1 ~km~ = {\color{red}  99 321 }~hm
\item   826,39 ~mL~ = {\color{red}  0,082 639 }~daL
\item   6 938,3 ~dag~ = {\color{red}  69 383 000 }~mg
\item   915,62 ~mg~ = {\color{red}  9,156 2 }~dg
\item   299,42 ~dg~ = {\color{red}  2,994 2 }~dag
\item   724,66 ~mm~ = {\color{red}  72,466 }~cm
\item   2 710,8 ~daL~ = {\color{red}  27 108 }~L
\item   417,07 ~L~ = {\color{red}  41,707 }~daL
\item   3 006,8 ~cm~ = {\color{red}  0,030 068 }~km
\end{itemize}
\end{multicols}
\end{document}
