\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 384}

\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=384}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0384}
\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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,258  ~ \(\times\)  ~ 10
\item   0,014  ~ \(\times\)  ~ 10
\item   3,97  ~ \(\times\)  ~ 10
\item   0,148  ~ \(\times\)  ~ 100
\item   1,95  ~ \(\times\)  ~ 1 000
\item   0,075  ~ \(\times\)  ~ 1 000
\item   0,074  ~ \(\times\)  ~ 1 000
\item   0,45  ~ \(\times\)  ~ 100
\item   0,506  ~ \(\times\)  ~ 100
\item   0,059  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   46,75  ~ : ~ 10
\item   492,1  ~ : ~ 100
\item   3,004  ~ : ~ 100
\item   38,77  ~ : ~ 1 000
\item   7,637  ~ : ~ 1 000
\item   45,39  ~ : ~ 1 000
\item   9,31  ~ : ~ 1 000
\item   0,506  ~ : ~ 100
\item   546,2  ~ : ~ 10
\item   3 881  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,969  ~ \(\times\)  ~ ... ~ = ~ 9,69
\item   0,11  ~ \(\times\)  ~ ... ~ = ~ 1,1
\item   41,3  ~ \(\times\)  ~ ... ~ = ~ 4 130
\item   2,92  ~ \(\times\)  ~ ... ~ = ~ 292
\item   38  ~ \(\times\)  ~ ... ~ = ~ 3 800
\item   27  ~ \(\times\)  ~ ... ~ = ~ 27 000
\item   263  ~ \(\times\)  ~ ... ~ = ~ 26 300
\item   0,23  ~ \(\times\)  ~ ... ~ = ~ 2,3
\item   0,056  ~ \(\times\)  ~ ... ~ = ~ 0,56
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 0,22
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   834,8  ~ \(\times\)  ~ 0,01
\item   6,572  ~ \(\times\)  ~ 0,01
\item   13,05  ~ \(\times\)  ~ 0,001
\item   2 152  ~ \(\times\)  ~ 0,01
\item   1 675  ~ \(\times\)  ~ 0,01
\item   63,7  ~ \(\times\)  ~ 0,001
\item   47,49  ~ \(\times\)  ~ 0,001
\item   18,15  ~ \(\times\)  ~ 0,1
\item   937,1  ~ \(\times\)  ~ 0,001
\item   49,68  ~ \(\times\)  ~ 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   9,68  ~ \(\times\)  ~ ... ~ = ~  0,009 68
\item   8 752  ~ \(\times\)  ~ ... ~ = ~  87,52
\item   34,55  ~ \(\times\)  ~ ... ~ = ~  3,455
\item   8,163  ~ \(\times\)  ~ ... ~ = ~  0,008 163
\item   0,157  ~ \(\times\)  ~ ... ~ = ~  0,000 157
\item   5 261  ~ \(\times\)  ~ ... ~ = ~  526,1
\item   823  ~ \(\times\)  ~ ... ~ = ~  82,3
\item   1 942  ~ \(\times\)  ~ ... ~ = ~  1,942
\item   27,9  ~ \(\times\)  ~ ... ~ = ~  0,279
\item   69,67  ~ \(\times\)  ~ ... ~ = ~  0,696 7
\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 ~dm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   262,88 ~dg~ = ...~mg
\item   431,97 ~mg~ = ...~hg
\item   1 485,4 ~kL~ = ...~L
\item   7 737,5 ~km~ = ...~m
\item   4 810,3 ~kg~ = ...~hg
\item   623,3 ~dag~ = ...~mg
\item   884,12 ~kg~ = ...~g
\item   5 760 ~mm~ = ...~hm
\item   7 924,2 ~dg~ = ...~kg
\item   5 708,9 ~km~ = ...~hm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{790}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{920}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{580}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,258  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,58}
\item   0,014  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,14}
\item   3,97  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 39,7}
\item   0,148  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14,8}
\item   1,95  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 950}
\item   0,075  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 75}
\item   0,074  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 74}
\item   0,45  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 45}
\item   0,506  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 50,6}
\item   0,059  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   46,75 ~ : ~ 10 ~ = ~{\color{red} 4,675}
\item   492,1 ~ : ~ 100 ~ = ~{\color{red} 4,921}
\item   3,004 ~ : ~ 100 ~ = ~{\color{red} 0,030 04}
\item   38,77 ~ : ~ 1 000 ~ = ~{\color{red} 0,038 77}
\item   7,637 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 637}
\item   45,39 ~ : ~ 1 000 ~ = ~{\color{red} 0,045 39}
\item   9,31 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 31}
\item   0,506 ~ : ~ 100 ~ = ~{\color{red} 0,005 06}
\item   546,2 ~ : ~ 10 ~ = ~{\color{red} 54,62}
\item   3 881 ~ : ~ 1 000 ~ = ~{\color{red} 3,881}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,969 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,69
\item   0,11 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,1
\item   41,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 130
\item   2,92 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~292
\item   38 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 800
\item   27 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27 000
\item   263 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~26 300
\item   0,23 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,3
\item   0,056 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,56
\item   0,022 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,22
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   834,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,348
}\item   6,572 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,065 72
}\item   13,05 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,013 05
}\item   2 152 ~ \(\times\)  0,01 ~ = ~{\color{red} 21,52
}\item   1 675 ~ \(\times\)  0,01 ~ = ~{\color{red} 16,75
}\item   63,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,063 7
}\item   47,49 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,047 49
}\item   18,15 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,815
}\item   937,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,937 1
}\item   49,68 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,968
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,68 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 68
\item   8 752 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 87,52
\item   34,55 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,455
\item   8,163 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 163
\item   0,157 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 157
\item   5 261 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 526,1
\item   823 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 82,3
\item   1 942 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,942
\item   27,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,279
\item   69,67 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,696 7
\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 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   262,88 ~dg~ = {\color{red}  26 288 }~mg
\item   431,97 ~mg~ = {\color{red}  0,004 319 7 }~hg
\item   1 485,4 ~kL~ = {\color{red}  1 485 400 }~L
\item   7 737,5 ~km~ = {\color{red}  7 737 500 }~m
\item   4 810,3 ~kg~ = {\color{red}  48 103 }~hg
\item   623,3 ~dag~ = {\color{red}  6 233 000 }~mg
\item   884,12 ~kg~ = {\color{red}  884 120 }~g
\item   5 760 ~mm~ = {\color{red}  0,057 6 }~hm
\item   7 924,2 ~dg~ = {\color{red}  0,792 42 }~kg
\item   5 708,9 ~km~ = {\color{red}  57 089 }~hm
\end{itemize}
\end{multicols}
\end{document}
