\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 59}

\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=59}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0059}
\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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,76  ~ \(\times\)  ~ 1 000
\item   0,003  ~ \(\times\)  ~ 10
\item   0,957  ~ \(\times\)  ~ 100
\item   0,051  ~ \(\times\)  ~ 100
\item   78,8  ~ \(\times\)  ~ 1 000
\item   6,05  ~ \(\times\)  ~ 1 000
\item   0,019  ~ \(\times\)  ~ 10
\item   1,12  ~ \(\times\)  ~ 1 000
\item   0,5  ~ \(\times\)  ~ 100
\item   99  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 455  ~ : ~ 100
\item   4 989  ~ : ~ 1 000
\item   9 577  ~ : ~ 100
\item   950,5  ~ : ~ 1 000
\item   6 730  ~ : ~ 10
\item   75,13  ~ : ~ 1 000
\item   841,6  ~ : ~ 100
\item   8,579  ~ : ~ 1 000
\item   511,7  ~ : ~ 10
\item   6,431  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,81  ~ \(\times\)  ~ ... ~ = ~ 381
\item   0,016  ~ \(\times\)  ~ ... ~ = ~ 0,16
\item   0,05  ~ \(\times\)  ~ ... ~ = ~ 0,5
\item   0,257  ~ \(\times\)  ~ ... ~ = ~ 2,57
\item   0,055  ~ \(\times\)  ~ ... ~ = ~ 5,5
\item   0,025  ~ \(\times\)  ~ ... ~ = ~ 2,5
\item   552  ~ \(\times\)  ~ ... ~ = ~ 55 200
\item   871  ~ \(\times\)  ~ ... ~ = ~ 87 100
\item   9,39  ~ \(\times\)  ~ ... ~ = ~ 9 390
\item   414  ~ \(\times\)  ~ ... ~ = ~ 4 140
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,57  ~ \(\times\)  ~ 0,1
\item   4,148  ~ \(\times\)  ~ 0,1
\item   6,977  ~ \(\times\)  ~ 0,1
\item   49,26  ~ \(\times\)  ~ 0,001
\item   55,5  ~ \(\times\)  ~ 0,001
\item   17,46  ~ \(\times\)  ~ 0,1
\item   4,981  ~ \(\times\)  ~ 0,001
\item   1,585  ~ \(\times\)  ~ 0,1
\item   382,8  ~ \(\times\)  ~ 0,01
\item   2 029  ~ \(\times\)  ~ 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   5,315  ~ \(\times\)  ~ ... ~ = ~  0,005 315
\item   6 095  ~ \(\times\)  ~ ... ~ = ~  609,5
\item   20,9  ~ \(\times\)  ~ ... ~ = ~  2,09
\item   3 708  ~ \(\times\)  ~ ... ~ = ~  37,08
\item   4,292  ~ \(\times\)  ~ ... ~ = ~  0,042 92
\item   6 871  ~ \(\times\)  ~ ... ~ = ~  6,871
\item   948,9  ~ \(\times\)  ~ ... ~ = ~  94,89
\item   4 173  ~ \(\times\)  ~ ... ~ = ~  417,3
\item   483,6  ~ \(\times\)  ~ ... ~ = ~  4,836
\item   315,6  ~ \(\times\)  ~ ... ~ = ~  31,56
\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 ~hm~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 456,7 ~kL~ = ...~dL
\item   6 825,2 ~mL~ = ...~hL
\item   3 248,5 ~hg~ = ...~kg
\item   972,81 ~kg~ = ...~dag
\item   455,8 ~cm~ = ...~dm
\item   761,51 ~km~ = ...~cm
\item   4 354,7 ~dg~ = ...~dag
\item   954,1 ~km~ = ...~dm
\item   210,02 ~cg~ = ...~hg
\item   5 125,3 ~kg~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{9400}{100}\) = \(\dfrac{940}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{130}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{280}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,76  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 760}
\item   0,003  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,03}
\item   0,957  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 95,7}
\item   0,051  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,1}
\item   78,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 78 800}
\item   6,05  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 050}
\item   0,019  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,19}
\item   1,12  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 120}
\item   0,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 50}
\item   99  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 990}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 455 ~ : ~ 100 ~ = ~{\color{red} 14,55}
\item   4 989 ~ : ~ 1 000 ~ = ~{\color{red} 4,989}
\item   9 577 ~ : ~ 100 ~ = ~{\color{red} 95,77}
\item   950,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,950 5}
\item   6 730 ~ : ~ 10 ~ = ~{\color{red} 673}
\item   75,13 ~ : ~ 1 000 ~ = ~{\color{red} 0,075 13}
\item   841,6 ~ : ~ 100 ~ = ~{\color{red} 8,416}
\item   8,579 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 579}
\item   511,7 ~ : ~ 10 ~ = ~{\color{red} 51,17}
\item   6,431 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 431}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,81 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~381
\item   0,016 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,16
\item   0,05 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,5
\item   0,257 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,57
\item   0,055 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,5
\item   0,025 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,5
\item   552 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~55 200
\item   871 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~87 100
\item   9,39 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 390
\item   414 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 140
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,57 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,957
}\item   4,148 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,414 8
}\item   6,977 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,697 7
}\item   49,26 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,049 26
}\item   55,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,055 5
}\item   17,46 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,746
}\item   4,981 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 981
}\item   1,585 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,158 5
}\item   382,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,828
}\item   2 029 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,029
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,315 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 315
\item   6 095 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 609,5
\item   20,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,09
\item   3 708 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 37,08
\item   4,292 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,042 92
\item   6 871 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,871
\item   948,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 94,89
\item   4 173 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 417,3
\item   483,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,836
\item   315,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 31,56
\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 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 456,7 ~kL~ = {\color{red}  24 567 000 }~dL
\item   6 825,2 ~mL~ = {\color{red}  0,068 252 }~hL
\item   3 248,5 ~hg~ = {\color{red}  324,85 }~kg
\item   972,81 ~kg~ = {\color{red}  97 281 }~dag
\item   455,8 ~cm~ = {\color{red}  45,58 }~dm
\item   761,51 ~km~ = {\color{red}  76 151 000 }~cm
\item   4 354,7 ~dg~ = {\color{red}  43,547 }~dag
\item   954,1 ~km~ = {\color{red}  9 541 000 }~dm
\item   210,02 ~cg~ = {\color{red}  0,021 002 }~hg
\item   5 125,3 ~kg~ = {\color{red}  5 125 300 000 }~mg
\end{itemize}
\end{multicols}
\end{document}
