\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 250}

\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=250}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0250}
\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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   729  ~ \(\times\)  ~ 1 000
\item   25,5  ~ \(\times\)  ~ 100
\item   0,941  ~ \(\times\)  ~ 100
\item   0,98  ~ \(\times\)  ~ 100
\item   0,067  ~ \(\times\)  ~ 1 000
\item   0,033  ~ \(\times\)  ~ 1 000
\item   17,1  ~ \(\times\)  ~ 100
\item   70,2  ~ \(\times\)  ~ 100
\item   29,1  ~ \(\times\)  ~ 1 000
\item   0,868  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,043  ~ : ~ 1 000
\item   9,583  ~ : ~ 100
\item   363  ~ : ~ 100
\item   76,09  ~ : ~ 1 000
\item   596,8  ~ : ~ 10
\item   894  ~ : ~ 1 000
\item   0,85  ~ : ~ 100
\item   3,984  ~ : ~ 100
\item   515,8  ~ : ~ 100
\item   861,5  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\item   392  ~ \(\times\)  ~ ... ~ = ~ 3 920
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 0,69
\item   13,4  ~ \(\times\)  ~ ... ~ = ~ 1 340
\item   92,8  ~ \(\times\)  ~ ... ~ = ~ 92 800
\item   0,053  ~ \(\times\)  ~ ... ~ = ~ 0,53
\item   358  ~ \(\times\)  ~ ... ~ = ~ 358 000
\item   723  ~ \(\times\)  ~ ... ~ = ~ 7 230
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 0,69
\item   3,76  ~ \(\times\)  ~ ... ~ = ~ 3 760
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,3  ~ \(\times\)  ~ 0,001
\item   0,807  ~ \(\times\)  ~ 0,1
\item   2,307  ~ \(\times\)  ~ 0,001
\item   3,161  ~ \(\times\)  ~ 0,01
\item   2 332  ~ \(\times\)  ~ 0,1
\item   6,035  ~ \(\times\)  ~ 0,1
\item   8 847  ~ \(\times\)  ~ 0,001
\item   8,77  ~ \(\times\)  ~ 0,1
\item   38,41  ~ \(\times\)  ~ 0,01
\item   1 335  ~ \(\times\)  ~ 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   9,192  ~ \(\times\)  ~ ... ~ = ~  0,009 192
\item   7 157  ~ \(\times\)  ~ ... ~ = ~  71,57
\item   9,203  ~ \(\times\)  ~ ... ~ = ~  0,920 3
\item   7,853  ~ \(\times\)  ~ ... ~ = ~  0,078 53
\item   4,27  ~ \(\times\)  ~ ... ~ = ~  0,427
\item   7 819  ~ \(\times\)  ~ ... ~ = ~  7,819
\item   778,4  ~ \(\times\)  ~ ... ~ = ~  77,84
\item   5 780  ~ \(\times\)  ~ ... ~ = ~  57,8
\item   62,39  ~ \(\times\)  ~ ... ~ = ~  0,062 39
\item   3,359  ~ \(\times\)  ~ ... ~ = ~  0,033 59
\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 ~km~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 398,2 ~L~ = ...~dL
\item   5 576,6 ~L~ = ...~cL
\item   264,85 ~mL~ = ...~kL
\item   307,64 ~mm~ = ...~dm
\item   1 161 ~hg~ = ...~g
\item   6 742,4 ~cL~ = ...~dL
\item   6 123,3 ~g~ = ...~dg
\item   9 288 ~mL~ = ...~dL
\item   3 186,5 ~dg~ = ...~hg
\item   335,09 ~dam~ = ...~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   7 = \(\dfrac{70}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{3100}{100}\) = \(\dfrac{310}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{960}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{190}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   729  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 729 000}
\item   25,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 550}
\item   0,941  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 94,1}
\item   0,98  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 98}
\item   0,067  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 67}
\item   0,033  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 33}
\item   17,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 710}
\item   70,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 020}
\item   29,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 29 100}
\item   0,868  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 86,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,043 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 043}
\item   9,583 ~ : ~ 100 ~ = ~{\color{red} 0,095 83}
\item   363 ~ : ~ 100 ~ = ~{\color{red} 3,63}
\item   76,09 ~ : ~ 1 000 ~ = ~{\color{red} 0,076 09}
\item   596,8 ~ : ~ 10 ~ = ~{\color{red} 59,68}
\item   894 ~ : ~ 1 000 ~ = ~{\color{red} 0,894}
\item   0,85 ~ : ~ 100 ~ = ~{\color{red} 0,008 5}
\item   3,984 ~ : ~ 100 ~ = ~{\color{red} 0,039 84}
\item   515,8 ~ : ~ 100 ~ = ~{\color{red} 5,158}
\item   861,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,861 5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\item   392 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 920
\item   0,069 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,69
\item   13,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 340
\item   92,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~92 800
\item   0,053 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,53
\item   358 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~358 000
\item   723 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 230
\item   0,069 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,69
\item   3,76 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 760
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,087 3
}\item   0,807 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,080 7
}\item   2,307 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 307
}\item   3,161 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,031 61
}\item   2 332 ~ \(\times\)  0,1 ~ = ~{\color{red} 233,2
}\item   6,035 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,603 5
}\item   8 847 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,847
}\item   8,77 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,877
}\item   38,41 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,384 1
}\item   1 335 ~ \(\times\)  0,01 ~ = ~{\color{red} 13,35
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,192 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 192
\item   7 157 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 71,57
\item   9,203 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,920 3
\item   7,853 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,078 53
\item   4,27 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,427
\item   7 819 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,819
\item   778,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 77,84
\item   5 780 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 57,8
\item   62,39 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,062 39
\item   3,359 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,033 59
\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 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 398,2 ~L~ = {\color{red}  83 982 }~dL
\item   5 576,6 ~L~ = {\color{red}  557 660 }~cL
\item   264,85 ~mL~ = {\color{red}  0,000 264 85 }~kL
\item   307,64 ~mm~ = {\color{red}  3,076 4 }~dm
\item   1 161 ~hg~ = {\color{red}  116 100 }~g
\item   6 742,4 ~cL~ = {\color{red}  674,24 }~dL
\item   6 123,3 ~g~ = {\color{red}  61 233 }~dg
\item   9 288 ~mL~ = {\color{red}  92,88 }~dL
\item   3 186,5 ~dg~ = {\color{red}  3,186 5 }~hg
\item   335,09 ~dam~ = {\color{red}  335 090 }~cm
\end{itemize}
\end{multicols}
\end{document}
