\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 353}

\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=353}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0353}
\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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{87}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{74}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,042  ~ \(\times\)  ~ 10
\item   0,078  ~ \(\times\)  ~ 100
\item   0,04  ~ \(\times\)  ~ 1 000
\item   0,037  ~ \(\times\)  ~ 10
\item   5,13  ~ \(\times\)  ~ 10
\item   313  ~ \(\times\)  ~ 100
\item   0,648  ~ \(\times\)  ~ 10
\item   78,9  ~ \(\times\)  ~ 100
\item   4,44  ~ \(\times\)  ~ 100
\item   0,681  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,22  ~ : ~ 100
\item   602,8  ~ : ~ 1 000
\item   9,208  ~ : ~ 100
\item   51,4  ~ : ~ 100
\item   0,348  ~ : ~ 10
\item   2 516  ~ : ~ 1 000
\item   882,2  ~ : ~ 1 000
\item   5 365  ~ : ~ 1 000
\item   6,037  ~ : ~ 100
\item   563,3  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   576  ~ \(\times\)  ~ ... ~ = ~ 576 000
\item   10,1  ~ \(\times\)  ~ ... ~ = ~ 10 100
\item   5,38  ~ \(\times\)  ~ ... ~ = ~ 53,8
\item   0,285  ~ \(\times\)  ~ ... ~ = ~ 28,5
\item   8,64  ~ \(\times\)  ~ ... ~ = ~ 86,4
\item   0,085  ~ \(\times\)  ~ ... ~ = ~ 85
\item   51,1  ~ \(\times\)  ~ ... ~ = ~ 51 100
\item   8,79  ~ \(\times\)  ~ ... ~ = ~ 8 790
\item   964  ~ \(\times\)  ~ ... ~ = ~ 9 640
\item   5,7  ~ \(\times\)  ~ ... ~ = ~ 57
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   648,9  ~ \(\times\)  ~ 0,01
\item   934,9  ~ \(\times\)  ~ 0,1
\item   488,4  ~ \(\times\)  ~ 0,01
\item   36,84  ~ \(\times\)  ~ 0,1
\item   2,444  ~ \(\times\)  ~ 0,1
\item   975,2  ~ \(\times\)  ~ 0,01
\item   54,8  ~ \(\times\)  ~ 0,1
\item   415,1  ~ \(\times\)  ~ 0,01
\item   8 276  ~ \(\times\)  ~ 0,001
\item   5 312  ~ \(\times\)  ~ 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   65,55  ~ \(\times\)  ~ ... ~ = ~  0,655 5
\item   736  ~ \(\times\)  ~ ... ~ = ~  73,6
\item   4,164  ~ \(\times\)  ~ ... ~ = ~  0,004 164
\item   8 316  ~ \(\times\)  ~ ... ~ = ~  831,6
\item   587,2  ~ \(\times\)  ~ ... ~ = ~  0,587 2
\item   67,4  ~ \(\times\)  ~ ... ~ = ~  0,067 4
\item   1,437  ~ \(\times\)  ~ ... ~ = ~  0,143 7
\item   372,9  ~ \(\times\)  ~ ... ~ = ~  37,29
\item   59,21  ~ \(\times\)  ~ ... ~ = ~  0,059 21
\item   26,3  ~ \(\times\)  ~ ... ~ = ~  0,263
\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~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   801,41 ~dag~ = ...~hg
\item   684,89 ~kg~ = ...~hg
\item   645,44 ~dag~ = ...~cg
\item   907,88 ~dm~ = ...~m
\item   199,01 ~hL~ = ...~cL
\item   544,3 ~mg~ = ...~g
\item   286,09 ~dg~ = ...~dag
\item   962,51 ~cL~ = ...~mL
\item   203,64 ~dg~ = ...~cg
\item   792,66 ~g~ = ...~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   2 = \(\dfrac{20}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{5900}{100}\) = \(\dfrac{590}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{87}{10}\) = \(\dfrac{870}{100}\)
\item   \(\dfrac{74}{100}\) = \(\dfrac{740}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,042  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,42}
\item   0,078  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,8}
\item   0,04  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 40}
\item   0,037  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,37}
\item   5,13  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 51,3}
\item   313  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 31 300}
\item   0,648  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,48}
\item   78,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 890}
\item   4,44  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 444}
\item   0,681  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 68,1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,22 ~ : ~ 100 ~ = ~{\color{red} 0,872 2}
\item   602,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,602 8}
\item   9,208 ~ : ~ 100 ~ = ~{\color{red} 0,092 08}
\item   51,4 ~ : ~ 100 ~ = ~{\color{red} 0,514}
\item   0,348 ~ : ~ 10 ~ = ~{\color{red} 0,034 8}
\item   2 516 ~ : ~ 1 000 ~ = ~{\color{red} 2,516}
\item   882,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,882 2}
\item   5 365 ~ : ~ 1 000 ~ = ~{\color{red} 5,365}
\item   6,037 ~ : ~ 100 ~ = ~{\color{red} 0,060 37}
\item   563,3 ~ : ~ 100 ~ = ~{\color{red} 5,633}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   576 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~576 000
\item   10,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~10 100
\item   5,38 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~53,8
\item   0,285 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~28,5
\item   8,64 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~86,4
\item   0,085 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~85
\item   51,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~51 100
\item   8,79 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 790
\item   964 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 640
\item   5,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~57
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   648,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,489
}\item   934,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 93,49
}\item   488,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,884
}\item   36,84 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,684
}\item   2,444 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,244 4
}\item   975,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,752
}\item   54,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,48
}\item   415,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,151
}\item   8 276 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,276
}\item   5 312 ~ \(\times\)  0,01 ~ = ~{\color{red} 53,12
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   65,55 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,655 5
\item   736 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 73,6
\item   4,164 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 164
\item   8 316 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 831,6
\item   587,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,587 2
\item   67,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,067 4
\item   1,437 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,143 7
\item   372,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 37,29
\item   59,21 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,059 21
\item   26,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,263
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   801,41 ~dag~ = {\color{red}  80,141 }~hg
\item   684,89 ~kg~ = {\color{red}  6 848,9 }~hg
\item   645,44 ~dag~ = {\color{red}  645 440 }~cg
\item   907,88 ~dm~ = {\color{red}  90,788 }~m
\item   199,01 ~hL~ = {\color{red}  1 990 100 }~cL
\item   544,3 ~mg~ = {\color{red}  0,544 3 }~g
\item   286,09 ~dg~ = {\color{red}  2,860 9 }~dag
\item   962,51 ~cL~ = {\color{red}  9 625,1 }~mL
\item   203,64 ~dg~ = {\color{red}  2 036,4 }~cg
\item   792,66 ~g~ = {\color{red}  792 660 }~mg
\end{itemize}
\end{multicols}
\end{document}
