\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 396}

\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=396}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0396}
\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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{82}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,362  ~ \(\times\)  ~ 10
\item   0,039  ~ \(\times\)  ~ 100
\item   0,635  ~ \(\times\)  ~ 10
\item   4,34  ~ \(\times\)  ~ 100
\item   0,184  ~ \(\times\)  ~ 100
\item   3,32  ~ \(\times\)  ~ 10
\item   623  ~ \(\times\)  ~ 1 000
\item   5,66  ~ \(\times\)  ~ 1 000
\item   5,47  ~ \(\times\)  ~ 100
\item   1,38  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   332,4  ~ : ~ 100
\item   10,23  ~ : ~ 100
\item   63,94  ~ : ~ 1 000
\item   8 420  ~ : ~ 100
\item   798,8  ~ : ~ 10
\item   62,57  ~ : ~ 10
\item   5 957  ~ : ~ 10
\item   1 713  ~ : ~ 100
\item   801,1  ~ : ~ 100
\item   6 189  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,885  ~ \(\times\)  ~ ... ~ = ~ 88,5
\item   65,7  ~ \(\times\)  ~ ... ~ = ~ 657
\item   90  ~ \(\times\)  ~ ... ~ = ~ 9 000
\item   0,34  ~ \(\times\)  ~ ... ~ = ~ 340
\item   0,007  ~ \(\times\)  ~ ... ~ = ~ 0,07
\item   0,825  ~ \(\times\)  ~ ... ~ = ~ 825
\item   2,44  ~ \(\times\)  ~ ... ~ = ~ 24,4
\item   0,22  ~ \(\times\)  ~ ... ~ = ~ 2,2
\item   32,7  ~ \(\times\)  ~ ... ~ = ~ 3 270
\item   0,009  ~ \(\times\)  ~ ... ~ = ~ 0,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 710  ~ \(\times\)  ~ 0,001
\item   4 760  ~ \(\times\)  ~ 0,1
\item   540,6  ~ \(\times\)  ~ 0,1
\item   7,913  ~ \(\times\)  ~ 0,01
\item   7,737  ~ \(\times\)  ~ 0,001
\item   1 971  ~ \(\times\)  ~ 0,1
\item   42,34  ~ \(\times\)  ~ 0,1
\item   2,619  ~ \(\times\)  ~ 0,01
\item   1 530  ~ \(\times\)  ~ 0,001
\item   4 004  ~ \(\times\)  ~ 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   510,7  ~ \(\times\)  ~ ... ~ = ~  5,107
\item   284  ~ \(\times\)  ~ ... ~ = ~  2,84
\item   4,443  ~ \(\times\)  ~ ... ~ = ~  0,044 43
\item   705,3  ~ \(\times\)  ~ ... ~ = ~  0,705 3
\item   8,817  ~ \(\times\)  ~ ... ~ = ~  0,881 7
\item   279,9  ~ \(\times\)  ~ ... ~ = ~  2,799
\item   14,41  ~ \(\times\)  ~ ... ~ = ~  0,014 41
\item   50,5  ~ \(\times\)  ~ ... ~ = ~  5,05
\item   85,08  ~ \(\times\)  ~ ... ~ = ~  0,085 08
\item   7 353  ~ \(\times\)  ~ ... ~ = ~  7,353
\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 ~km~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   663,65 ~dg~ = ...~kg
\item   4 953,2 ~dam~ = ...~dm
\item   9 328,5 ~kg~ = ...~dg
\item   4 025,3 ~dam~ = ...~m
\item   7 034,3 ~dag~ = ...~g
\item   492,73 ~hm~ = ...~m
\item   189,65 ~kg~ = ...~mg
\item   9 144,5 ~dL~ = ...~daL
\item   9 964,6 ~cg~ = ...~hg
\item   216,15 ~daL~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{9400}{100}\) = \(\dfrac{940}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{82}{10}\) = \(\dfrac{820}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{290}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,362  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,62}
\item   0,039  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,9}
\item   0,635  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,35}
\item   4,34  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 434}
\item   0,184  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 18,4}
\item   3,32  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 33,2}
\item   623  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 623 000}
\item   5,66  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 660}
\item   5,47  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 547}
\item   1,38  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 138}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   332,4 ~ : ~ 100 ~ = ~{\color{red} 3,324}
\item   10,23 ~ : ~ 100 ~ = ~{\color{red} 0,102 3}
\item   63,94 ~ : ~ 1 000 ~ = ~{\color{red} 0,063 94}
\item   8 420 ~ : ~ 100 ~ = ~{\color{red} 84,2}
\item   798,8 ~ : ~ 10 ~ = ~{\color{red} 79,88}
\item   62,57 ~ : ~ 10 ~ = ~{\color{red} 6,257}
\item   5 957 ~ : ~ 10 ~ = ~{\color{red} 595,7}
\item   1 713 ~ : ~ 100 ~ = ~{\color{red} 17,13}
\item   801,1 ~ : ~ 100 ~ = ~{\color{red} 8,011}
\item   6 189 ~ : ~ 1 000 ~ = ~{\color{red} 6,189}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,885 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88,5
\item   65,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~657
\item   90 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 000
\item   0,34 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~340
\item   0,007 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,07
\item   0,825 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~825
\item   2,44 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~24,4
\item   0,22 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,2
\item   32,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 270
\item   0,009 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 710 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,71
}\item   4 760 ~ \(\times\)  0,1 ~ = ~{\color{red} 476
}\item   540,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 54,06
}\item   7,913 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,079 13
}\item   7,737 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 737
}\item   1 971 ~ \(\times\)  0,1 ~ = ~{\color{red} 197,1
}\item   42,34 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,234
}\item   2,619 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,026 19
}\item   1 530 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,53
}\item   4 004 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,004
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   510,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,107
\item   284 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,84
\item   4,443 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,044 43
\item   705,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,705 3
\item   8,817 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,881 7
\item   279,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,799
\item   14,41 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,014 41
\item   50,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,05
\item   85,08 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,085 08
\item   7 353 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,353
\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 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   663,65 ~dg~ = {\color{red}  0,066 365 }~kg
\item   4 953,2 ~dam~ = {\color{red}  495 320 }~dm
\item   9 328,5 ~kg~ = {\color{red}  93 285 000 }~dg
\item   4 025,3 ~dam~ = {\color{red}  40 253 }~m
\item   7 034,3 ~dag~ = {\color{red}  70 343 }~g
\item   492,73 ~hm~ = {\color{red}  49 273 }~m
\item   189,65 ~kg~ = {\color{red}  189 650 000 }~mg
\item   9 144,5 ~dL~ = {\color{red}  91,445 }~daL
\item   9 964,6 ~cg~ = {\color{red}  0,996 46 }~hg
\item   216,15 ~daL~ = {\color{red}  2,161 5 }~kL
\end{itemize}
\end{multicols}
\end{document}
