\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 107}

\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=107}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0107}
\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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{28}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{65}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   566  ~ \(\times\)  ~ 100
\item   0,031  ~ \(\times\)  ~ 10
\item   7,34  ~ \(\times\)  ~ 100
\item   20,3  ~ \(\times\)  ~ 1 000
\item   20,7  ~ \(\times\)  ~ 1 000
\item   55,6  ~ \(\times\)  ~ 10
\item   390  ~ \(\times\)  ~ 10
\item   98,7  ~ \(\times\)  ~ 10
\item   51,3  ~ \(\times\)  ~ 10
\item   4,78  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   40,84  ~ : ~ 100
\item   721,6  ~ : ~ 10
\item   5,162  ~ : ~ 100
\item   4 991  ~ : ~ 100
\item   499,3  ~ : ~ 10
\item   3 694  ~ : ~ 1 000
\item   727,9  ~ : ~ 1 000
\item   36,7  ~ : ~ 100
\item   8,242  ~ : ~ 100
\item   0,218  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 0,96
\item   0,515  ~ \(\times\)  ~ ... ~ = ~ 515
\item   0,013  ~ \(\times\)  ~ ... ~ = ~ 1,3
\item   266  ~ \(\times\)  ~ ... ~ = ~ 2 660
\item   0,042  ~ \(\times\)  ~ ... ~ = ~ 42
\item   3  ~ \(\times\)  ~ ... ~ = ~ 300
\item   4,03  ~ \(\times\)  ~ ... ~ = ~ 4 030
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 95
\item   89,4  ~ \(\times\)  ~ ... ~ = ~ 8 940
\item   0,961  ~ \(\times\)  ~ ... ~ = ~ 96,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,347  ~ \(\times\)  ~ 0,001
\item   7,407  ~ \(\times\)  ~ 0,001
\item   7 129  ~ \(\times\)  ~ 0,01
\item   226  ~ \(\times\)  ~ 0,1
\item   2 551  ~ \(\times\)  ~ 0,01
\item   41,35  ~ \(\times\)  ~ 0,01
\item   2,622  ~ \(\times\)  ~ 0,1
\item   5,58  ~ \(\times\)  ~ 0,1
\item   66,03  ~ \(\times\)  ~ 0,01
\item   177,2  ~ \(\times\)  ~ 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   735  ~ \(\times\)  ~ ... ~ = ~  7,35
\item   3 465  ~ \(\times\)  ~ ... ~ = ~  3,465
\item   2 116  ~ \(\times\)  ~ ... ~ = ~  21,16
\item   2,706  ~ \(\times\)  ~ ... ~ = ~  0,002 706
\item   7 071  ~ \(\times\)  ~ ... ~ = ~  7,071
\item   301,2  ~ \(\times\)  ~ ... ~ = ~  3,012
\item   42,67  ~ \(\times\)  ~ ... ~ = ~  0,042 67
\item   5 098  ~ \(\times\)  ~ ... ~ = ~  509,8
\item   761,9  ~ \(\times\)  ~ ... ~ = ~  76,19
\item   255  ~ \(\times\)  ~ ... ~ = ~  25,5
\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~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 922,6 ~L~ = ...~cL
\item   4 730,5 ~hm~ = ...~km
\item   1 224,8 ~mg~ = ...~g
\item   179,34 ~hL~ = ...~L
\item   3 907,6 ~mL~ = ...~hL
\item   708,54 ~kg~ = ...~dg
\item   342,18 ~dg~ = ...~g
\item   389,02 ~cm~ = ...~dam
\item   5 697,9 ~dg~ = ...~kg
\item   7 250,8 ~hg~ = ...~cg
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{720}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{28}{10}\) = \(\dfrac{280}{100}\)
\item   \(\dfrac{65}{100}\) = \(\dfrac{650}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   566  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 56 600}
\item   0,031  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,31}
\item   7,34  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 734}
\item   20,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 20 300}
\item   20,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 20 700}
\item   55,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 556}
\item   390  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 900}
\item   98,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 987}
\item   51,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 513}
\item   4,78  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 47,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   40,84 ~ : ~ 100 ~ = ~{\color{red} 0,408 4}
\item   721,6 ~ : ~ 10 ~ = ~{\color{red} 72,16}
\item   5,162 ~ : ~ 100 ~ = ~{\color{red} 0,051 62}
\item   4 991 ~ : ~ 100 ~ = ~{\color{red} 49,91}
\item   499,3 ~ : ~ 10 ~ = ~{\color{red} 49,93}
\item   3 694 ~ : ~ 1 000 ~ = ~{\color{red} 3,694}
\item   727,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,727 9}
\item   36,7 ~ : ~ 100 ~ = ~{\color{red} 0,367}
\item   8,242 ~ : ~ 100 ~ = ~{\color{red} 0,082 42}
\item   0,218 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 218}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,096 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,96
\item   0,515 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~515
\item   0,013 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,3
\item   266 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 660
\item   0,042 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~42
\item   3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~300
\item   4,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 030
\item   0,095 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~95
\item   89,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 940
\item   0,961 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,347 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 347
}\item   7,407 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 407
}\item   7 129 ~ \(\times\)  0,01 ~ = ~{\color{red} 71,29
}\item   226 ~ \(\times\)  0,1 ~ = ~{\color{red} 22,6
}\item   2 551 ~ \(\times\)  0,01 ~ = ~{\color{red} 25,51
}\item   41,35 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,413 5
}\item   2,622 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,262 2
}\item   5,58 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,558
}\item   66,03 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,660 3
}\item   177,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 17,72
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   735 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,35
\item   3 465 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,465
\item   2 116 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 21,16
\item   2,706 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 706
\item   7 071 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,071
\item   301,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,012
\item   42,67 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,042 67
\item   5 098 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 509,8
\item   761,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 76,19
\item   255 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 25,5
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 922,6 ~L~ = {\color{red}  192 260 }~cL
\item   4 730,5 ~hm~ = {\color{red}  473,05 }~km
\item   1 224,8 ~mg~ = {\color{red}  1,224 8 }~g
\item   179,34 ~hL~ = {\color{red}  17 934 }~L
\item   3 907,6 ~mL~ = {\color{red}  0,039 076 }~hL
\item   708,54 ~kg~ = {\color{red}  7 085 400 }~dg
\item   342,18 ~dg~ = {\color{red}  34,218 }~g
\item   389,02 ~cm~ = {\color{red}  0,389 02 }~dam
\item   5 697,9 ~dg~ = {\color{red}  0,569 79 }~kg
\item   7 250,8 ~hg~ = {\color{red}  72 508 000 }~cg
\end{itemize}
\end{multicols}
\end{document}
