\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 132}

\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=132}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0132}
\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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   323  ~ \(\times\)  ~ 1 000
\item   3,4  ~ \(\times\)  ~ 100
\item   27,4  ~ \(\times\)  ~ 100
\item   0,018  ~ \(\times\)  ~ 100
\item   0,262  ~ \(\times\)  ~ 1 000
\item   0,083  ~ \(\times\)  ~ 1 000
\item   5,81  ~ \(\times\)  ~ 100
\item   0,094  ~ \(\times\)  ~ 100
\item   209  ~ \(\times\)  ~ 1 000
\item   0,005  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 797  ~ : ~ 1 000
\item   25,87  ~ : ~ 10
\item   47,93  ~ : ~ 100
\item   2 250  ~ : ~ 1 000
\item   800,8  ~ : ~ 10
\item   758,1  ~ : ~ 10
\item   9 758  ~ : ~ 100
\item   5,756  ~ : ~ 10
\item   14,43  ~ : ~ 1 000
\item   14,59  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,2  ~ \(\times\)  ~ ... ~ = ~ 8 020
\item   66,4  ~ \(\times\)  ~ ... ~ = ~ 664
\item   15,2  ~ \(\times\)  ~ ... ~ = ~ 15 200
\item   0,119  ~ \(\times\)  ~ ... ~ = ~ 119
\item   254  ~ \(\times\)  ~ ... ~ = ~ 25 400
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 7,7
\item   0,02  ~ \(\times\)  ~ ... ~ = ~ 2
\item   0,047  ~ \(\times\)  ~ ... ~ = ~ 0,47
\item   77,7  ~ \(\times\)  ~ ... ~ = ~ 777
\item   76,5  ~ \(\times\)  ~ ... ~ = ~ 765
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,239  ~ \(\times\)  ~ 0,01
\item   9,339  ~ \(\times\)  ~ 0,1
\item   9,835  ~ \(\times\)  ~ 0,01
\item   3,463  ~ \(\times\)  ~ 0,1
\item   615,6  ~ \(\times\)  ~ 0,1
\item   25,84  ~ \(\times\)  ~ 0,001
\item   415  ~ \(\times\)  ~ 0,001
\item   0,819  ~ \(\times\)  ~ 0,01
\item   8 377  ~ \(\times\)  ~ 0,001
\item   994  ~ \(\times\)  ~ 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   430,3  ~ \(\times\)  ~ ... ~ = ~  4,303
\item   6,61  ~ \(\times\)  ~ ... ~ = ~  0,661
\item   6 104  ~ \(\times\)  ~ ... ~ = ~  61,04
\item   60,69  ~ \(\times\)  ~ ... ~ = ~  0,606 9
\item   2 693  ~ \(\times\)  ~ ... ~ = ~  26,93
\item   3 355  ~ \(\times\)  ~ ... ~ = ~  3,355
\item   1,733  ~ \(\times\)  ~ ... ~ = ~  0,001 733
\item   4,227  ~ \(\times\)  ~ ... ~ = ~  0,422 7
\item   1,393  ~ \(\times\)  ~ ... ~ = ~  0,001 393
\item   13,99  ~ \(\times\)  ~ ... ~ = ~  1,399
\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 ~hm~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   197,69 ~dg~ = ...~dag
\item   410,83 ~hg~ = ...~cg
\item   580,23 ~mg~ = ...~cg
\item   2 852,4 ~dag~ = ...~kg
\item   503,95 ~kL~ = ...~cL
\item   2 682,3 ~hL~ = ...~daL
\item   862,54 ~L~ = ...~kL
\item   5 540,6 ~mL~ = ...~cL
\item   425,95 ~hL~ = ...~cL
\item   8 158,6 ~L~ = ...~mL
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{320}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{160}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   323  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 323 000}
\item   3,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 340}
\item   27,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 740}
\item   0,018  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,8}
\item   0,262  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 262}
\item   0,083  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 83}
\item   5,81  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 581}
\item   0,094  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,4}
\item   209  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 209 000}
\item   0,005  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 797 ~ : ~ 1 000 ~ = ~{\color{red} 8,797}
\item   25,87 ~ : ~ 10 ~ = ~{\color{red} 2,587}
\item   47,93 ~ : ~ 100 ~ = ~{\color{red} 0,479 3}
\item   2 250 ~ : ~ 1 000 ~ = ~{\color{red} 2,25}
\item   800,8 ~ : ~ 10 ~ = ~{\color{red} 80,08}
\item   758,1 ~ : ~ 10 ~ = ~{\color{red} 75,81}
\item   9 758 ~ : ~ 100 ~ = ~{\color{red} 97,58}
\item   5,756 ~ : ~ 10 ~ = ~{\color{red} 0,575 6}
\item   14,43 ~ : ~ 1 000 ~ = ~{\color{red} 0,014 43}
\item   14,59 ~ : ~ 100 ~ = ~{\color{red} 0,145 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 020
\item   66,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~664
\item   15,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~15 200
\item   0,119 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~119
\item   254 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~25 400
\item   0,077 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,7
\item   0,02 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2
\item   0,047 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,47
\item   77,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~777
\item   76,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~765
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,239 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,002 39
}\item   9,339 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,933 9
}\item   9,835 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,098 35
}\item   3,463 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,346 3
}\item   615,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 61,56
}\item   25,84 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,025 84
}\item   415 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,415
}\item   0,819 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,008 19
}\item   8 377 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,377
}\item   994 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,994
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   430,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,303
\item   6,61 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,661
\item   6 104 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 61,04
\item   60,69 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,606 9
\item   2 693 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 26,93
\item   3 355 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,355
\item   1,733 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 733
\item   4,227 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,422 7
\item   1,393 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 393
\item   13,99 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,399
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   197,69 ~dg~ = {\color{red}  1,976 9 }~dag
\item   410,83 ~hg~ = {\color{red}  4 108 300 }~cg
\item   580,23 ~mg~ = {\color{red}  58,023 }~cg
\item   2 852,4 ~dag~ = {\color{red}  28,524 }~kg
\item   503,95 ~kL~ = {\color{red}  50 395 000 }~cL
\item   2 682,3 ~hL~ = {\color{red}  26 823 }~daL
\item   862,54 ~L~ = {\color{red}  0,862 54 }~kL
\item   5 540,6 ~mL~ = {\color{red}  554,06 }~cL
\item   425,95 ~hL~ = {\color{red}  4 259 500 }~cL
\item   8 158,6 ~L~ = {\color{red}  8 158 600 }~mL
\end{itemize}
\end{multicols}
\end{document}
