\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 179}

\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=179}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0179}
\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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{49}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   463  ~ \(\times\)  ~ 1 000
\item   8,37  ~ \(\times\)  ~ 10
\item   0,088  ~ \(\times\)  ~ 10
\item   3,16  ~ \(\times\)  ~ 1 000
\item   51,9  ~ \(\times\)  ~ 100
\item   91,3  ~ \(\times\)  ~ 1 000
\item   0,064  ~ \(\times\)  ~ 100
\item   17,9  ~ \(\times\)  ~ 10
\item   0,91  ~ \(\times\)  ~ 10
\item   793  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 837  ~ : ~ 1 000
\item   9 779  ~ : ~ 100
\item   1 352  ~ : ~ 1 000
\item   355  ~ : ~ 1 000
\item   93,33  ~ : ~ 10
\item   550,7  ~ : ~ 10
\item   213,6  ~ : ~ 1 000
\item   1,676  ~ : ~ 1 000
\item   8,463  ~ : ~ 1 000
\item   0,692  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,078  ~ \(\times\)  ~ ... ~ = ~ 7,8
\item   0,012  ~ \(\times\)  ~ ... ~ = ~ 12
\item   79,5  ~ \(\times\)  ~ ... ~ = ~ 7 950
\item   782  ~ \(\times\)  ~ ... ~ = ~ 7 820
\item   2,8  ~ \(\times\)  ~ ... ~ = ~ 28
\item   946  ~ \(\times\)  ~ ... ~ = ~ 946 000
\item   90  ~ \(\times\)  ~ ... ~ = ~ 900
\item   37  ~ \(\times\)  ~ ... ~ = ~ 370
\item   6,1  ~ \(\times\)  ~ ... ~ = ~ 6 100
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   27,79  ~ \(\times\)  ~ 0,1
\item   303,9  ~ \(\times\)  ~ 0,01
\item   88,27  ~ \(\times\)  ~ 0,01
\item   839,6  ~ \(\times\)  ~ 0,1
\item   322,2  ~ \(\times\)  ~ 0,001
\item   955,2  ~ \(\times\)  ~ 0,01
\item   71,1  ~ \(\times\)  ~ 0,1
\item   59,94  ~ \(\times\)  ~ 0,1
\item   1,41  ~ \(\times\)  ~ 0,1
\item   3 510  ~ \(\times\)  ~ 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   1,185  ~ \(\times\)  ~ ... ~ = ~  0,118 5
\item   833,6  ~ \(\times\)  ~ ... ~ = ~  0,833 6
\item   92,99  ~ \(\times\)  ~ ... ~ = ~  0,929 9
\item   385,8  ~ \(\times\)  ~ ... ~ = ~  3,858
\item   489  ~ \(\times\)  ~ ... ~ = ~  4,89
\item   1,21  ~ \(\times\)  ~ ... ~ = ~  0,001 21
\item   56,96  ~ \(\times\)  ~ ... ~ = ~  0,056 96
\item   3,316  ~ \(\times\)  ~ ... ~ = ~  0,003 316
\item   8,686  ~ \(\times\)  ~ ... ~ = ~  0,008 686
\item   6,366  ~ \(\times\)  ~ ... ~ = ~  0,006 366
\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 ~km~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   279,34 ~dL~ = ...~L
\item   2 319,3 ~mm~ = ...~cm
\item   380,09 ~dag~ = ...~dg
\item   8 530,8 ~hL~ = ...~daL
\item   6 819,3 ~kg~ = ...~g
\item   375,91 ~m~ = ...~km
\item   930,21 ~L~ = ...~dL
\item   361,8 ~cL~ = ...~dL
\item   184,85 ~daL~ = ...~dL
\item   691,64 ~mm~ = ...~dam
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{190}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{770}{100}\)
\item   \(\dfrac{49}{100}\) = \(\dfrac{490}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   463  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 463 000}
\item   8,37  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 83,7}
\item   0,088  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,88}
\item   3,16  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 160}
\item   51,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 190}
\item   91,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 91 300}
\item   0,064  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,4}
\item   17,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 179}
\item   0,91  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,1}
\item   793  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 79 300}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 837 ~ : ~ 1 000 ~ = ~{\color{red} 1,837}
\item   9 779 ~ : ~ 100 ~ = ~{\color{red} 97,79}
\item   1 352 ~ : ~ 1 000 ~ = ~{\color{red} 1,352}
\item   355 ~ : ~ 1 000 ~ = ~{\color{red} 0,355}
\item   93,33 ~ : ~ 10 ~ = ~{\color{red} 9,333}
\item   550,7 ~ : ~ 10 ~ = ~{\color{red} 55,07}
\item   213,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,213 6}
\item   1,676 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 676}
\item   8,463 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 463}
\item   0,692 ~ : ~ 100 ~ = ~{\color{red} 0,006 92}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,078 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,8
\item   0,012 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~12
\item   79,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 950
\item   782 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 820
\item   2,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~28
\item   946 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~946 000
\item   90 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~900
\item   37 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~370
\item   6,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 100
\item   0,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   27,79 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,779
}\item   303,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,039
}\item   88,27 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,882 7
}\item   839,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 83,96
}\item   322,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,322 2
}\item   955,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,552
}\item   71,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,11
}\item   59,94 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,994
}\item   1,41 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,141
}\item   3 510 ~ \(\times\)  0,01 ~ = ~{\color{red} 35,1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,185 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,118 5
\item   833,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,833 6
\item   92,99 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,929 9
\item   385,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,858
\item   489 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,89
\item   1,21 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 21
\item   56,96 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,056 96
\item   3,316 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 316
\item   8,686 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 686
\item   6,366 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 366
\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 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   279,34 ~dL~ = {\color{red}  27,934 }~L
\item   2 319,3 ~mm~ = {\color{red}  231,93 }~cm
\item   380,09 ~dag~ = {\color{red}  38 009 }~dg
\item   8 530,8 ~hL~ = {\color{red}  85 308 }~daL
\item   6 819,3 ~kg~ = {\color{red}  6 819 300 }~g
\item   375,91 ~m~ = {\color{red}  0,375 91 }~km
\item   930,21 ~L~ = {\color{red}  9 302,1 }~dL
\item   361,8 ~cL~ = {\color{red}  36,18 }~dL
\item   184,85 ~daL~ = {\color{red}  18 485 }~dL
\item   691,64 ~mm~ = {\color{red}  0,069 164 }~dam
\end{itemize}
\end{multicols}
\end{document}
