\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 319}

\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=319}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0319}
\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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,3  ~ \(\times\)  ~ 10
\item   36,4  ~ \(\times\)  ~ 1 000
\item   0,081  ~ \(\times\)  ~ 100
\item   18,8  ~ \(\times\)  ~ 100
\item   0,099  ~ \(\times\)  ~ 1 000
\item   6,25  ~ \(\times\)  ~ 10
\item   0,474  ~ \(\times\)  ~ 10
\item   0,976  ~ \(\times\)  ~ 10
\item   3,9  ~ \(\times\)  ~ 100
\item   490  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,329  ~ : ~ 100
\item   3,211  ~ : ~ 1 000
\item   33,26  ~ : ~ 1 000
\item   524,4  ~ : ~ 100
\item   4 277  ~ : ~ 1 000
\item   5,859  ~ : ~ 10
\item   2,217  ~ : ~ 100
\item   622,1  ~ : ~ 1 000
\item   1,243  ~ : ~ 100
\item   42,26  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   738  ~ \(\times\)  ~ ... ~ = ~ 73 800
\item   54,8  ~ \(\times\)  ~ ... ~ = ~ 548
\item   36,5  ~ \(\times\)  ~ ... ~ = ~ 365
\item   69,9  ~ \(\times\)  ~ ... ~ = ~ 6 990
\item   740  ~ \(\times\)  ~ ... ~ = ~ 74 000
\item   0,191  ~ \(\times\)  ~ ... ~ = ~ 19,1
\item   0,406  ~ \(\times\)  ~ ... ~ = ~ 40,6
\item   6,04  ~ \(\times\)  ~ ... ~ = ~ 6 040
\item   6,01  ~ \(\times\)  ~ ... ~ = ~ 6 010
\item   98  ~ \(\times\)  ~ ... ~ = ~ 980
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 006  ~ \(\times\)  ~ 0,1
\item   1,473  ~ \(\times\)  ~ 0,01
\item   4 445  ~ \(\times\)  ~ 0,01
\item   8,932  ~ \(\times\)  ~ 0,001
\item   881,1  ~ \(\times\)  ~ 0,01
\item   14,77  ~ \(\times\)  ~ 0,1
\item   7 132  ~ \(\times\)  ~ 0,001
\item   567,7  ~ \(\times\)  ~ 0,01
\item   698  ~ \(\times\)  ~ 0,1
\item   6 287  ~ \(\times\)  ~ 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   1,814  ~ \(\times\)  ~ ... ~ = ~  0,018 14
\item   1,811  ~ \(\times\)  ~ ... ~ = ~  0,001 811
\item   85,99  ~ \(\times\)  ~ ... ~ = ~  0,859 9
\item   6,475  ~ \(\times\)  ~ ... ~ = ~  0,647 5
\item   256,5  ~ \(\times\)  ~ ... ~ = ~  2,565
\item   525,9  ~ \(\times\)  ~ ... ~ = ~  5,259
\item   95,15  ~ \(\times\)  ~ ... ~ = ~  9,515
\item   62,7  ~ \(\times\)  ~ ... ~ = ~  0,062 7
\item   2,805  ~ \(\times\)  ~ ... ~ = ~  0,028 05
\item   847,3  ~ \(\times\)  ~ ... ~ = ~  0,847 3
\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 ~dam~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~m~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 175,6 ~hm~ = ...~km
\item   2 207,2 ~cg~ = ...~hg
\item   5 610 ~km~ = ...~hm
\item   7 380 ~m~ = ...~dam
\item   2 418 ~hm~ = ...~dm
\item   4 845,5 ~cm~ = ...~dam
\item   7 178 ~dg~ = ...~kg
\item   7 357,2 ~hL~ = ...~kL
\item   9 671,4 ~L~ = ...~dL
\item   703,35 ~mL~ = ...~hL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{790}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{900}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{190}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 23}
\item   36,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 36 400}
\item   0,081  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,1}
\item   18,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 880}
\item   0,099  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 99}
\item   6,25  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 62,5}
\item   0,474  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,74}
\item   0,976  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,76}
\item   3,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 390}
\item   490  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 900}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,329 ~ : ~ 100 ~ = ~{\color{red} 0,083 29}
\item   3,211 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 211}
\item   33,26 ~ : ~ 1 000 ~ = ~{\color{red} 0,033 26}
\item   524,4 ~ : ~ 100 ~ = ~{\color{red} 5,244}
\item   4 277 ~ : ~ 1 000 ~ = ~{\color{red} 4,277}
\item   5,859 ~ : ~ 10 ~ = ~{\color{red} 0,585 9}
\item   2,217 ~ : ~ 100 ~ = ~{\color{red} 0,022 17}
\item   622,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,622 1}
\item   1,243 ~ : ~ 100 ~ = ~{\color{red} 0,012 43}
\item   42,26 ~ : ~ 10 ~ = ~{\color{red} 4,226}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   738 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~73 800
\item   54,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~548
\item   36,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~365
\item   69,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 990
\item   740 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74 000
\item   0,191 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~19,1
\item   0,406 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~40,6
\item   6,04 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 040
\item   6,01 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 010
\item   98 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~980
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 006 ~ \(\times\)  0,1 ~ = ~{\color{red} 200,6
}\item   1,473 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,014 73
}\item   4 445 ~ \(\times\)  0,01 ~ = ~{\color{red} 44,45
}\item   8,932 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 932
}\item   881,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,811
}\item   14,77 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,477
}\item   7 132 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,132
}\item   567,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,677
}\item   698 ~ \(\times\)  0,1 ~ = ~{\color{red} 69,8
}\item   6 287 ~ \(\times\)  0,1 ~ = ~{\color{red} 628,7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,814 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,018 14
\item   1,811 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 811
\item   85,99 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,859 9
\item   6,475 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,647 5
\item   256,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,565
\item   525,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,259
\item   95,15 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,515
\item   62,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,062 7
\item   2,805 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,028 05
\item   847,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,847 3
\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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 175,6 ~hm~ = {\color{red}  817,56 }~km
\item   2 207,2 ~cg~ = {\color{red}  0,220 72 }~hg
\item   5 610 ~km~ = {\color{red}  56 100 }~hm
\item   7 380 ~m~ = {\color{red}  738 }~dam
\item   2 418 ~hm~ = {\color{red}  2 418 000 }~dm
\item   4 845,5 ~cm~ = {\color{red}  4,845 5 }~dam
\item   7 178 ~dg~ = {\color{red}  0,717 8 }~kg
\item   7 357,2 ~hL~ = {\color{red}  735,72 }~kL
\item   9 671,4 ~L~ = {\color{red}  96 714 }~dL
\item   703,35 ~mL~ = {\color{red}  0,007 033 5 }~hL
\end{itemize}
\end{multicols}
\end{document}
