\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 48}

\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=48}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0048}
\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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   0,082  ~ \(\times\)  ~ 10
\item   0,74  ~ \(\times\)  ~ 10
\item   167  ~ \(\times\)  ~ 100
\item   67,3  ~ \(\times\)  ~ 10
\item   0,079  ~ \(\times\)  ~ 1 000
\item   0,088  ~ \(\times\)  ~ 10
\item   49,2  ~ \(\times\)  ~ 10
\item   0,084  ~ \(\times\)  ~ 10
\item   0,144  ~ \(\times\)  ~ 1 000
\item   17,5  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,81  ~ : ~ 100
\item   5 634  ~ : ~ 10
\item   45,56  ~ : ~ 1 000
\item   3,39  ~ : ~ 1 000
\item   23,65  ~ : ~ 1 000
\item   726,8  ~ : ~ 10
\item   66,83  ~ : ~ 10
\item   6 103  ~ : ~ 100
\item   94,82  ~ : ~ 1 000
\item   8 243  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24  ~ \(\times\)  ~ ... ~ = ~ 2 400
\item   0,049  ~ \(\times\)  ~ ... ~ = ~ 49
\item   0,335  ~ \(\times\)  ~ ... ~ = ~ 3,35
\item   801  ~ \(\times\)  ~ ... ~ = ~ 80 100
\item   0,441  ~ \(\times\)  ~ ... ~ = ~ 44,1
\item   0,001  ~ \(\times\)  ~ ... ~ = ~ 1
\item   0,663  ~ \(\times\)  ~ ... ~ = ~ 66,3
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 4,5
\item   1,67  ~ \(\times\)  ~ ... ~ = ~ 16,7
\item   0,049  ~ \(\times\)  ~ ... ~ = ~ 49
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   375,3  ~ \(\times\)  ~ 0,1
\item   264,3  ~ \(\times\)  ~ 0,01
\item   9,618  ~ \(\times\)  ~ 0,001
\item   8,747  ~ \(\times\)  ~ 0,001
\item   7 138  ~ \(\times\)  ~ 0,01
\item   87,76  ~ \(\times\)  ~ 0,1
\item   1 650  ~ \(\times\)  ~ 0,1
\item   1,48  ~ \(\times\)  ~ 0,01
\item   1,592  ~ \(\times\)  ~ 0,001
\item   7 292  ~ \(\times\)  ~ 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   9 679  ~ \(\times\)  ~ ... ~ = ~  96,79
\item   271,7  ~ \(\times\)  ~ ... ~ = ~  27,17
\item   334,1  ~ \(\times\)  ~ ... ~ = ~  3,341
\item   0,624  ~ \(\times\)  ~ ... ~ = ~  0,000 624
\item   7 073  ~ \(\times\)  ~ ... ~ = ~  70,73
\item   4,27  ~ \(\times\)  ~ ... ~ = ~  0,042 7
\item   7 014  ~ \(\times\)  ~ ... ~ = ~  7,014
\item   3,88  ~ \(\times\)  ~ ... ~ = ~  0,038 8
\item   2 142  ~ \(\times\)  ~ ... ~ = ~  214,2
\item   325  ~ \(\times\)  ~ ... ~ = ~  32,5
\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~ = ...~m
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 888,2 ~g~ = ...~dag
\item   625,43 ~cL~ = ...~dL
\item   6 822,3 ~dam~ = ...~km
\item   5 311,1 ~km~ = ...~dam
\item   9 087,8 ~cm~ = ...~dam
\item   7 544,2 ~cm~ = ...~m
\item   2 394 ~g~ = ...~dg
\item   9 502,7 ~cL~ = ...~hL
\item   499,08 ~cL~ = ...~daL
\item   8 964 ~dm~ = ...~m
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{2700}{100}\) = \(\dfrac{270}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{790}{100}\)
\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   0,082  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,82}
\item   0,74  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,4}
\item   167  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 16 700}
\item   67,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 673}
\item   0,079  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 79}
\item   0,088  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,88}
\item   49,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 492}
\item   0,084  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,84}
\item   0,144  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 144}
\item   17,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 175}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,81 ~ : ~ 100 ~ = ~{\color{red} 0,908 1}
\item   5 634 ~ : ~ 10 ~ = ~{\color{red} 563,4}
\item   45,56 ~ : ~ 1 000 ~ = ~{\color{red} 0,045 56}
\item   3,39 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 39}
\item   23,65 ~ : ~ 1 000 ~ = ~{\color{red} 0,023 65}
\item   726,8 ~ : ~ 10 ~ = ~{\color{red} 72,68}
\item   66,83 ~ : ~ 10 ~ = ~{\color{red} 6,683}
\item   6 103 ~ : ~ 100 ~ = ~{\color{red} 61,03}
\item   94,82 ~ : ~ 1 000 ~ = ~{\color{red} 0,094 82}
\item   8 243 ~ : ~ 10 ~ = ~{\color{red} 824,3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 400
\item   0,049 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~49
\item   0,335 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,35
\item   801 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~80 100
\item   0,441 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~44,1
\item   0,001 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1
\item   0,663 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~66,3
\item   0,045 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4,5
\item   1,67 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~16,7
\item   0,049 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~49
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   375,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 37,53
}\item   264,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,643
}\item   9,618 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 618
}\item   8,747 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 747
}\item   7 138 ~ \(\times\)  0,01 ~ = ~{\color{red} 71,38
}\item   87,76 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,776
}\item   1 650 ~ \(\times\)  0,1 ~ = ~{\color{red} 165
}\item   1,48 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,014 8
}\item   1,592 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 592
}\item   7 292 ~ \(\times\)  0,01 ~ = ~{\color{red} 72,92
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 679 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 96,79
\item   271,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 27,17
\item   334,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,341
\item   0,624 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 624
\item   7 073 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 70,73
\item   4,27 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,042 7
\item   7 014 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,014
\item   3,88 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,038 8
\item   2 142 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 214,2
\item   325 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 32,5
\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~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 888,2 ~g~ = {\color{red}  188,82 }~dag
\item   625,43 ~cL~ = {\color{red}  62,543 }~dL
\item   6 822,3 ~dam~ = {\color{red}  68,223 }~km
\item   5 311,1 ~km~ = {\color{red}  531 110 }~dam
\item   9 087,8 ~cm~ = {\color{red}  9,087 8 }~dam
\item   7 544,2 ~cm~ = {\color{red}  75,442 }~m
\item   2 394 ~g~ = {\color{red}  23 940 }~dg
\item   9 502,7 ~cL~ = {\color{red}  0,950 27 }~hL
\item   499,08 ~cL~ = {\color{red}  0,499 08 }~daL
\item   8 964 ~dm~ = {\color{red}  896,4 }~m
\end{itemize}
\end{multicols}
\end{document}
