\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 336}

\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=336}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0336}
\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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,9  ~ \(\times\)  ~ 1 000
\item   0,035  ~ \(\times\)  ~ 1 000
\item   359  ~ \(\times\)  ~ 100
\item   0,097  ~ \(\times\)  ~ 100
\item   5,93  ~ \(\times\)  ~ 10
\item   9,32  ~ \(\times\)  ~ 100
\item   89,3  ~ \(\times\)  ~ 100
\item   0,055  ~ \(\times\)  ~ 1 000
\item   8,1  ~ \(\times\)  ~ 10
\item   409  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,218  ~ : ~ 10
\item   6 087  ~ : ~ 100
\item   7 169  ~ : ~ 100
\item   3,335  ~ : ~ 100
\item   737,7  ~ : ~ 100
\item   796,5  ~ : ~ 100
\item   3,667  ~ : ~ 100
\item   2,46  ~ : ~ 100
\item   14,92  ~ : ~ 100
\item   4,63  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,481  ~ \(\times\)  ~ ... ~ = ~ 481
\item   0,664  ~ \(\times\)  ~ ... ~ = ~ 66,4
\item   74,7  ~ \(\times\)  ~ ... ~ = ~ 747
\item   1,5  ~ \(\times\)  ~ ... ~ = ~ 150
\item   885  ~ \(\times\)  ~ ... ~ = ~ 8 850
\item   8,54  ~ \(\times\)  ~ ... ~ = ~ 85,4
\item   0,6  ~ \(\times\)  ~ ... ~ = ~ 60
\item   89,7  ~ \(\times\)  ~ ... ~ = ~ 89 700
\item   0,747  ~ \(\times\)  ~ ... ~ = ~ 747
\item   0,03  ~ \(\times\)  ~ ... ~ = ~ 30
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,756  ~ \(\times\)  ~ 0,01
\item   95,89  ~ \(\times\)  ~ 0,001
\item   7 663  ~ \(\times\)  ~ 0,01
\item   8 884  ~ \(\times\)  ~ 0,001
\item   5,477  ~ \(\times\)  ~ 0,1
\item   156,8  ~ \(\times\)  ~ 0,01
\item   49,37  ~ \(\times\)  ~ 0,001
\item   5 628  ~ \(\times\)  ~ 0,01
\item   2,27  ~ \(\times\)  ~ 0,01
\item   8,851  ~ \(\times\)  ~ 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   35,08  ~ \(\times\)  ~ ... ~ = ~  0,350 8
\item   3,651  ~ \(\times\)  ~ ... ~ = ~  0,365 1
\item   479  ~ \(\times\)  ~ ... ~ = ~  4,79
\item   55,97  ~ \(\times\)  ~ ... ~ = ~  0,055 97
\item   405,3  ~ \(\times\)  ~ ... ~ = ~  0,405 3
\item   2,272  ~ \(\times\)  ~ ... ~ = ~  0,002 272
\item   7,979  ~ \(\times\)  ~ ... ~ = ~  0,079 79
\item   14,05  ~ \(\times\)  ~ ... ~ = ~  0,014 05
\item   5 977  ~ \(\times\)  ~ ... ~ = ~  59,77
\item   393  ~ \(\times\)  ~ ... ~ = ~  3,93
\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 ~m~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 395,7 ~mg~ = ...~g
\item   772,7 ~m~ = ...~hm
\item   3 715,5 ~hm~ = ...~km
\item   3 335,4 ~cg~ = ...~dag
\item   4 094,7 ~L~ = ...~hL
\item   4 193,3 ~mL~ = ...~L
\item   1 416,4 ~dag~ = ...~kg
\item   9 681,7 ~hm~ = ...~m
\item   4 884,4 ~mg~ = ...~hg
\item   6 828 ~kg~ = ...~dag
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{290}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{570}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{340}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 900}
\item   0,035  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 35}
\item   359  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 35 900}
\item   0,097  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,7}
\item   5,93  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 59,3}
\item   9,32  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 932}
\item   89,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 930}
\item   0,055  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 55}
\item   8,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 81}
\item   409  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 40 900}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,218 ~ : ~ 10 ~ = ~{\color{red} 0,821 8}
\item   6 087 ~ : ~ 100 ~ = ~{\color{red} 60,87}
\item   7 169 ~ : ~ 100 ~ = ~{\color{red} 71,69}
\item   3,335 ~ : ~ 100 ~ = ~{\color{red} 0,033 35}
\item   737,7 ~ : ~ 100 ~ = ~{\color{red} 7,377}
\item   796,5 ~ : ~ 100 ~ = ~{\color{red} 7,965}
\item   3,667 ~ : ~ 100 ~ = ~{\color{red} 0,036 67}
\item   2,46 ~ : ~ 100 ~ = ~{\color{red} 0,024 6}
\item   14,92 ~ : ~ 100 ~ = ~{\color{red} 0,149 2}
\item   4,63 ~ : ~ 100 ~ = ~{\color{red} 0,046 3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,481 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~481
\item   0,664 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~66,4
\item   74,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~747
\item   1,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~150
\item   885 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 850
\item   8,54 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~85,4
\item   0,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~60
\item   89,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~89 700
\item   0,747 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~747
\item   0,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~30
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,756 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,087 56
}\item   95,89 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,095 89
}\item   7 663 ~ \(\times\)  0,01 ~ = ~{\color{red} 76,63
}\item   8 884 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,884
}\item   5,477 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,547 7
}\item   156,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,568
}\item   49,37 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,049 37
}\item   5 628 ~ \(\times\)  0,01 ~ = ~{\color{red} 56,28
}\item   2,27 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,022 7
}\item   8,851 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,885 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   35,08 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,350 8
\item   3,651 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,365 1
\item   479 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,79
\item   55,97 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,055 97
\item   405,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,405 3
\item   2,272 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 272
\item   7,979 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,079 79
\item   14,05 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,014 05
\item   5 977 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 59,77
\item   393 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,93
\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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 395,7 ~mg~ = {\color{red}  4,395 7 }~g
\item   772,7 ~m~ = {\color{red}  7,727 }~hm
\item   3 715,5 ~hm~ = {\color{red}  371,55 }~km
\item   3 335,4 ~cg~ = {\color{red}  3,335 4 }~dag
\item   4 094,7 ~L~ = {\color{red}  40,947 }~hL
\item   4 193,3 ~mL~ = {\color{red}  4,193 3 }~L
\item   1 416,4 ~dag~ = {\color{red}  14,164 }~kg
\item   9 681,7 ~hm~ = {\color{red}  968 170 }~m
\item   4 884,4 ~mg~ = {\color{red}  0,048 844 }~hg
\item   6 828 ~kg~ = {\color{red}  682 800 }~dag
\end{itemize}
\end{multicols}
\end{document}
