\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 303}

\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=303}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0303}
\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   \(\dfrac{3500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,027  ~ \(\times\)  ~ 1 000
\item   41,6  ~ \(\times\)  ~ 100
\item   0,049  ~ \(\times\)  ~ 10
\item   0,027  ~ \(\times\)  ~ 1 000
\item   799  ~ \(\times\)  ~ 1 000
\item   850  ~ \(\times\)  ~ 1 000
\item   40,9  ~ \(\times\)  ~ 100
\item   305  ~ \(\times\)  ~ 1 000
\item   0,7  ~ \(\times\)  ~ 100
\item   731  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,28  ~ : ~ 10
\item   267,2  ~ : ~ 1 000
\item   4 913  ~ : ~ 1 000
\item   41,74  ~ : ~ 1 000
\item   4 185  ~ : ~ 100
\item   461,1  ~ : ~ 1 000
\item   5 875  ~ : ~ 1 000
\item   818,3  ~ : ~ 100
\item   916,6  ~ : ~ 10
\item   2,954  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,196  ~ \(\times\)  ~ ... ~ = ~ 1,96
\item   0,034  ~ \(\times\)  ~ ... ~ = ~ 34
\item   96,3  ~ \(\times\)  ~ ... ~ = ~ 963
\item   743  ~ \(\times\)  ~ ... ~ = ~ 743 000
\item   450  ~ \(\times\)  ~ ... ~ = ~ 4 500
\item   34  ~ \(\times\)  ~ ... ~ = ~ 340
\item   26,6  ~ \(\times\)  ~ ... ~ = ~ 26 600
\item   708  ~ \(\times\)  ~ ... ~ = ~ 708 000
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 88
\item   0,13  ~ \(\times\)  ~ ... ~ = ~ 130
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   555  ~ \(\times\)  ~ 0,01
\item   326,8  ~ \(\times\)  ~ 0,001
\item   6 274  ~ \(\times\)  ~ 0,01
\item   829,7  ~ \(\times\)  ~ 0,001
\item   3 124  ~ \(\times\)  ~ 0,1
\item   8,053  ~ \(\times\)  ~ 0,1
\item   3,566  ~ \(\times\)  ~ 0,001
\item   5,825  ~ \(\times\)  ~ 0,01
\item   0,734  ~ \(\times\)  ~ 0,001
\item   7,76  ~ \(\times\)  ~ 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   87,65  ~ \(\times\)  ~ ... ~ = ~  0,876 5
\item   7 194  ~ \(\times\)  ~ ... ~ = ~  719,4
\item   760,3  ~ \(\times\)  ~ ... ~ = ~  7,603
\item   8,94  ~ \(\times\)  ~ ... ~ = ~  0,008 94
\item   14,97  ~ \(\times\)  ~ ... ~ = ~  0,014 97
\item   265  ~ \(\times\)  ~ ... ~ = ~  2,65
\item   45,21  ~ \(\times\)  ~ ... ~ = ~  0,045 21
\item   39,49  ~ \(\times\)  ~ ... ~ = ~  0,394 9
\item   4 470  ~ \(\times\)  ~ ... ~ = ~  4,47
\item   429,5  ~ \(\times\)  ~ ... ~ = ~  4,295
\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~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   664,65 ~cg~ = ...~mg
\item   464,21 ~km~ = ...~cm
\item   9 854,1 ~cL~ = ...~daL
\item   7 580,8 ~dag~ = ...~cg
\item   1 256,7 ~dm~ = ...~mm
\item   587,59 ~mg~ = ...~dg
\item   317,2 ~dL~ = ...~hL
\item   4 694,7 ~m~ = ...~dam
\item   394,54 ~km~ = ...~hm
\item   2 844,1 ~hm~ = ...~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   1 = \(\dfrac{10}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{3500}{100}\) = \(\dfrac{350}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{900}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,027  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 27}
\item   41,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 160}
\item   0,049  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,49}
\item   0,027  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 27}
\item   799  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 799 000}
\item   850  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 850 000}
\item   40,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 090}
\item   305  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 305 000}
\item   0,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 70}
\item   731  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 310}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,28 ~ : ~ 10 ~ = ~{\color{red} 3,628}
\item   267,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,267 2}
\item   4 913 ~ : ~ 1 000 ~ = ~{\color{red} 4,913}
\item   41,74 ~ : ~ 1 000 ~ = ~{\color{red} 0,041 74}
\item   4 185 ~ : ~ 100 ~ = ~{\color{red} 41,85}
\item   461,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,461 1}
\item   5 875 ~ : ~ 1 000 ~ = ~{\color{red} 5,875}
\item   818,3 ~ : ~ 100 ~ = ~{\color{red} 8,183}
\item   916,6 ~ : ~ 10 ~ = ~{\color{red} 91,66}
\item   2,954 ~ : ~ 10 ~ = ~{\color{red} 0,295 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,196 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,96
\item   0,034 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~34
\item   96,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~963
\item   743 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~743 000
\item   450 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 500
\item   34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~340
\item   26,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~26 600
\item   708 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~708 000
\item   0,088 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~88
\item   0,13 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~130
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   555 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,55
}\item   326,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,326 8
}\item   6 274 ~ \(\times\)  0,01 ~ = ~{\color{red} 62,74
}\item   829,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,829 7
}\item   3 124 ~ \(\times\)  0,1 ~ = ~{\color{red} 312,4
}\item   8,053 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,805 3
}\item   3,566 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 566
}\item   5,825 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,058 25
}\item   0,734 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 734
}\item   7,76 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,776
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,65 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,876 5
\item   7 194 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 719,4
\item   760,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,603
\item   8,94 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 94
\item   14,97 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,014 97
\item   265 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,65
\item   45,21 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,045 21
\item   39,49 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,394 9
\item   4 470 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,47
\item   429,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,295
\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}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   664,65 ~cg~ = {\color{red}  6 646,5 }~mg
\item   464,21 ~km~ = {\color{red}  46 421 000 }~cm
\item   9 854,1 ~cL~ = {\color{red}  9,854 1 }~daL
\item   7 580,8 ~dag~ = {\color{red}  7 580 800 }~cg
\item   1 256,7 ~dm~ = {\color{red}  125 670 }~mm
\item   587,59 ~mg~ = {\color{red}  5,875 9 }~dg
\item   317,2 ~dL~ = {\color{red}  0,317 2 }~hL
\item   4 694,7 ~m~ = {\color{red}  469,47 }~dam
\item   394,54 ~km~ = {\color{red}  3 945,4 }~hm
\item   2 844,1 ~hm~ = {\color{red}  28 441 }~dam
\end{itemize}
\end{multicols}
\end{document}
