\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 80}

\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=80}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0080}
\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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,554  ~ \(\times\)  ~ 100
\item   0,003  ~ \(\times\)  ~ 100
\item   95,9  ~ \(\times\)  ~ 1 000
\item   0,064  ~ \(\times\)  ~ 10
\item   0,018  ~ \(\times\)  ~ 1 000
\item   2,4  ~ \(\times\)  ~ 100
\item   64,5  ~ \(\times\)  ~ 10
\item   2,45  ~ \(\times\)  ~ 100
\item   61,5  ~ \(\times\)  ~ 1 000
\item   2,17  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   13,96  ~ : ~ 10
\item   361  ~ : ~ 10
\item   87,42  ~ : ~ 100
\item   6 126  ~ : ~ 100
\item   8 291  ~ : ~ 10
\item   82,44  ~ : ~ 1 000
\item   0,961  ~ : ~ 10
\item   46,51  ~ : ~ 100
\item   5 778  ~ : ~ 1 000
\item   0,769  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   136  ~ \(\times\)  ~ ... ~ = ~ 1 360
\item   178  ~ \(\times\)  ~ ... ~ = ~ 178 000
\item   2,82  ~ \(\times\)  ~ ... ~ = ~ 282
\item   721  ~ \(\times\)  ~ ... ~ = ~ 721 000
\item   0,91  ~ \(\times\)  ~ ... ~ = ~ 91
\item   88,4  ~ \(\times\)  ~ ... ~ = ~ 8 840
\item   43,8  ~ \(\times\)  ~ ... ~ = ~ 438
\item   0,232  ~ \(\times\)  ~ ... ~ = ~ 23,2
\item   66,9  ~ \(\times\)  ~ ... ~ = ~ 669
\item   8,3  ~ \(\times\)  ~ ... ~ = ~ 830
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43,55  ~ \(\times\)  ~ 0,01
\item   8,826  ~ \(\times\)  ~ 0,1
\item   966,5  ~ \(\times\)  ~ 0,001
\item   91,56  ~ \(\times\)  ~ 0,01
\item   92,21  ~ \(\times\)  ~ 0,1
\item   9 396  ~ \(\times\)  ~ 0,01
\item   6,091  ~ \(\times\)  ~ 0,01
\item   25,9  ~ \(\times\)  ~ 0,001
\item   12,76  ~ \(\times\)  ~ 0,1
\item   93,09  ~ \(\times\)  ~ 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   53,62  ~ \(\times\)  ~ ... ~ = ~  0,536 2
\item   985,4  ~ \(\times\)  ~ ... ~ = ~  98,54
\item   357,1  ~ \(\times\)  ~ ... ~ = ~  35,71
\item   2 942  ~ \(\times\)  ~ ... ~ = ~  29,42
\item   4 466  ~ \(\times\)  ~ ... ~ = ~  4,466
\item   815,7  ~ \(\times\)  ~ ... ~ = ~  81,57
\item   168,5  ~ \(\times\)  ~ ... ~ = ~  0,168 5
\item   88,7  ~ \(\times\)  ~ ... ~ = ~  0,887
\item   55,58  ~ \(\times\)  ~ ... ~ = ~  5,558
\item   558,6  ~ \(\times\)  ~ ... ~ = ~  55,86
\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~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 546,5 ~L~ = ...~hL
\item   379,37 ~cL~ = ...~L
\item   4 254,4 ~hm~ = ...~dam
\item   9 087,6 ~cg~ = ...~dag
\item   8 905,5 ~km~ = ...~dm
\item   2 428,8 ~mg~ = ...~hg
\item   7 172,5 ~mm~ = ...~km
\item   827,18 ~mm~ = ...~cm
\item   8 845,4 ~g~ = ...~cg
\item   9 584,7 ~L~ = ...~cL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{8000}{100}\) = \(\dfrac{800}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{580}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{570}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,554  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 55,4}
\item   0,003  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,3}
\item   95,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 95 900}
\item   0,064  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,64}
\item   0,018  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 18}
\item   2,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 240}
\item   64,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 645}
\item   2,45  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 245}
\item   61,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 61 500}
\item   2,17  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 217}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   13,96 ~ : ~ 10 ~ = ~{\color{red} 1,396}
\item   361 ~ : ~ 10 ~ = ~{\color{red} 36,1}
\item   87,42 ~ : ~ 100 ~ = ~{\color{red} 0,874 2}
\item   6 126 ~ : ~ 100 ~ = ~{\color{red} 61,26}
\item   8 291 ~ : ~ 10 ~ = ~{\color{red} 829,1}
\item   82,44 ~ : ~ 1 000 ~ = ~{\color{red} 0,082 44}
\item   0,961 ~ : ~ 10 ~ = ~{\color{red} 0,096 1}
\item   46,51 ~ : ~ 100 ~ = ~{\color{red} 0,465 1}
\item   5 778 ~ : ~ 1 000 ~ = ~{\color{red} 5,778}
\item   0,769 ~ : ~ 10 ~ = ~{\color{red} 0,076 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   136 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 360
\item   178 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~178 000
\item   2,82 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~282
\item   721 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~721 000
\item   0,91 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~91
\item   88,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 840
\item   43,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~438
\item   0,232 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~23,2
\item   66,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~669
\item   8,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~830
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43,55 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,435 5
}\item   8,826 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,882 6
}\item   966,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,966 5
}\item   91,56 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,915 6
}\item   92,21 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,221
}\item   9 396 ~ \(\times\)  0,01 ~ = ~{\color{red} 93,96
}\item   6,091 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,060 91
}\item   25,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,025 9
}\item   12,76 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,276
}\item   93,09 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,930 9
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   53,62 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,536 2
\item   985,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 98,54
\item   357,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 35,71
\item   2 942 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 29,42
\item   4 466 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,466
\item   815,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 81,57
\item   168,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,168 5
\item   88,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,887
\item   55,58 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,558
\item   558,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 55,86
\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}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 546,5 ~L~ = {\color{red}  25,465 }~hL
\item   379,37 ~cL~ = {\color{red}  3,793 7 }~L
\item   4 254,4 ~hm~ = {\color{red}  42 544 }~dam
\item   9 087,6 ~cg~ = {\color{red}  9,087 6 }~dag
\item   8 905,5 ~km~ = {\color{red}  89 055 000 }~dm
\item   2 428,8 ~mg~ = {\color{red}  0,024 288 }~hg
\item   7 172,5 ~mm~ = {\color{red}  0,007 172 5 }~km
\item   827,18 ~mm~ = {\color{red}  82,718 }~cm
\item   8 845,4 ~g~ = {\color{red}  884 540 }~cg
\item   9 584,7 ~L~ = {\color{red}  958 470 }~cL
\end{itemize}
\end{multicols}
\end{document}
