\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 5}

\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=5}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0005}
\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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{14}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,3  ~ \(\times\)  ~ 1 000
\item   6,2  ~ \(\times\)  ~ 10
\item   0,389  ~ \(\times\)  ~ 10
\item   0,04  ~ \(\times\)  ~ 10
\item   59,6  ~ \(\times\)  ~ 10
\item   75,7  ~ \(\times\)  ~ 100
\item   29,5  ~ \(\times\)  ~ 100
\item   172  ~ \(\times\)  ~ 10
\item   0,064  ~ \(\times\)  ~ 100
\item   13,8  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,8  ~ : ~ 10
\item   281,8  ~ : ~ 100
\item   523,9  ~ : ~ 1 000
\item   345,6  ~ : ~ 1 000
\item   3,326  ~ : ~ 100
\item   4,54  ~ : ~ 100
\item   282  ~ : ~ 100
\item   11,68  ~ : ~ 100
\item   9 704  ~ : ~ 1 000
\item   5 637  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,72  ~ \(\times\)  ~ ... ~ = ~ 372
\item   7,22  ~ \(\times\)  ~ ... ~ = ~ 72,2
\item   0,501  ~ \(\times\)  ~ ... ~ = ~ 501
\item   189  ~ \(\times\)  ~ ... ~ = ~ 18 900
\item   970  ~ \(\times\)  ~ ... ~ = ~ 970 000
\item   0,375  ~ \(\times\)  ~ ... ~ = ~ 3,75
\item   0,571  ~ \(\times\)  ~ ... ~ = ~ 57,1
\item   0,039  ~ \(\times\)  ~ ... ~ = ~ 0,39
\item   472  ~ \(\times\)  ~ ... ~ = ~ 472 000
\item   0,019  ~ \(\times\)  ~ ... ~ = ~ 0,19
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   205,1  ~ \(\times\)  ~ 0,01
\item   57,43  ~ \(\times\)  ~ 0,001
\item   4,211  ~ \(\times\)  ~ 0,1
\item   97,63  ~ \(\times\)  ~ 0,01
\item   0,701  ~ \(\times\)  ~ 0,1
\item   35,16  ~ \(\times\)  ~ 0,001
\item   604,2  ~ \(\times\)  ~ 0,01
\item   4 617  ~ \(\times\)  ~ 0,01
\item   52,91  ~ \(\times\)  ~ 0,1
\item   138,2  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,168  ~ \(\times\)  ~ ... ~ = ~  0,516 8
\item   896  ~ \(\times\)  ~ ... ~ = ~  0,896
\item   8,842  ~ \(\times\)  ~ ... ~ = ~  0,884 2
\item   39,89  ~ \(\times\)  ~ ... ~ = ~  0,398 9
\item   7,566  ~ \(\times\)  ~ ... ~ = ~  0,756 6
\item   1 013  ~ \(\times\)  ~ ... ~ = ~  10,13
\item   557,6  ~ \(\times\)  ~ ... ~ = ~  55,76
\item   934,2  ~ \(\times\)  ~ ... ~ = ~  0,934 2
\item   6 881  ~ \(\times\)  ~ ... ~ = ~  688,1
\item   72,2  ~ \(\times\)  ~ ... ~ = ~  7,22
\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~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   673,67 ~hm~ = ...~cm
\item   810,37 ~cm~ = ...~dam
\item   571,3 ~cg~ = ...~dag
\item   655,7 ~cg~ = ...~hg
\item   3 461,4 ~mL~ = ...~hL
\item   8 846,5 ~cg~ = ...~dg
\item   235,39 ~mg~ = ...~dg
\item   1 935,7 ~hL~ = ...~cL
\item   407,77 ~hm~ = ...~mm
\item   874,09 ~kL~ = ...~L
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{990}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{14}{10}\) = \(\dfrac{140}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{700}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 80 300}
\item   6,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 62}
\item   0,389  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,89}
\item   0,04  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,4}
\item   59,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 596}
\item   75,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 570}
\item   29,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 950}
\item   172  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 720}
\item   0,064  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,4}
\item   13,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 138}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,8 ~ : ~ 10 ~ = ~{\color{red} 1,88}
\item   281,8 ~ : ~ 100 ~ = ~{\color{red} 2,818}
\item   523,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,523 9}
\item   345,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,345 6}
\item   3,326 ~ : ~ 100 ~ = ~{\color{red} 0,033 26}
\item   4,54 ~ : ~ 100 ~ = ~{\color{red} 0,045 4}
\item   282 ~ : ~ 100 ~ = ~{\color{red} 2,82}
\item   11,68 ~ : ~ 100 ~ = ~{\color{red} 0,116 8}
\item   9 704 ~ : ~ 1 000 ~ = ~{\color{red} 9,704}
\item   5 637 ~ : ~ 100 ~ = ~{\color{red} 56,37}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,72 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~372
\item   7,22 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~72,2
\item   0,501 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~501
\item   189 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~18 900
\item   970 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~970 000
\item   0,375 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,75
\item   0,571 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~57,1
\item   0,039 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,39
\item   472 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~472 000
\item   0,019 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,19
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   205,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,051
}\item   57,43 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,057 43
}\item   4,211 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,421 1
}\item   97,63 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,976 3
}\item   0,701 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,070 1
}\item   35,16 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,035 16
}\item   604,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,042
}\item   4 617 ~ \(\times\)  0,01 ~ = ~{\color{red} 46,17
}\item   52,91 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,291
}\item   138,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,138 2
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,168 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,516 8
\item   896 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,896
\item   8,842 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,884 2
\item   39,89 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,398 9
\item   7,566 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,756 6
\item   1 013 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 10,13
\item   557,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 55,76
\item   934,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,934 2
\item   6 881 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 688,1
\item   72,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,22
\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}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   673,67 ~hm~ = {\color{red}  6 736 700 }~cm
\item   810,37 ~cm~ = {\color{red}  0,810 37 }~dam
\item   571,3 ~cg~ = {\color{red}  0,571 3 }~dag
\item   655,7 ~cg~ = {\color{red}  0,065 57 }~hg
\item   3 461,4 ~mL~ = {\color{red}  0,034 614 }~hL
\item   8 846,5 ~cg~ = {\color{red}  884,65 }~dg
\item   235,39 ~mg~ = {\color{red}  2,353 9 }~dg
\item   1 935,7 ~hL~ = {\color{red}  19 357 000 }~cL
\item   407,77 ~hm~ = {\color{red}  40 777 000 }~mm
\item   874,09 ~kL~ = {\color{red}  874 090 }~L
\end{itemize}
\end{multicols}
\end{document}
