\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 187}

\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=187}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0187}
\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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{85}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{14}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,084  ~ \(\times\)  ~ 1 000
\item   0,26  ~ \(\times\)  ~ 1 000
\item   0,735  ~ \(\times\)  ~ 10
\item   0,613  ~ \(\times\)  ~ 100
\item   2,33  ~ \(\times\)  ~ 10
\item   0,027  ~ \(\times\)  ~ 1 000
\item   6,2  ~ \(\times\)  ~ 100
\item   802  ~ \(\times\)  ~ 100
\item   0,07  ~ \(\times\)  ~ 1 000
\item   0,41  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   309,8  ~ : ~ 1 000
\item   799,9  ~ : ~ 100
\item   48,56  ~ : ~ 10
\item   2,257  ~ : ~ 10
\item   59,22  ~ : ~ 100
\item   69,86  ~ : ~ 100
\item   1 104  ~ : ~ 10
\item   59,98  ~ : ~ 100
\item   57,3  ~ : ~ 1 000
\item   5,311  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,066  ~ \(\times\)  ~ ... ~ = ~ 66
\item   0,331  ~ \(\times\)  ~ ... ~ = ~ 3,31
\item   0,868  ~ \(\times\)  ~ ... ~ = ~ 868
\item   67,5  ~ \(\times\)  ~ ... ~ = ~ 675
\item   3,87  ~ \(\times\)  ~ ... ~ = ~ 38,7
\item   969  ~ \(\times\)  ~ ... ~ = ~ 96 900
\item   5,93  ~ \(\times\)  ~ ... ~ = ~ 59,3
\item   0,05  ~ \(\times\)  ~ ... ~ = ~ 0,5
\item   417  ~ \(\times\)  ~ ... ~ = ~ 417 000
\item   0,425  ~ \(\times\)  ~ ... ~ = ~ 42,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,02  ~ \(\times\)  ~ 0,1
\item   84  ~ \(\times\)  ~ 0,001
\item   38,06  ~ \(\times\)  ~ 0,1
\item   8 222  ~ \(\times\)  ~ 0,1
\item   3 150  ~ \(\times\)  ~ 0,01
\item   5 671  ~ \(\times\)  ~ 0,1
\item   8,094  ~ \(\times\)  ~ 0,1
\item   50,88  ~ \(\times\)  ~ 0,01
\item   394,3  ~ \(\times\)  ~ 0,01
\item   4 593  ~ \(\times\)  ~ 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   701,3  ~ \(\times\)  ~ ... ~ = ~  0,701 3
\item   85,8  ~ \(\times\)  ~ ... ~ = ~  8,58
\item   0,663  ~ \(\times\)  ~ ... ~ = ~  0,006 63
\item   874,1  ~ \(\times\)  ~ ... ~ = ~  8,741
\item   1,234  ~ \(\times\)  ~ ... ~ = ~  0,012 34
\item   4 535  ~ \(\times\)  ~ ... ~ = ~  453,5
\item   206  ~ \(\times\)  ~ ... ~ = ~  2,06
\item   20,22  ~ \(\times\)  ~ ... ~ = ~  0,202 2
\item   0,825  ~ \(\times\)  ~ ... ~ = ~  0,082 5
\item   9,387  ~ \(\times\)  ~ ... ~ = ~  0,009 387
\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 ~dam~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 612,5 ~cm~ = ...~dam
\item   6 393,6 ~daL~ = ...~cL
\item   6 457,7 ~L~ = ...~dL
\item   5 418,7 ~daL~ = ...~kL
\item   116,2 ~m~ = ...~dam
\item   8 172,7 ~dm~ = ...~m
\item   580,75 ~L~ = ...~daL
\item   6 717,2 ~dg~ = ...~kg
\item   572,72 ~hg~ = ...~kg
\item   322,62 ~dag~ = ...~kg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{8600}{100}\) = \(\dfrac{860}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{85}{10}\) = \(\dfrac{850}{100}\)
\item   \(\dfrac{14}{100}\) = \(\dfrac{140}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,084  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84}
\item   0,26  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 260}
\item   0,735  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,35}
\item   0,613  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 61,3}
\item   2,33  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 23,3}
\item   0,027  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 27}
\item   6,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 620}
\item   802  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80 200}
\item   0,07  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 70}
\item   0,41  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 410}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   309,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,309 8}
\item   799,9 ~ : ~ 100 ~ = ~{\color{red} 7,999}
\item   48,56 ~ : ~ 10 ~ = ~{\color{red} 4,856}
\item   2,257 ~ : ~ 10 ~ = ~{\color{red} 0,225 7}
\item   59,22 ~ : ~ 100 ~ = ~{\color{red} 0,592 2}
\item   69,86 ~ : ~ 100 ~ = ~{\color{red} 0,698 6}
\item   1 104 ~ : ~ 10 ~ = ~{\color{red} 110,4}
\item   59,98 ~ : ~ 100 ~ = ~{\color{red} 0,599 8}
\item   57,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,057 3}
\item   5,311 ~ : ~ 10 ~ = ~{\color{red} 0,531 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,066 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~66
\item   0,331 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,31
\item   0,868 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~868
\item   67,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~675
\item   3,87 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~38,7
\item   969 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96 900
\item   5,93 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~59,3
\item   0,05 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,5
\item   417 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~417 000
\item   0,425 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~42,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,02 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,702
}\item   84 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,084
}\item   38,06 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,806
}\item   8 222 ~ \(\times\)  0,1 ~ = ~{\color{red} 822,2
}\item   3 150 ~ \(\times\)  0,01 ~ = ~{\color{red} 31,5
}\item   5 671 ~ \(\times\)  0,1 ~ = ~{\color{red} 567,1
}\item   8,094 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,809 4
}\item   50,88 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,508 8
}\item   394,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,943
}\item   4 593 ~ \(\times\)  0,1 ~ = ~{\color{red} 459,3
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   701,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,701 3
\item   85,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,58
\item   0,663 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,006 63
\item   874,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,741
\item   1,234 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,012 34
\item   4 535 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 453,5
\item   206 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,06
\item   20,22 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,202 2
\item   0,825 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,082 5
\item   9,387 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 387
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 612,5 ~cm~ = {\color{red}  8,612 5 }~dam
\item   6 393,6 ~daL~ = {\color{red}  6 393 600 }~cL
\item   6 457,7 ~L~ = {\color{red}  64 577 }~dL
\item   5 418,7 ~daL~ = {\color{red}  54,187 }~kL
\item   116,2 ~m~ = {\color{red}  11,62 }~dam
\item   8 172,7 ~dm~ = {\color{red}  817,27 }~m
\item   580,75 ~L~ = {\color{red}  58,075 }~daL
\item   6 717,2 ~dg~ = {\color{red}  0,671 72 }~kg
\item   572,72 ~hg~ = {\color{red}  57,272 }~kg
\item   322,62 ~dag~ = {\color{red}  3,226 2 }~kg
\end{itemize}
\end{multicols}
\end{document}
