\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 164}

\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=164}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0164}
\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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{73}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{88}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   402  ~ \(\times\)  ~ 10
\item   0,433  ~ \(\times\)  ~ 10
\item   0,086  ~ \(\times\)  ~ 10
\item   1,67  ~ \(\times\)  ~ 100
\item   666  ~ \(\times\)  ~ 100
\item   625  ~ \(\times\)  ~ 1 000
\item   0,087  ~ \(\times\)  ~ 10
\item   734  ~ \(\times\)  ~ 1 000
\item   384  ~ \(\times\)  ~ 100
\item   725  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 639  ~ : ~ 1 000
\item   877  ~ : ~ 100
\item   1 498  ~ : ~ 10
\item   32,86  ~ : ~ 10
\item   3 376  ~ : ~ 1 000
\item   743,8  ~ : ~ 100
\item   103,7  ~ : ~ 1 000
\item   63,94  ~ : ~ 10
\item   753,2  ~ : ~ 1 000
\item   57,32  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   635  ~ \(\times\)  ~ ... ~ = ~ 63 500
\item   4,09  ~ \(\times\)  ~ ... ~ = ~ 40,9
\item   0,419  ~ \(\times\)  ~ ... ~ = ~ 419
\item   3,2  ~ \(\times\)  ~ ... ~ = ~ 3 200
\item   0,27  ~ \(\times\)  ~ ... ~ = ~ 27
\item   2,16  ~ \(\times\)  ~ ... ~ = ~ 21,6
\item   89,1  ~ \(\times\)  ~ ... ~ = ~ 8 910
\item   27  ~ \(\times\)  ~ ... ~ = ~ 270
\item   0,081  ~ \(\times\)  ~ ... ~ = ~ 81
\item   0,074  ~ \(\times\)  ~ ... ~ = ~ 74
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   132,3  ~ \(\times\)  ~ 0,01
\item   72,9  ~ \(\times\)  ~ 0,001
\item   3 582  ~ \(\times\)  ~ 0,1
\item   81,61  ~ \(\times\)  ~ 0,001
\item   3,111  ~ \(\times\)  ~ 0,1
\item   856,3  ~ \(\times\)  ~ 0,01
\item   794,6  ~ \(\times\)  ~ 0,1
\item   71,26  ~ \(\times\)  ~ 0,1
\item   7,736  ~ \(\times\)  ~ 0,001
\item   6,208  ~ \(\times\)  ~ 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   8 108  ~ \(\times\)  ~ ... ~ = ~  8,108
\item   0,621  ~ \(\times\)  ~ ... ~ = ~  0,006 21
\item   3,872  ~ \(\times\)  ~ ... ~ = ~  0,003 872
\item   7,156  ~ \(\times\)  ~ ... ~ = ~  0,071 56
\item   888,5  ~ \(\times\)  ~ ... ~ = ~  88,85
\item   3,13  ~ \(\times\)  ~ ... ~ = ~  0,031 3
\item   717,7  ~ \(\times\)  ~ ... ~ = ~  7,177
\item   118,4  ~ \(\times\)  ~ ... ~ = ~  0,118 4
\item   4,924  ~ \(\times\)  ~ ... ~ = ~  0,049 24
\item   8 201  ~ \(\times\)  ~ ... ~ = ~  8,201
\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~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   735,26 ~dg~ = ...~kg
\item   228,75 ~m~ = ...~cm
\item   1 172,7 ~kg~ = ...~dag
\item   6 532,6 ~mg~ = ...~dag
\item   1 640,6 ~daL~ = ...~kL
\item   1 375,9 ~cg~ = ...~kg
\item   5 749,5 ~hm~ = ...~cm
\item   8 487 ~daL~ = ...~L
\item   5 082,1 ~dag~ = ...~hg
\item   648,9 ~dm~ = ...~mm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{4300}{100}\) = \(\dfrac{430}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{73}{10}\) = \(\dfrac{730}{100}\)
\item   \(\dfrac{88}{100}\) = \(\dfrac{880}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   402  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 020}
\item   0,433  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,33}
\item   0,086  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,86}
\item   1,67  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 167}
\item   666  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66 600}
\item   625  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 625 000}
\item   0,087  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,87}
\item   734  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 734 000}
\item   384  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 38 400}
\item   725  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 725 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 639 ~ : ~ 1 000 ~ = ~{\color{red} 5,639}
\item   877 ~ : ~ 100 ~ = ~{\color{red} 8,77}
\item   1 498 ~ : ~ 10 ~ = ~{\color{red} 149,8}
\item   32,86 ~ : ~ 10 ~ = ~{\color{red} 3,286}
\item   3 376 ~ : ~ 1 000 ~ = ~{\color{red} 3,376}
\item   743,8 ~ : ~ 100 ~ = ~{\color{red} 7,438}
\item   103,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,103 7}
\item   63,94 ~ : ~ 10 ~ = ~{\color{red} 6,394}
\item   753,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,753 2}
\item   57,32 ~ : ~ 10 ~ = ~{\color{red} 5,732}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   635 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~63 500
\item   4,09 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~40,9
\item   0,419 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~419
\item   3,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 200
\item   0,27 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~27
\item   2,16 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~21,6
\item   89,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 910
\item   27 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~270
\item   0,081 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~81
\item   0,074 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~74
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   132,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,323
}\item   72,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,072 9
}\item   3 582 ~ \(\times\)  0,1 ~ = ~{\color{red} 358,2
}\item   81,61 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,081 61
}\item   3,111 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,311 1
}\item   856,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,563
}\item   794,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 79,46
}\item   71,26 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,126
}\item   7,736 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 736
}\item   6,208 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,620 8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 108 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,108
\item   0,621 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,006 21
\item   3,872 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 872
\item   7,156 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,071 56
\item   888,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 88,85
\item   3,13 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,031 3
\item   717,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,177
\item   118,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,118 4
\item   4,924 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,049 24
\item   8 201 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,201
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   735,26 ~dg~ = {\color{red}  0,073 526 }~kg
\item   228,75 ~m~ = {\color{red}  22 875 }~cm
\item   1 172,7 ~kg~ = {\color{red}  117 270 }~dag
\item   6 532,6 ~mg~ = {\color{red}  0,653 26 }~dag
\item   1 640,6 ~daL~ = {\color{red}  16,406 }~kL
\item   1 375,9 ~cg~ = {\color{red}  0,013 759 }~kg
\item   5 749,5 ~hm~ = {\color{red}  57 495 000 }~cm
\item   8 487 ~daL~ = {\color{red}  84 870 }~L
\item   5 082,1 ~dag~ = {\color{red}  508,21 }~hg
\item   648,9 ~dm~ = {\color{red}  64 890 }~mm
\end{itemize}
\end{multicols}
\end{document}
