\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 163}

\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=163}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0163}
\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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,3  ~ \(\times\)  ~ 10
\item   38,1  ~ \(\times\)  ~ 10
\item   0,019  ~ \(\times\)  ~ 10
\item   720  ~ \(\times\)  ~ 100
\item   161  ~ \(\times\)  ~ 1 000
\item   915  ~ \(\times\)  ~ 100
\item   562  ~ \(\times\)  ~ 1 000
\item   5,41  ~ \(\times\)  ~ 100
\item   1,7  ~ \(\times\)  ~ 1 000
\item   65,6  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,63  ~ : ~ 1 000
\item   5,791  ~ : ~ 100
\item   536,5  ~ : ~ 10
\item   9 576  ~ : ~ 1 000
\item   6 103  ~ : ~ 1 000
\item   9 264  ~ : ~ 10
\item   279,3  ~ : ~ 10
\item   392,5  ~ : ~ 1 000
\item   0,461  ~ : ~ 100
\item   18,4  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,92  ~ \(\times\)  ~ ... ~ = ~ 792
\item   1,56  ~ \(\times\)  ~ ... ~ = ~ 156
\item   7,65  ~ \(\times\)  ~ ... ~ = ~ 7 650
\item   3,25  ~ \(\times\)  ~ ... ~ = ~ 3 250
\item   874  ~ \(\times\)  ~ ... ~ = ~ 87 400
\item   54,7  ~ \(\times\)  ~ ... ~ = ~ 547
\item   97,1  ~ \(\times\)  ~ ... ~ = ~ 971
\item   0,27  ~ \(\times\)  ~ ... ~ = ~ 27
\item   462  ~ \(\times\)  ~ ... ~ = ~ 46 200
\item   7,29  ~ \(\times\)  ~ ... ~ = ~ 729
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 317  ~ \(\times\)  ~ 0,001
\item   3 965  ~ \(\times\)  ~ 0,1
\item   60,24  ~ \(\times\)  ~ 0,001
\item   822,3  ~ \(\times\)  ~ 0,001
\item   40  ~ \(\times\)  ~ 0,01
\item   3,365  ~ \(\times\)  ~ 0,001
\item   3,406  ~ \(\times\)  ~ 0,001
\item   527,2  ~ \(\times\)  ~ 0,001
\item   1,245  ~ \(\times\)  ~ 0,1
\item   8 361  ~ \(\times\)  ~ 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   1,4  ~ \(\times\)  ~ ... ~ = ~  0,14
\item   50,51  ~ \(\times\)  ~ ... ~ = ~  5,051
\item   8,765  ~ \(\times\)  ~ ... ~ = ~  0,008 765
\item   83,2  ~ \(\times\)  ~ ... ~ = ~  8,32
\item   23,95  ~ \(\times\)  ~ ... ~ = ~  2,395
\item   61,35  ~ \(\times\)  ~ ... ~ = ~  0,061 35
\item   94,47  ~ \(\times\)  ~ ... ~ = ~  0,944 7
\item   6 973  ~ \(\times\)  ~ ... ~ = ~  697,3
\item   295,9  ~ \(\times\)  ~ ... ~ = ~  2,959
\item   591,5  ~ \(\times\)  ~ ... ~ = ~  59,15
\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 ~m~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   610,84 ~L~ = ...~dL
\item   1 800,6 ~kL~ = ...~mL
\item   1 404,7 ~cL~ = ...~dL
\item   4 391,7 ~mL~ = ...~L
\item   5 790 ~dg~ = ...~cg
\item   1 761,3 ~m~ = ...~mm
\item   250,23 ~hg~ = ...~dag
\item   124,83 ~dam~ = ...~hm
\item   284,38 ~kL~ = ...~L
\item   7 698,6 ~cL~ = ...~mL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{8500}{100}\) = \(\dfrac{850}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{740}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{470}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 23}
\item   38,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 381}
\item   0,019  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,19}
\item   720  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 72 000}
\item   161  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 161 000}
\item   915  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 91 500}
\item   562  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 562 000}
\item   5,41  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 541}
\item   1,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 700}
\item   65,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 65 600}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,63 ~ : ~ 1 000 ~ = ~{\color{red} 0,011 63}
\item   5,791 ~ : ~ 100 ~ = ~{\color{red} 0,057 91}
\item   536,5 ~ : ~ 10 ~ = ~{\color{red} 53,65}
\item   9 576 ~ : ~ 1 000 ~ = ~{\color{red} 9,576}
\item   6 103 ~ : ~ 1 000 ~ = ~{\color{red} 6,103}
\item   9 264 ~ : ~ 10 ~ = ~{\color{red} 926,4}
\item   279,3 ~ : ~ 10 ~ = ~{\color{red} 27,93}
\item   392,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,392 5}
\item   0,461 ~ : ~ 100 ~ = ~{\color{red} 0,004 61}
\item   18,4 ~ : ~ 10 ~ = ~{\color{red} 1,84}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,92 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~792
\item   1,56 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~156
\item   7,65 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 650
\item   3,25 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 250
\item   874 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~87 400
\item   54,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~547
\item   97,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~971
\item   0,27 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~27
\item   462 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~46 200
\item   7,29 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~729
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 317 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,317
}\item   3 965 ~ \(\times\)  0,1 ~ = ~{\color{red} 396,5
}\item   60,24 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,060 24
}\item   822,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,822 3
}\item   40 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,4
}\item   3,365 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 365
}\item   3,406 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 406
}\item   527,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,527 2
}\item   1,245 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,124 5
}\item   8 361 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,361
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,14
\item   50,51 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,051
\item   8,765 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 765
\item   83,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,32
\item   23,95 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,395
\item   61,35 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,061 35
\item   94,47 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,944 7
\item   6 973 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 697,3
\item   295,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,959
\item   591,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 59,15
\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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   610,84 ~L~ = {\color{red}  6 108,4 }~dL
\item   1 800,6 ~kL~ = {\color{red}  1 800 600 000 }~mL
\item   1 404,7 ~cL~ = {\color{red}  140,47 }~dL
\item   4 391,7 ~mL~ = {\color{red}  4,391 7 }~L
\item   5 790 ~dg~ = {\color{red}  57 900 }~cg
\item   1 761,3 ~m~ = {\color{red}  1 761 300 }~mm
\item   250,23 ~hg~ = {\color{red}  2 502,3 }~dag
\item   124,83 ~dam~ = {\color{red}  12,483 }~hm
\item   284,38 ~kL~ = {\color{red}  284 380 }~L
\item   7 698,6 ~cL~ = {\color{red}  76 986 }~mL
\end{itemize}
\end{multicols}
\end{document}
