\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 65}

\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=65}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0065}
\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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{67}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,048  ~ \(\times\)  ~ 100
\item   5,73  ~ \(\times\)  ~ 1 000
\item   45,5  ~ \(\times\)  ~ 10
\item   0,092  ~ \(\times\)  ~ 100
\item   27,9  ~ \(\times\)  ~ 1 000
\item   0,049  ~ \(\times\)  ~ 1 000
\item   0,55  ~ \(\times\)  ~ 10
\item   0,017  ~ \(\times\)  ~ 1 000
\item   88,8  ~ \(\times\)  ~ 1 000
\item   852  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,44  ~ : ~ 1 000
\item   610,5  ~ : ~ 1 000
\item   3,829  ~ : ~ 100
\item   7 900  ~ : ~ 1 000
\item   2 606  ~ : ~ 100
\item   42,02  ~ : ~ 100
\item   23,4  ~ : ~ 1 000
\item   7 148  ~ : ~ 100
\item   9 068  ~ : ~ 10
\item   2,753  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,014  ~ \(\times\)  ~ ... ~ = ~ 1,4
\item   7,67  ~ \(\times\)  ~ ... ~ = ~ 76,7
\item   2,52  ~ \(\times\)  ~ ... ~ = ~ 2 520
\item   37,2  ~ \(\times\)  ~ ... ~ = ~ 3 720
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 60
\item   901  ~ \(\times\)  ~ ... ~ = ~ 90 100
\item   693  ~ \(\times\)  ~ ... ~ = ~ 69 300
\item   0,304  ~ \(\times\)  ~ ... ~ = ~ 3,04
\item   89,6  ~ \(\times\)  ~ ... ~ = ~ 896
\item   1,02  ~ \(\times\)  ~ ... ~ = ~ 1 020
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,169  ~ \(\times\)  ~ 0,001
\item   6 220  ~ \(\times\)  ~ 0,001
\item   9,422  ~ \(\times\)  ~ 0,1
\item   2,765  ~ \(\times\)  ~ 0,01
\item   4,904  ~ \(\times\)  ~ 0,01
\item   83,68  ~ \(\times\)  ~ 0,1
\item   9,851  ~ \(\times\)  ~ 0,001
\item   9 293  ~ \(\times\)  ~ 0,1
\item   30,6  ~ \(\times\)  ~ 0,001
\item   61,9  ~ \(\times\)  ~ 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   359  ~ \(\times\)  ~ ... ~ = ~  3,59
\item   490,2  ~ \(\times\)  ~ ... ~ = ~  4,902
\item   657,3  ~ \(\times\)  ~ ... ~ = ~  6,573
\item   23,64  ~ \(\times\)  ~ ... ~ = ~  0,023 64
\item   1,613  ~ \(\times\)  ~ ... ~ = ~  0,016 13
\item   372,1  ~ \(\times\)  ~ ... ~ = ~  37,21
\item   8,728  ~ \(\times\)  ~ ... ~ = ~  0,008 728
\item   44,27  ~ \(\times\)  ~ ... ~ = ~  4,427
\item   37,31  ~ \(\times\)  ~ ... ~ = ~  3,731
\item   49,55  ~ \(\times\)  ~ ... ~ = ~  0,495 5
\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 ~cm~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 409,8 ~m~ = ...~mm
\item   3 888,4 ~mg~ = ...~kg
\item   8 109,6 ~cg~ = ...~dag
\item   976,42 ~mL~ = ...~cL
\item   640,88 ~hm~ = ...~cm
\item   740,08 ~kg~ = ...~hg
\item   3 870,3 ~km~ = ...~hm
\item   9 555,1 ~dag~ = ...~dg
\item   4 812,2 ~L~ = ...~dL
\item   9 852 ~L~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{470}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{390}{100}\)
\item   \(\dfrac{67}{100}\) = \(\dfrac{670}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,048  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,8}
\item   5,73  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 730}
\item   45,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 455}
\item   0,092  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,2}
\item   27,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 27 900}
\item   0,049  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 49}
\item   0,55  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,5}
\item   0,017  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 17}
\item   88,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 88 800}
\item   852  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 520}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,44 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 44}
\item   610,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,610 5}
\item   3,829 ~ : ~ 100 ~ = ~{\color{red} 0,038 29}
\item   7 900 ~ : ~ 1 000 ~ = ~{\color{red} 7,9}
\item   2 606 ~ : ~ 100 ~ = ~{\color{red} 26,06}
\item   42,02 ~ : ~ 100 ~ = ~{\color{red} 0,420 2}
\item   23,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,023 4}
\item   7 148 ~ : ~ 100 ~ = ~{\color{red} 71,48}
\item   9 068 ~ : ~ 10 ~ = ~{\color{red} 906,8}
\item   2,753 ~ : ~ 100 ~ = ~{\color{red} 0,027 53}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,014 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,4
\item   7,67 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~76,7
\item   2,52 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 520
\item   37,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 720
\item   0,06 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~60
\item   901 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~90 100
\item   693 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~69 300
\item   0,304 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,04
\item   89,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~896
\item   1,02 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 020
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,169 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 169
}\item   6 220 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,22
}\item   9,422 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,942 2
}\item   2,765 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,027 65
}\item   4,904 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,049 04
}\item   83,68 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,368
}\item   9,851 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 851
}\item   9 293 ~ \(\times\)  0,1 ~ = ~{\color{red} 929,3
}\item   30,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 6
}\item   61,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,619
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   359 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,59
\item   490,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,902
\item   657,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,573
\item   23,64 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,023 64
\item   1,613 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,016 13
\item   372,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 37,21
\item   8,728 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 728
\item   44,27 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,427
\item   37,31 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,731
\item   49,55 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,495 5
\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 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\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   2 409,8 ~m~ = {\color{red}  2 409 800 }~mm
\item   3 888,4 ~mg~ = {\color{red}  0,003 888 4 }~kg
\item   8 109,6 ~cg~ = {\color{red}  8,109 6 }~dag
\item   976,42 ~mL~ = {\color{red}  97,642 }~cL
\item   640,88 ~hm~ = {\color{red}  6 408 800 }~cm
\item   740,08 ~kg~ = {\color{red}  7 400,8 }~hg
\item   3 870,3 ~km~ = {\color{red}  38 703 }~hm
\item   9 555,1 ~dag~ = {\color{red}  955 510 }~dg
\item   4 812,2 ~L~ = {\color{red}  48 122 }~dL
\item   9 852 ~L~ = {\color{red}  9,852 }~kL
\end{itemize}
\end{multicols}
\end{document}
