\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 300}

\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=300}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0300}
\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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{55}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,851  ~ \(\times\)  ~ 1 000
\item   60,2  ~ \(\times\)  ~ 10
\item   0,133  ~ \(\times\)  ~ 100
\item   0,039  ~ \(\times\)  ~ 10
\item   65,5  ~ \(\times\)  ~ 10
\item   0,093  ~ \(\times\)  ~ 1 000
\item   0,08  ~ \(\times\)  ~ 10
\item   715  ~ \(\times\)  ~ 100
\item   0,031  ~ \(\times\)  ~ 10
\item   5,29  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 841  ~ : ~ 10
\item   152,7  ~ : ~ 100
\item   5 045  ~ : ~ 1 000
\item   2 933  ~ : ~ 1 000
\item   8,001  ~ : ~ 10
\item   454,3  ~ : ~ 1 000
\item   657  ~ : ~ 1 000
\item   680,2  ~ : ~ 100
\item   24,05  ~ : ~ 100
\item   711,8  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,078  ~ \(\times\)  ~ ... ~ = ~ 78
\item   0,662  ~ \(\times\)  ~ ... ~ = ~ 6,62
\item   790  ~ \(\times\)  ~ ... ~ = ~ 7 900
\item   0,283  ~ \(\times\)  ~ ... ~ = ~ 283
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 0,22
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 2,8
\item   0,013  ~ \(\times\)  ~ ... ~ = ~ 13
\item   0,78  ~ \(\times\)  ~ ... ~ = ~ 7,8
\item   18,9  ~ \(\times\)  ~ ... ~ = ~ 1 890
\item   53,8  ~ \(\times\)  ~ ... ~ = ~ 53 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,04  ~ \(\times\)  ~ 0,001
\item   1,54  ~ \(\times\)  ~ 0,01
\item   8,51  ~ \(\times\)  ~ 0,1
\item   484,4  ~ \(\times\)  ~ 0,1
\item   7 392  ~ \(\times\)  ~ 0,001
\item   157,7  ~ \(\times\)  ~ 0,1
\item   846  ~ \(\times\)  ~ 0,1
\item   8,134  ~ \(\times\)  ~ 0,01
\item   6,016  ~ \(\times\)  ~ 0,01
\item   67,38  ~ \(\times\)  ~ 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   9,495  ~ \(\times\)  ~ ... ~ = ~  0,094 95
\item   835,6  ~ \(\times\)  ~ ... ~ = ~  83,56
\item   76,11  ~ \(\times\)  ~ ... ~ = ~  0,761 1
\item   516  ~ \(\times\)  ~ ... ~ = ~  0,516
\item   36,61  ~ \(\times\)  ~ ... ~ = ~  0,036 61
\item   2 102  ~ \(\times\)  ~ ... ~ = ~  210,2
\item   30,74  ~ \(\times\)  ~ ... ~ = ~  0,030 74
\item   31,87  ~ \(\times\)  ~ ... ~ = ~  0,031 87
\item   56,26  ~ \(\times\)  ~ ... ~ = ~  5,626
\item   583,7  ~ \(\times\)  ~ ... ~ = ~  0,583 7
\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~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   391,21 ~dag~ = ...~kg
\item   634,95 ~m~ = ...~mm
\item   3 603,9 ~daL~ = ...~kL
\item   128,86 ~km~ = ...~m
\item   815,81 ~dL~ = ...~daL
\item   3 261,6 ~m~ = ...~hm
\item   431,84 ~dL~ = ...~L
\item   215,35 ~cm~ = ...~dm
\item   4 228,8 ~daL~ = ...~mL
\item   962,65 ~km~ = ...~hm
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{110}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{55}{10}\) = \(\dfrac{550}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{780}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,851  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 851}
\item   60,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 602}
\item   0,133  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 13,3}
\item   0,039  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,39}
\item   65,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 655}
\item   0,093  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 93}
\item   0,08  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,8}
\item   715  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 71 500}
\item   0,031  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,31}
\item   5,29  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 290}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 841 ~ : ~ 10 ~ = ~{\color{red} 584,1}
\item   152,7 ~ : ~ 100 ~ = ~{\color{red} 1,527}
\item   5 045 ~ : ~ 1 000 ~ = ~{\color{red} 5,045}
\item   2 933 ~ : ~ 1 000 ~ = ~{\color{red} 2,933}
\item   8,001 ~ : ~ 10 ~ = ~{\color{red} 0,800 1}
\item   454,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,454 3}
\item   657 ~ : ~ 1 000 ~ = ~{\color{red} 0,657}
\item   680,2 ~ : ~ 100 ~ = ~{\color{red} 6,802}
\item   24,05 ~ : ~ 100 ~ = ~{\color{red} 0,240 5}
\item   711,8 ~ : ~ 100 ~ = ~{\color{red} 7,118}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,078 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~78
\item   0,662 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,62
\item   790 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 900
\item   0,283 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~283
\item   0,022 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,22
\item   0,028 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,8
\item   0,013 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~13
\item   0,78 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,8
\item   18,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 890
\item   53,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~53 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,04 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 04
}\item   1,54 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,015 4
}\item   8,51 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,851
}\item   484,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 48,44
}\item   7 392 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,392
}\item   157,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 15,77
}\item   846 ~ \(\times\)  0,1 ~ = ~{\color{red} 84,6
}\item   8,134 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,081 34
}\item   6,016 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,060 16
}\item   67,38 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,067 38
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,495 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,094 95
\item   835,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 83,56
\item   76,11 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,761 1
\item   516 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,516
\item   36,61 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,036 61
\item   2 102 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 210,2
\item   30,74 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,030 74
\item   31,87 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,031 87
\item   56,26 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,626
\item   583,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,583 7
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   391,21 ~dag~ = {\color{red}  3,912 1 }~kg
\item   634,95 ~m~ = {\color{red}  634 950 }~mm
\item   3 603,9 ~daL~ = {\color{red}  36,039 }~kL
\item   128,86 ~km~ = {\color{red}  128 860 }~m
\item   815,81 ~dL~ = {\color{red}  8,158 1 }~daL
\item   3 261,6 ~m~ = {\color{red}  32,616 }~hm
\item   431,84 ~dL~ = {\color{red}  43,184 }~L
\item   215,35 ~cm~ = {\color{red}  21,535 }~dm
\item   4 228,8 ~daL~ = {\color{red}  42 288 000 }~mL
\item   962,65 ~km~ = {\color{red}  9 626,5 }~hm
\end{itemize}
\end{multicols}
\end{document}
