\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 347}

\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=347}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0347}
\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   \(\dfrac{4600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,98  ~ \(\times\)  ~ 100
\item   0,179  ~ \(\times\)  ~ 10
\item   54  ~ \(\times\)  ~ 100
\item   827  ~ \(\times\)  ~ 1 000
\item   0,35  ~ \(\times\)  ~ 10
\item   55,8  ~ \(\times\)  ~ 10
\item   0,538  ~ \(\times\)  ~ 1 000
\item   0,955  ~ \(\times\)  ~ 1 000
\item   0,563  ~ \(\times\)  ~ 100
\item   7,64  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,96  ~ : ~ 100
\item   793,7  ~ : ~ 100
\item   4,048  ~ : ~ 10
\item   2 055  ~ : ~ 100
\item   368,1  ~ : ~ 100
\item   9 368  ~ : ~ 10
\item   321,2  ~ : ~ 100
\item   3,692  ~ : ~ 1 000
\item   8,602  ~ : ~ 10
\item   76,59  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85  ~ \(\times\)  ~ ... ~ = ~ 850
\item   4,71  ~ \(\times\)  ~ ... ~ = ~ 471
\item   7,04  ~ \(\times\)  ~ ... ~ = ~ 70,4
\item   8,54  ~ \(\times\)  ~ ... ~ = ~ 854
\item   0,024  ~ \(\times\)  ~ ... ~ = ~ 0,24
\item   0,087  ~ \(\times\)  ~ ... ~ = ~ 0,87
\item   0,009  ~ \(\times\)  ~ ... ~ = ~ 0,9
\item   0,087  ~ \(\times\)  ~ ... ~ = ~ 87
\item   0,749  ~ \(\times\)  ~ ... ~ = ~ 74,9
\item   0,465  ~ \(\times\)  ~ ... ~ = ~ 46,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 657  ~ \(\times\)  ~ 0,1
\item   4,922  ~ \(\times\)  ~ 0,1
\item   12,46  ~ \(\times\)  ~ 0,001
\item   38,94  ~ \(\times\)  ~ 0,1
\item   60,75  ~ \(\times\)  ~ 0,1
\item   33,62  ~ \(\times\)  ~ 0,1
\item   46,34  ~ \(\times\)  ~ 0,1
\item   212  ~ \(\times\)  ~ 0,01
\item   37,93  ~ \(\times\)  ~ 0,01
\item   263,6  ~ \(\times\)  ~ 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   68,72  ~ \(\times\)  ~ ... ~ = ~  0,687 2
\item   3 886  ~ \(\times\)  ~ ... ~ = ~  3,886
\item   34,16  ~ \(\times\)  ~ ... ~ = ~  0,341 6
\item   5,224  ~ \(\times\)  ~ ... ~ = ~  0,052 24
\item   8 076  ~ \(\times\)  ~ ... ~ = ~  807,6
\item   2,016  ~ \(\times\)  ~ ... ~ = ~  0,002 016
\item   2 813  ~ \(\times\)  ~ ... ~ = ~  2,813
\item   1,492  ~ \(\times\)  ~ ... ~ = ~  0,001 492
\item   89,97  ~ \(\times\)  ~ ... ~ = ~  0,899 7
\item   94,8  ~ \(\times\)  ~ ... ~ = ~  0,948
\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~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   358,84 ~mg~ = ...~hg
\item   774,33 ~mL~ = ...~daL
\item   3 201,4 ~mm~ = ...~km
\item   991,71 ~mL~ = ...~cL
\item   8 229,3 ~kL~ = ...~mL
\item   7 383,9 ~dg~ = ...~g
\item   5 359 ~cg~ = ...~dag
\item   9 401,5 ~kL~ = ...~daL
\item   239,45 ~g~ = ...~kg
\item   591,96 ~kL~ = ...~cL
\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   \(\dfrac{4600}{100}\) = \(\dfrac{460}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{410}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,98  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 898}
\item   0,179  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,79}
\item   54  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 400}
\item   827  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 827 000}
\item   0,35  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,5}
\item   55,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 558}
\item   0,538  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 538}
\item   0,955  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 955}
\item   0,563  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 56,3}
\item   7,64  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 640}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,96 ~ : ~ 100 ~ = ~{\color{red} 0,519 6}
\item   793,7 ~ : ~ 100 ~ = ~{\color{red} 7,937}
\item   4,048 ~ : ~ 10 ~ = ~{\color{red} 0,404 8}
\item   2 055 ~ : ~ 100 ~ = ~{\color{red} 20,55}
\item   368,1 ~ : ~ 100 ~ = ~{\color{red} 3,681}
\item   9 368 ~ : ~ 10 ~ = ~{\color{red} 936,8}
\item   321,2 ~ : ~ 100 ~ = ~{\color{red} 3,212}
\item   3,692 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 692}
\item   8,602 ~ : ~ 10 ~ = ~{\color{red} 0,860 2}
\item   76,59 ~ : ~ 100 ~ = ~{\color{red} 0,765 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~850
\item   4,71 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~471
\item   7,04 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~70,4
\item   8,54 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~854
\item   0,024 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,24
\item   0,087 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,87
\item   0,009 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,9
\item   0,087 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~87
\item   0,749 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74,9
\item   0,465 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~46,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 657 ~ \(\times\)  0,1 ~ = ~{\color{red} 565,7
}\item   4,922 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,492 2
}\item   12,46 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,012 46
}\item   38,94 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,894
}\item   60,75 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,075
}\item   33,62 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,362
}\item   46,34 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,634
}\item   212 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,12
}\item   37,93 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,379 3
}\item   263,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 26,36
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68,72 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,687 2
\item   3 886 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,886
\item   34,16 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,341 6
\item   5,224 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,052 24
\item   8 076 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 807,6
\item   2,016 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 016
\item   2 813 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,813
\item   1,492 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 492
\item   89,97 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,899 7
\item   94,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,948
\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~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   358,84 ~mg~ = {\color{red}  0,003 588 4 }~hg
\item   774,33 ~mL~ = {\color{red}  0,077 433 }~daL
\item   3 201,4 ~mm~ = {\color{red}  0,003 201 4 }~km
\item   991,71 ~mL~ = {\color{red}  99,171 }~cL
\item   8 229,3 ~kL~ = {\color{red}  8 229 300 000 }~mL
\item   7 383,9 ~dg~ = {\color{red}  738,39 }~g
\item   5 359 ~cg~ = {\color{red}  5,359 }~dag
\item   9 401,5 ~kL~ = {\color{red}  940 150 }~daL
\item   239,45 ~g~ = {\color{red}  0,239 45 }~kg
\item   591,96 ~kL~ = {\color{red}  59 196 000 }~cL
\end{itemize}
\end{multicols}
\end{document}
