\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 360}

\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=360}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0360}
\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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{97}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,016  ~ \(\times\)  ~ 10
\item   8,9  ~ \(\times\)  ~ 10
\item   739  ~ \(\times\)  ~ 100
\item   47,5  ~ \(\times\)  ~ 1 000
\item   0,064  ~ \(\times\)  ~ 100
\item   0,947  ~ \(\times\)  ~ 100
\item   67,6  ~ \(\times\)  ~ 100
\item   3,82  ~ \(\times\)  ~ 10
\item   0,336  ~ \(\times\)  ~ 10
\item   67,5  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,04  ~ : ~ 10
\item   881,9  ~ : ~ 1 000
\item   9 011  ~ : ~ 100
\item   55,13  ~ : ~ 10
\item   7 773  ~ : ~ 10
\item   7 030  ~ : ~ 10
\item   30,03  ~ : ~ 10
\item   568,7  ~ : ~ 10
\item   652,4  ~ : ~ 10
\item   7 483  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   509  ~ \(\times\)  ~ ... ~ = ~ 50 900
\item   614  ~ \(\times\)  ~ ... ~ = ~ 614 000
\item   0,059  ~ \(\times\)  ~ ... ~ = ~ 5,9
\item   9,53  ~ \(\times\)  ~ ... ~ = ~ 953
\item   25,6  ~ \(\times\)  ~ ... ~ = ~ 25 600
\item   7,6  ~ \(\times\)  ~ ... ~ = ~ 7 600
\item   0,039  ~ \(\times\)  ~ ... ~ = ~ 39
\item   1,13  ~ \(\times\)  ~ ... ~ = ~ 11,3
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 8,9
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 0,02
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 638  ~ \(\times\)  ~ 0,1
\item   4,627  ~ \(\times\)  ~ 0,001
\item   21,8  ~ \(\times\)  ~ 0,1
\item   5,01  ~ \(\times\)  ~ 0,001
\item   339,3  ~ \(\times\)  ~ 0,001
\item   9,615  ~ \(\times\)  ~ 0,01
\item   42,63  ~ \(\times\)  ~ 0,01
\item   6 415  ~ \(\times\)  ~ 0,001
\item   1,324  ~ \(\times\)  ~ 0,001
\item   16,62  ~ \(\times\)  ~ 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   383  ~ \(\times\)  ~ ... ~ = ~  38,3
\item   19,16  ~ \(\times\)  ~ ... ~ = ~  0,019 16
\item   1,445  ~ \(\times\)  ~ ... ~ = ~  0,014 45
\item   38,13  ~ \(\times\)  ~ ... ~ = ~  3,813
\item   57,76  ~ \(\times\)  ~ ... ~ = ~  0,057 76
\item   8 066  ~ \(\times\)  ~ ... ~ = ~  8,066
\item   6 425  ~ \(\times\)  ~ ... ~ = ~  64,25
\item   269,6  ~ \(\times\)  ~ ... ~ = ~  2,696
\item   7 816  ~ \(\times\)  ~ ... ~ = ~  7,816
\item   9 437  ~ \(\times\)  ~ ... ~ = ~  943,7
\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~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 429,3 ~kg~ = ...~hg
\item   191,08 ~cL~ = ...~kL
\item   805,71 ~kL~ = ...~daL
\item   850,59 ~dam~ = ...~km
\item   4 304,3 ~g~ = ...~hg
\item   4 261,4 ~hL~ = ...~mL
\item   9 850,2 ~dm~ = ...~cm
\item   2 083,3 ~mg~ = ...~cg
\item   873,63 ~dL~ = ...~mL
\item   222,31 ~hg~ = ...~g
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{370}{100}\)
\item   \(\dfrac{97}{100}\) = \(\dfrac{970}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,016  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,16}
\item   8,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 89}
\item   739  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 73 900}
\item   47,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 47 500}
\item   0,064  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,4}
\item   0,947  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 94,7}
\item   67,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 760}
\item   3,82  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 38,2}
\item   0,336  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,36}
\item   67,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 750}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,04 ~ : ~ 10 ~ = ~{\color{red} 6,904}
\item   881,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,881 9}
\item   9 011 ~ : ~ 100 ~ = ~{\color{red} 90,11}
\item   55,13 ~ : ~ 10 ~ = ~{\color{red} 5,513}
\item   7 773 ~ : ~ 10 ~ = ~{\color{red} 777,3}
\item   7 030 ~ : ~ 10 ~ = ~{\color{red} 703}
\item   30,03 ~ : ~ 10 ~ = ~{\color{red} 3,003}
\item   568,7 ~ : ~ 10 ~ = ~{\color{red} 56,87}
\item   652,4 ~ : ~ 10 ~ = ~{\color{red} 65,24}
\item   7 483 ~ : ~ 1 000 ~ = ~{\color{red} 7,483}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   509 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~50 900
\item   614 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~614 000
\item   0,059 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,9
\item   9,53 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~953
\item   25,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~25 600
\item   7,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 600
\item   0,039 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~39
\item   1,13 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~11,3
\item   0,089 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,9
\item   0,002 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,02
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 638 ~ \(\times\)  0,1 ~ = ~{\color{red} 863,8
}\item   4,627 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 627
}\item   21,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,18
}\item   5,01 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 01
}\item   339,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,339 3
}\item   9,615 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,096 15
}\item   42,63 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,426 3
}\item   6 415 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,415
}\item   1,324 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 324
}\item   16,62 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,662
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   383 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 38,3
\item   19,16 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,019 16
\item   1,445 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,014 45
\item   38,13 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,813
\item   57,76 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,057 76
\item   8 066 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,066
\item   6 425 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 64,25
\item   269,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,696
\item   7 816 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,816
\item   9 437 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 943,7
\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~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 429,3 ~kg~ = {\color{red}  74 293 }~hg
\item   191,08 ~cL~ = {\color{red}  0,001 910 8 }~kL
\item   805,71 ~kL~ = {\color{red}  80 571 }~daL
\item   850,59 ~dam~ = {\color{red}  8,505 9 }~km
\item   4 304,3 ~g~ = {\color{red}  43,043 }~hg
\item   4 261,4 ~hL~ = {\color{red}  426 140 000 }~mL
\item   9 850,2 ~dm~ = {\color{red}  98 502 }~cm
\item   2 083,3 ~mg~ = {\color{red}  208,33 }~cg
\item   873,63 ~dL~ = {\color{red}  87 363 }~mL
\item   222,31 ~hg~ = {\color{red}  22 231 }~g
\end{itemize}
\end{multicols}
\end{document}
