\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 256}

\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=256}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0256}
\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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{59}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,477  ~ \(\times\)  ~ 10
\item   53,3  ~ \(\times\)  ~ 100
\item   6,92  ~ \(\times\)  ~ 1 000
\item   3,39  ~ \(\times\)  ~ 1 000
\item   0,009  ~ \(\times\)  ~ 100
\item   57,8  ~ \(\times\)  ~ 1 000
\item   288  ~ \(\times\)  ~ 1 000
\item   488  ~ \(\times\)  ~ 1 000
\item   0,882  ~ \(\times\)  ~ 10
\item   0,073  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,86  ~ : ~ 10
\item   322,4  ~ : ~ 100
\item   61,18  ~ : ~ 100
\item   4,711  ~ : ~ 10
\item   27,47  ~ : ~ 100
\item   672,1  ~ : ~ 10
\item   9,424  ~ : ~ 1 000
\item   346  ~ : ~ 100
\item   78,3  ~ : ~ 100
\item   1 969  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,3  ~ \(\times\)  ~ ... ~ = ~ 903
\item   42,3  ~ \(\times\)  ~ ... ~ = ~ 4 230
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 0,88
\item   5,54  ~ \(\times\)  ~ ... ~ = ~ 554
\item   0,006  ~ \(\times\)  ~ ... ~ = ~ 0,6
\item   7,55  ~ \(\times\)  ~ ... ~ = ~ 755
\item   508  ~ \(\times\)  ~ ... ~ = ~ 50 800
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 5,8
\item   574  ~ \(\times\)  ~ ... ~ = ~ 574 000
\item   7,21  ~ \(\times\)  ~ ... ~ = ~ 721
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 285  ~ \(\times\)  ~ 0,1
\item   6 406  ~ \(\times\)  ~ 0,01
\item   3 929  ~ \(\times\)  ~ 0,01
\item   3 821  ~ \(\times\)  ~ 0,001
\item   8 553  ~ \(\times\)  ~ 0,001
\item   199  ~ \(\times\)  ~ 0,1
\item   49,35  ~ \(\times\)  ~ 0,01
\item   9 269  ~ \(\times\)  ~ 0,1
\item   481,2  ~ \(\times\)  ~ 0,01
\item   175,2  ~ \(\times\)  ~ 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   4,159  ~ \(\times\)  ~ ... ~ = ~  0,415 9
\item   64,65  ~ \(\times\)  ~ ... ~ = ~  0,646 5
\item   38,85  ~ \(\times\)  ~ ... ~ = ~  3,885
\item   60,34  ~ \(\times\)  ~ ... ~ = ~  0,603 4
\item   420,4  ~ \(\times\)  ~ ... ~ = ~  4,204
\item   8,485  ~ \(\times\)  ~ ... ~ = ~  0,848 5
\item   334  ~ \(\times\)  ~ ... ~ = ~  3,34
\item   504,3  ~ \(\times\)  ~ ... ~ = ~  5,043
\item   95,41  ~ \(\times\)  ~ ... ~ = ~  9,541
\item   77,54  ~ \(\times\)  ~ ... ~ = ~  0,077 54
\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 ~dm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 849,7 ~m~ = ...~cm
\item   633,08 ~hL~ = ...~kL
\item   752,65 ~cm~ = ...~m
\item   4 856,1 ~dm~ = ...~cm
\item   8 410,1 ~g~ = ...~cg
\item   202,05 ~dm~ = ...~hm
\item   176,3 ~m~ = ...~km
\item   1 576,1 ~dm~ = ...~dam
\item   5 458,9 ~hL~ = ...~dL
\item   988,12 ~dag~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{59}{10}\) = \(\dfrac{590}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{160}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,477  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,77}
\item   53,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 330}
\item   6,92  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 920}
\item   3,39  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 390}
\item   0,009  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,9}
\item   57,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 57 800}
\item   288  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 288 000}
\item   488  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 488 000}
\item   0,882  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,82}
\item   0,073  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,73}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,86 ~ : ~ 10 ~ = ~{\color{red} 0,486}
\item   322,4 ~ : ~ 100 ~ = ~{\color{red} 3,224}
\item   61,18 ~ : ~ 100 ~ = ~{\color{red} 0,611 8}
\item   4,711 ~ : ~ 10 ~ = ~{\color{red} 0,471 1}
\item   27,47 ~ : ~ 100 ~ = ~{\color{red} 0,274 7}
\item   672,1 ~ : ~ 10 ~ = ~{\color{red} 67,21}
\item   9,424 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 424}
\item   346 ~ : ~ 100 ~ = ~{\color{red} 3,46}
\item   78,3 ~ : ~ 100 ~ = ~{\color{red} 0,783}
\item   1 969 ~ : ~ 10 ~ = ~{\color{red} 196,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~903
\item   42,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 230
\item   0,088 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,88
\item   5,54 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~554
\item   0,006 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,6
\item   7,55 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~755
\item   508 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~50 800
\item   0,058 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,8
\item   574 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~574 000
\item   7,21 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~721
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 285 ~ \(\times\)  0,1 ~ = ~{\color{red} 728,5
}\item   6 406 ~ \(\times\)  0,01 ~ = ~{\color{red} 64,06
}\item   3 929 ~ \(\times\)  0,01 ~ = ~{\color{red} 39,29
}\item   3 821 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,821
}\item   8 553 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,553
}\item   199 ~ \(\times\)  0,1 ~ = ~{\color{red} 19,9
}\item   49,35 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,493 5
}\item   9 269 ~ \(\times\)  0,1 ~ = ~{\color{red} 926,9
}\item   481,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,812
}\item   175,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,175 2
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,159 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,415 9
\item   64,65 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,646 5
\item   38,85 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,885
\item   60,34 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,603 4
\item   420,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,204
\item   8,485 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,848 5
\item   334 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,34
\item   504,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,043
\item   95,41 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,541
\item   77,54 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,077 54
\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 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 849,7 ~m~ = {\color{red}  584 970 }~cm
\item   633,08 ~hL~ = {\color{red}  63,308 }~kL
\item   752,65 ~cm~ = {\color{red}  7,526 5 }~m
\item   4 856,1 ~dm~ = {\color{red}  48 561 }~cm
\item   8 410,1 ~g~ = {\color{red}  841 010 }~cg
\item   202,05 ~dm~ = {\color{red}  0,202 05 }~hm
\item   176,3 ~m~ = {\color{red}  0,176 3 }~km
\item   1 576,1 ~dm~ = {\color{red}  15,761 }~dam
\item   5 458,9 ~hL~ = {\color{red}  5 458 900 }~dL
\item   988,12 ~dag~ = {\color{red}  9 881 200 }~mg
\end{itemize}
\end{multicols}
\end{document}
