\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 208}

\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=208}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0208}
\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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,857  ~ \(\times\)  ~ 100
\item   0,845  ~ \(\times\)  ~ 100
\item   43,9  ~ \(\times\)  ~ 10
\item   2,41  ~ \(\times\)  ~ 1 000
\item   0,089  ~ \(\times\)  ~ 10
\item   0,97  ~ \(\times\)  ~ 100
\item   3,95  ~ \(\times\)  ~ 1 000
\item   21,9  ~ \(\times\)  ~ 1 000
\item   55,8  ~ \(\times\)  ~ 1 000
\item   42  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,578  ~ : ~ 100
\item   379,4  ~ : ~ 1 000
\item   3 581  ~ : ~ 1 000
\item   5,77  ~ : ~ 1 000
\item   61,5  ~ : ~ 1 000
\item   4,291  ~ : ~ 1 000
\item   58,4  ~ : ~ 1 000
\item   4,12  ~ : ~ 1 000
\item   2,969  ~ : ~ 100
\item   0,583  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,01  ~ \(\times\)  ~ ... ~ = ~ 0,1
\item   80,3  ~ \(\times\)  ~ ... ~ = ~ 803
\item   74,1  ~ \(\times\)  ~ ... ~ = ~ 7 410
\item   0,054  ~ \(\times\)  ~ ... ~ = ~ 5,4
\item   40,7  ~ \(\times\)  ~ ... ~ = ~ 4 070
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 7,7
\item   0,45  ~ \(\times\)  ~ ... ~ = ~ 45
\item   3,3  ~ \(\times\)  ~ ... ~ = ~ 33
\item   752  ~ \(\times\)  ~ ... ~ = ~ 75 200
\item   2,58  ~ \(\times\)  ~ ... ~ = ~ 25,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   225,5  ~ \(\times\)  ~ 0,01
\item   775,1  ~ \(\times\)  ~ 0,01
\item   51,91  ~ \(\times\)  ~ 0,1
\item   5 246  ~ \(\times\)  ~ 0,01
\item   25,2  ~ \(\times\)  ~ 0,1
\item   800,7  ~ \(\times\)  ~ 0,01
\item   437,3  ~ \(\times\)  ~ 0,1
\item   7,268  ~ \(\times\)  ~ 0,1
\item   711,2  ~ \(\times\)  ~ 0,001
\item   35,75  ~ \(\times\)  ~ 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   7 206  ~ \(\times\)  ~ ... ~ = ~  720,6
\item   536,5  ~ \(\times\)  ~ ... ~ = ~  53,65
\item   5 195  ~ \(\times\)  ~ ... ~ = ~  519,5
\item   530  ~ \(\times\)  ~ ... ~ = ~  53
\item   9,244  ~ \(\times\)  ~ ... ~ = ~  0,009 244
\item   79,46  ~ \(\times\)  ~ ... ~ = ~  0,794 6
\item   59,04  ~ \(\times\)  ~ ... ~ = ~  0,059 04
\item   253,3  ~ \(\times\)  ~ ... ~ = ~  2,533
\item   0,535  ~ \(\times\)  ~ ... ~ = ~  0,000 535
\item   519,7  ~ \(\times\)  ~ ... ~ = ~  0,519 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 ~dam~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   749,3 ~cm~ = ...~dam
\item   6 789,7 ~dam~ = ...~mm
\item   5 782 ~kg~ = ...~hg
\item   503,89 ~dg~ = ...~cg
\item   5 917,6 ~mm~ = ...~m
\item   269,25 ~hL~ = ...~kL
\item   4 663,9 ~km~ = ...~hm
\item   7 346,4 ~km~ = ...~dam
\item   5 197,8 ~m~ = ...~hm
\item   560,2 ~dag~ = ...~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   5 = \(\dfrac{50}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{1800}{100}\) = \(\dfrac{180}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{900}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,857  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 85,7}
\item   0,845  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 84,5}
\item   43,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 439}
\item   2,41  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 410}
\item   0,089  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,89}
\item   0,97  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 97}
\item   3,95  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 950}
\item   21,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 21 900}
\item   55,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 55 800}
\item   42  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 420}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,578 ~ : ~ 100 ~ = ~{\color{red} 0,095 78}
\item   379,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,379 4}
\item   3 581 ~ : ~ 1 000 ~ = ~{\color{red} 3,581}
\item   5,77 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 77}
\item   61,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,061 5}
\item   4,291 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 291}
\item   58,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 4}
\item   4,12 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 12}
\item   2,969 ~ : ~ 100 ~ = ~{\color{red} 0,029 69}
\item   0,583 ~ : ~ 10 ~ = ~{\color{red} 0,058 3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,01 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,1
\item   80,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~803
\item   74,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 410
\item   0,054 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,4
\item   40,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 070
\item   0,077 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,7
\item   0,45 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~45
\item   3,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~33
\item   752 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~75 200
\item   2,58 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~25,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   225,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,255
}\item   775,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,751
}\item   51,91 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,191
}\item   5 246 ~ \(\times\)  0,01 ~ = ~{\color{red} 52,46
}\item   25,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,52
}\item   800,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,007
}\item   437,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 43,73
}\item   7,268 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,726 8
}\item   711,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,711 2
}\item   35,75 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,575
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 206 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 720,6
\item   536,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 53,65
\item   5 195 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 519,5
\item   530 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 53
\item   9,244 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 244
\item   79,46 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,794 6
\item   59,04 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,059 04
\item   253,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,533
\item   0,535 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 535
\item   519,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,519 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 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   749,3 ~cm~ = {\color{red}  0,749 3 }~dam
\item   6 789,7 ~dam~ = {\color{red}  67 897 000 }~mm
\item   5 782 ~kg~ = {\color{red}  57 820 }~hg
\item   503,89 ~dg~ = {\color{red}  5 038,9 }~cg
\item   5 917,6 ~mm~ = {\color{red}  5,917 6 }~m
\item   269,25 ~hL~ = {\color{red}  26,925 }~kL
\item   4 663,9 ~km~ = {\color{red}  46 639 }~hm
\item   7 346,4 ~km~ = {\color{red}  734 640 }~dam
\item   5 197,8 ~m~ = {\color{red}  51,978 }~hm
\item   560,2 ~dag~ = {\color{red}  5 602 }~g
\end{itemize}
\end{multicols}
\end{document}
