\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 295}

\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=295}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0295}
\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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   253  ~ \(\times\)  ~ 10
\item   83,3  ~ \(\times\)  ~ 1 000
\item   3,17  ~ \(\times\)  ~ 100
\item   748  ~ \(\times\)  ~ 10
\item   0,419  ~ \(\times\)  ~ 10
\item   0,62  ~ \(\times\)  ~ 10
\item   0,006  ~ \(\times\)  ~ 1 000
\item   1,42  ~ \(\times\)  ~ 100
\item   231  ~ \(\times\)  ~ 10
\item   86,1  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,389  ~ : ~ 100
\item   493,2  ~ : ~ 10
\item   0,311  ~ : ~ 100
\item   235,8  ~ : ~ 100
\item   0,342  ~ : ~ 1 000
\item   916,9  ~ : ~ 100
\item   86,29  ~ : ~ 10
\item   7 818  ~ : ~ 1 000
\item   9 682  ~ : ~ 10
\item   12,67  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,048  ~ \(\times\)  ~ ... ~ = ~ 0,48
\item   5,07  ~ \(\times\)  ~ ... ~ = ~ 50,7
\item   0,801  ~ \(\times\)  ~ ... ~ = ~ 8,01
\item   739  ~ \(\times\)  ~ ... ~ = ~ 7 390
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 0,64
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 67
\item   0,979  ~ \(\times\)  ~ ... ~ = ~ 97,9
\item   390  ~ \(\times\)  ~ ... ~ = ~ 3 900
\item   98,5  ~ \(\times\)  ~ ... ~ = ~ 9 850
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   856,7  ~ \(\times\)  ~ 0,01
\item   8 753  ~ \(\times\)  ~ 0,1
\item   30,86  ~ \(\times\)  ~ 0,001
\item   8,574  ~ \(\times\)  ~ 0,1
\item   32,45  ~ \(\times\)  ~ 0,001
\item   81,6  ~ \(\times\)  ~ 0,1
\item   6,594  ~ \(\times\)  ~ 0,01
\item   84,09  ~ \(\times\)  ~ 0,01
\item   917,4  ~ \(\times\)  ~ 0,001
\item   40,5  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 780  ~ \(\times\)  ~ ... ~ = ~  178
\item   389,2  ~ \(\times\)  ~ ... ~ = ~  0,389 2
\item   3,102  ~ \(\times\)  ~ ... ~ = ~  0,003 102
\item   9,345  ~ \(\times\)  ~ ... ~ = ~  0,093 45
\item   208,8  ~ \(\times\)  ~ ... ~ = ~  0,208 8
\item   778  ~ \(\times\)  ~ ... ~ = ~  77,8
\item   518,8  ~ \(\times\)  ~ ... ~ = ~  0,518 8
\item   45,28  ~ \(\times\)  ~ ... ~ = ~  4,528
\item   47,41  ~ \(\times\)  ~ ... ~ = ~  0,474 1
\item   688,1  ~ \(\times\)  ~ ... ~ = ~  6,881
\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~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   774,64 ~dm~ = ...~mm
\item   9 667,5 ~dL~ = ...~cL
\item   4 334,7 ~m~ = ...~cm
\item   540,94 ~g~ = ...~dag
\item   3 412,5 ~mL~ = ...~dL
\item   5 318 ~mg~ = ...~cg
\item   5 915 ~dag~ = ...~hg
\item   838,69 ~dg~ = ...~hg
\item   5 705,3 ~mL~ = ...~daL
\item   768,09 ~kL~ = ...~hL
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{510}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{200}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{440}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   253  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 530}
\item   83,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 83 300}
\item   3,17  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 317}
\item   748  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 480}
\item   0,419  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,19}
\item   0,62  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,2}
\item   0,006  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6}
\item   1,42  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 142}
\item   231  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 310}
\item   86,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 861}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,389 ~ : ~ 100 ~ = ~{\color{red} 0,093 89}
\item   493,2 ~ : ~ 10 ~ = ~{\color{red} 49,32}
\item   0,311 ~ : ~ 100 ~ = ~{\color{red} 0,003 11}
\item   235,8 ~ : ~ 100 ~ = ~{\color{red} 2,358}
\item   0,342 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 342}
\item   916,9 ~ : ~ 100 ~ = ~{\color{red} 9,169}
\item   86,29 ~ : ~ 10 ~ = ~{\color{red} 8,629}
\item   7 818 ~ : ~ 1 000 ~ = ~{\color{red} 7,818}
\item   9 682 ~ : ~ 10 ~ = ~{\color{red} 968,2}
\item   12,67 ~ : ~ 10 ~ = ~{\color{red} 1,267}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,048 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,48
\item   5,07 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~50,7
\item   0,801 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,01
\item   739 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 390
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\item   0,064 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,64
\item   0,067 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~67
\item   0,979 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~97,9
\item   390 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 900
\item   98,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 850
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   856,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,567
}\item   8 753 ~ \(\times\)  0,1 ~ = ~{\color{red} 875,3
}\item   30,86 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 86
}\item   8,574 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,857 4
}\item   32,45 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,032 45
}\item   81,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,16
}\item   6,594 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,065 94
}\item   84,09 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,840 9
}\item   917,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,917 4
}\item   40,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,405
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 780 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 178
\item   389,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,389 2
\item   3,102 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 102
\item   9,345 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,093 45
\item   208,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,208 8
\item   778 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 77,8
\item   518,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,518 8
\item   45,28 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,528
\item   47,41 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,474 1
\item   688,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,881
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   774,64 ~dm~ = {\color{red}  77 464 }~mm
\item   9 667,5 ~dL~ = {\color{red}  96 675 }~cL
\item   4 334,7 ~m~ = {\color{red}  433 470 }~cm
\item   540,94 ~g~ = {\color{red}  54,094 }~dag
\item   3 412,5 ~mL~ = {\color{red}  34,125 }~dL
\item   5 318 ~mg~ = {\color{red}  531,8 }~cg
\item   5 915 ~dag~ = {\color{red}  591,5 }~hg
\item   838,69 ~dg~ = {\color{red}  0,838 69 }~hg
\item   5 705,3 ~mL~ = {\color{red}  0,570 53 }~daL
\item   768,09 ~kL~ = {\color{red}  7 680,9 }~hL
\end{itemize}
\end{multicols}
\end{document}
