\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 93}

\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=93}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0093}
\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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{56}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,185  ~ \(\times\)  ~ 10
\item   81,5  ~ \(\times\)  ~ 1 000
\item   0,004  ~ \(\times\)  ~ 1 000
\item   930  ~ \(\times\)  ~ 1 000
\item   6,45  ~ \(\times\)  ~ 100
\item   937  ~ \(\times\)  ~ 1 000
\item   8,1  ~ \(\times\)  ~ 10
\item   0,973  ~ \(\times\)  ~ 10
\item   6,15  ~ \(\times\)  ~ 1 000
\item   3,08  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 869  ~ : ~ 10
\item   100,8  ~ : ~ 1 000
\item   1 822  ~ : ~ 10
\item   4 716  ~ : ~ 10
\item   942,4  ~ : ~ 1 000
\item   642,6  ~ : ~ 100
\item   7 332  ~ : ~ 100
\item   654,5  ~ : ~ 1 000
\item   910,3  ~ : ~ 1 000
\item   8 911  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,69  ~ \(\times\)  ~ ... ~ = ~ 2 690
\item   0,009  ~ \(\times\)  ~ ... ~ = ~ 0,09
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 0,32
\item   0,044  ~ \(\times\)  ~ ... ~ = ~ 0,44
\item   0,003  ~ \(\times\)  ~ ... ~ = ~ 0,3
\item   20  ~ \(\times\)  ~ ... ~ = ~ 20 000
\item   43,2  ~ \(\times\)  ~ ... ~ = ~ 43 200
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 0,32
\item   28,2  ~ \(\times\)  ~ ... ~ = ~ 282
\item   368  ~ \(\times\)  ~ ... ~ = ~ 3 680
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   13,69  ~ \(\times\)  ~ 0,1
\item   8 017  ~ \(\times\)  ~ 0,001
\item   58,45  ~ \(\times\)  ~ 0,001
\item   2,956  ~ \(\times\)  ~ 0,01
\item   9,597  ~ \(\times\)  ~ 0,01
\item   2 377  ~ \(\times\)  ~ 0,01
\item   0,719  ~ \(\times\)  ~ 0,001
\item   18,7  ~ \(\times\)  ~ 0,001
\item   6,134  ~ \(\times\)  ~ 0,1
\item   55,07  ~ \(\times\)  ~ 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   176  ~ \(\times\)  ~ ... ~ = ~  1,76
\item   1 749  ~ \(\times\)  ~ ... ~ = ~  17,49
\item   211,9  ~ \(\times\)  ~ ... ~ = ~  0,211 9
\item   7 292  ~ \(\times\)  ~ ... ~ = ~  72,92
\item   8,098  ~ \(\times\)  ~ ... ~ = ~  0,809 8
\item   338,1  ~ \(\times\)  ~ ... ~ = ~  3,381
\item   874,9  ~ \(\times\)  ~ ... ~ = ~  87,49
\item   7 764  ~ \(\times\)  ~ ... ~ = ~  77,64
\item   698,4  ~ \(\times\)  ~ ... ~ = ~  6,984
\item   6,477  ~ \(\times\)  ~ ... ~ = ~  0,647 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 ~km~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   948,81 ~hg~ = ...~cg
\item   5 193,3 ~dam~ = ...~hm
\item   472,38 ~kg~ = ...~mg
\item   252,87 ~daL~ = ...~cL
\item   3 493,9 ~kg~ = ...~g
\item   1 444,9 ~kL~ = ...~cL
\item   4 379,4 ~dag~ = ...~mg
\item   140,8 ~g~ = ...~dag
\item   3 535,9 ~kL~ = ...~daL
\item   5 027,2 ~dm~ = ...~km
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{250}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{56}{10}\) = \(\dfrac{560}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{290}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,185  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,85}
\item   81,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 81 500}
\item   0,004  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4}
\item   930  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 930 000}
\item   6,45  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 645}
\item   937  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 937 000}
\item   8,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 81}
\item   0,973  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,73}
\item   6,15  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 150}
\item   3,08  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 30,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 869 ~ : ~ 10 ~ = ~{\color{red} 786,9}
\item   100,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,100 8}
\item   1 822 ~ : ~ 10 ~ = ~{\color{red} 182,2}
\item   4 716 ~ : ~ 10 ~ = ~{\color{red} 471,6}
\item   942,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,942 4}
\item   642,6 ~ : ~ 100 ~ = ~{\color{red} 6,426}
\item   7 332 ~ : ~ 100 ~ = ~{\color{red} 73,32}
\item   654,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,654 5}
\item   910,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,910 3}
\item   8 911 ~ : ~ 1 000 ~ = ~{\color{red} 8,911}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,69 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 690
\item   0,009 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,09
\item   0,032 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,32
\item   0,044 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,44
\item   0,003 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,3
\item   20 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~20 000
\item   43,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43 200
\item   0,032 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,32
\item   28,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~282
\item   368 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 680
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   13,69 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,369
}\item   8 017 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,017
}\item   58,45 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,058 45
}\item   2,956 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,029 56
}\item   9,597 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,095 97
}\item   2 377 ~ \(\times\)  0,01 ~ = ~{\color{red} 23,77
}\item   0,719 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 719
}\item   18,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,018 7
}\item   6,134 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,613 4
}\item   55,07 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,507
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   176 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,76
\item   1 749 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 17,49
\item   211,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,211 9
\item   7 292 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 72,92
\item   8,098 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,809 8
\item   338,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,381
\item   874,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 87,49
\item   7 764 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 77,64
\item   698,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,984
\item   6,477 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,647 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 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   948,81 ~hg~ = {\color{red}  9 488 100 }~cg
\item   5 193,3 ~dam~ = {\color{red}  519,33 }~hm
\item   472,38 ~kg~ = {\color{red}  472 380 000 }~mg
\item   252,87 ~daL~ = {\color{red}  252 870 }~cL
\item   3 493,9 ~kg~ = {\color{red}  3 493 900 }~g
\item   1 444,9 ~kL~ = {\color{red}  144 490 000 }~cL
\item   4 379,4 ~dag~ = {\color{red}  43 794 000 }~mg
\item   140,8 ~g~ = {\color{red}  14,08 }~dag
\item   3 535,9 ~kL~ = {\color{red}  353 590 }~daL
\item   5 027,2 ~dm~ = {\color{red}  0,502 72 }~km
\end{itemize}
\end{multicols}
\end{document}
