\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 395}

\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=395}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0395}
\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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{88}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   648  ~ \(\times\)  ~ 100
\item   0,84  ~ \(\times\)  ~ 10
\item   43,4  ~ \(\times\)  ~ 100
\item   0,056  ~ \(\times\)  ~ 100
\item   59,8  ~ \(\times\)  ~ 10
\item   4,05  ~ \(\times\)  ~ 1 000
\item   0,145  ~ \(\times\)  ~ 100
\item   0,072  ~ \(\times\)  ~ 1 000
\item   8,48  ~ \(\times\)  ~ 100
\item   90,8  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   341,8  ~ : ~ 10
\item   6 628  ~ : ~ 10
\item   685  ~ : ~ 1 000
\item   5 185  ~ : ~ 10
\item   3 858  ~ : ~ 1 000
\item   90,08  ~ : ~ 10
\item   19,53  ~ : ~ 10
\item   764,6  ~ : ~ 1 000
\item   1,555  ~ : ~ 100
\item   307,6  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68,6  ~ \(\times\)  ~ ... ~ = ~ 68 600
\item   4,87  ~ \(\times\)  ~ ... ~ = ~ 48,7
\item   0,137  ~ \(\times\)  ~ ... ~ = ~ 137
\item   27,8  ~ \(\times\)  ~ ... ~ = ~ 2 780
\item   1,1  ~ \(\times\)  ~ ... ~ = ~ 1 100
\item   11,2  ~ \(\times\)  ~ ... ~ = ~ 11 200
\item   0,217  ~ \(\times\)  ~ ... ~ = ~ 2,17
\item   48,2  ~ \(\times\)  ~ ... ~ = ~ 48 200
\item   645  ~ \(\times\)  ~ ... ~ = ~ 6 450
\item   0,624  ~ \(\times\)  ~ ... ~ = ~ 62,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26,32  ~ \(\times\)  ~ 0,01
\item   3 694  ~ \(\times\)  ~ 0,001
\item   8,751  ~ \(\times\)  ~ 0,01
\item   4,494  ~ \(\times\)  ~ 0,1
\item   9 126  ~ \(\times\)  ~ 0,01
\item   247,4  ~ \(\times\)  ~ 0,1
\item   6,092  ~ \(\times\)  ~ 0,1
\item   527,8  ~ \(\times\)  ~ 0,001
\item   124,8  ~ \(\times\)  ~ 0,01
\item   334,5  ~ \(\times\)  ~ 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   3,89  ~ \(\times\)  ~ ... ~ = ~  0,389
\item   651,3  ~ \(\times\)  ~ ... ~ = ~  0,651 3
\item   48,8  ~ \(\times\)  ~ ... ~ = ~  0,048 8
\item   464,1  ~ \(\times\)  ~ ... ~ = ~  46,41
\item   1 241  ~ \(\times\)  ~ ... ~ = ~  124,1
\item   51,03  ~ \(\times\)  ~ ... ~ = ~  0,510 3
\item   81,6  ~ \(\times\)  ~ ... ~ = ~  8,16
\item   770,3  ~ \(\times\)  ~ ... ~ = ~  77,03
\item   3,412  ~ \(\times\)  ~ ... ~ = ~  0,003 412
\item   7 894  ~ \(\times\)  ~ ... ~ = ~  789,4
\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 ~dm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   278,45 ~mm~ = ...~m
\item   713,05 ~L~ = ...~cL
\item   734,35 ~km~ = ...~cm
\item   9 555,6 ~hg~ = ...~dag
\item   9 894,5 ~hg~ = ...~kg
\item   355,88 ~mg~ = ...~kg
\item   9 638,3 ~dag~ = ...~dg
\item   7 914,9 ~L~ = ...~hL
\item   6 636,7 ~mg~ = ...~cg
\item   8 039,2 ~km~ = ...~hm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{130}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{960}{100}\)
\item   \(\dfrac{88}{100}\) = \(\dfrac{880}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   648  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 64 800}
\item   0,84  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,4}
\item   43,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 340}
\item   0,056  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,6}
\item   59,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 598}
\item   4,05  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 050}
\item   0,145  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14,5}
\item   0,072  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 72}
\item   8,48  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 848}
\item   90,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 080}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   341,8 ~ : ~ 10 ~ = ~{\color{red} 34,18}
\item   6 628 ~ : ~ 10 ~ = ~{\color{red} 662,8}
\item   685 ~ : ~ 1 000 ~ = ~{\color{red} 0,685}
\item   5 185 ~ : ~ 10 ~ = ~{\color{red} 518,5}
\item   3 858 ~ : ~ 1 000 ~ = ~{\color{red} 3,858}
\item   90,08 ~ : ~ 10 ~ = ~{\color{red} 9,008}
\item   19,53 ~ : ~ 10 ~ = ~{\color{red} 1,953}
\item   764,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,764 6}
\item   1,555 ~ : ~ 100 ~ = ~{\color{red} 0,015 55}
\item   307,6 ~ : ~ 100 ~ = ~{\color{red} 3,076}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~68 600
\item   4,87 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~48,7
\item   0,137 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~137
\item   27,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 780
\item   1,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 100
\item   11,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~11 200
\item   0,217 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,17
\item   48,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~48 200
\item   645 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 450
\item   0,624 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~62,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26,32 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,263 2
}\item   3 694 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,694
}\item   8,751 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,087 51
}\item   4,494 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,449 4
}\item   9 126 ~ \(\times\)  0,01 ~ = ~{\color{red} 91,26
}\item   247,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 24,74
}\item   6,092 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,609 2
}\item   527,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,527 8
}\item   124,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,248
}\item   334,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,334 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,89 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,389
\item   651,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,651 3
\item   48,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,048 8
\item   464,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 46,41
\item   1 241 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 124,1
\item   51,03 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,510 3
\item   81,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,16
\item   770,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 77,03
\item   3,412 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 412
\item   7 894 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 789,4
\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 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   278,45 ~mm~ = {\color{red}  0,278 45 }~m
\item   713,05 ~L~ = {\color{red}  71 305 }~cL
\item   734,35 ~km~ = {\color{red}  73 435 000 }~cm
\item   9 555,6 ~hg~ = {\color{red}  95 556 }~dag
\item   9 894,5 ~hg~ = {\color{red}  989,45 }~kg
\item   355,88 ~mg~ = {\color{red}  0,000 355 88 }~kg
\item   9 638,3 ~dag~ = {\color{red}  963 830 }~dg
\item   7 914,9 ~L~ = {\color{red}  79,149 }~hL
\item   6 636,7 ~mg~ = {\color{red}  663,67 }~cg
\item   8 039,2 ~km~ = {\color{red}  80 392 }~hm
\end{itemize}
\end{multicols}
\end{document}
