\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 129}

\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=129}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0129}
\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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   34,6  ~ \(\times\)  ~ 10
\item   0,073  ~ \(\times\)  ~ 10
\item   1,48  ~ \(\times\)  ~ 1 000
\item   24,6  ~ \(\times\)  ~ 100
\item   0,076  ~ \(\times\)  ~ 100
\item   146  ~ \(\times\)  ~ 100
\item   0,88  ~ \(\times\)  ~ 1 000
\item   756  ~ \(\times\)  ~ 100
\item   5,2  ~ \(\times\)  ~ 1 000
\item   188  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 035  ~ : ~ 100
\item   49,38  ~ : ~ 10
\item   5,232  ~ : ~ 1 000
\item   176,2  ~ : ~ 10
\item   2,702  ~ : ~ 10
\item   57  ~ : ~ 1 000
\item   6,106  ~ : ~ 100
\item   587,8  ~ : ~ 1 000
\item   863,5  ~ : ~ 100
\item   3 641  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   16,8  ~ \(\times\)  ~ ... ~ = ~ 1 680
\item   98,4  ~ \(\times\)  ~ ... ~ = ~ 98 400
\item   526  ~ \(\times\)  ~ ... ~ = ~ 526 000
\item   0,648  ~ \(\times\)  ~ ... ~ = ~ 6,48
\item   68,9  ~ \(\times\)  ~ ... ~ = ~ 689
\item   965  ~ \(\times\)  ~ ... ~ = ~ 96 500
\item   41  ~ \(\times\)  ~ ... ~ = ~ 410
\item   0,016  ~ \(\times\)  ~ ... ~ = ~ 0,16
\item   5,87  ~ \(\times\)  ~ ... ~ = ~ 587
\item   7,03  ~ \(\times\)  ~ ... ~ = ~ 703
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,393  ~ \(\times\)  ~ 0,01
\item   936,1  ~ \(\times\)  ~ 0,001
\item   3,486  ~ \(\times\)  ~ 0,1
\item   6,221  ~ \(\times\)  ~ 0,001
\item   879,7  ~ \(\times\)  ~ 0,001
\item   7,416  ~ \(\times\)  ~ 0,1
\item   5 049  ~ \(\times\)  ~ 0,001
\item   681  ~ \(\times\)  ~ 0,1
\item   8 255  ~ \(\times\)  ~ 0,001
\item   7,319  ~ \(\times\)  ~ 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   9 302  ~ \(\times\)  ~ ... ~ = ~  930,2
\item   4,136  ~ \(\times\)  ~ ... ~ = ~  0,041 36
\item   55,81  ~ \(\times\)  ~ ... ~ = ~  0,558 1
\item   97,79  ~ \(\times\)  ~ ... ~ = ~  9,779
\item   759  ~ \(\times\)  ~ ... ~ = ~  7,59
\item   449  ~ \(\times\)  ~ ... ~ = ~  0,449
\item   7 784  ~ \(\times\)  ~ ... ~ = ~  77,84
\item   8,539  ~ \(\times\)  ~ ... ~ = ~  0,008 539
\item   3 596  ~ \(\times\)  ~ ... ~ = ~  35,96
\item   382  ~ \(\times\)  ~ ... ~ = ~  3,82
\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 ~hm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   803,02 ~g~ = ...~cg
\item   2 641,2 ~dL~ = ...~daL
\item   672,23 ~mg~ = ...~dg
\item   3 664,1 ~dg~ = ...~cg
\item   8 504,9 ~hL~ = ...~cL
\item   211,01 ~kL~ = ...~daL
\item   175,09 ~km~ = ...~mm
\item   562,06 ~L~ = ...~cL
\item   1 400 ~kL~ = ...~mL
\item   6 761,1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{1600}{100}\) = \(\dfrac{160}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{910}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{390}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   34,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 346}
\item   0,073  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,73}
\item   1,48  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 480}
\item   24,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 460}
\item   0,076  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,6}
\item   146  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14 600}
\item   0,88  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 880}
\item   756  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 75 600}
\item   5,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 200}
\item   188  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 880}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 035 ~ : ~ 100 ~ = ~{\color{red} 80,35}
\item   49,38 ~ : ~ 10 ~ = ~{\color{red} 4,938}
\item   5,232 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 232}
\item   176,2 ~ : ~ 10 ~ = ~{\color{red} 17,62}
\item   2,702 ~ : ~ 10 ~ = ~{\color{red} 0,270 2}
\item   57 ~ : ~ 1 000 ~ = ~{\color{red} 0,057}
\item   6,106 ~ : ~ 100 ~ = ~{\color{red} 0,061 06}
\item   587,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,587 8}
\item   863,5 ~ : ~ 100 ~ = ~{\color{red} 8,635}
\item   3 641 ~ : ~ 10 ~ = ~{\color{red} 364,1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   16,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 680
\item   98,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~98 400
\item   526 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~526 000
\item   0,648 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,48
\item   68,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~689
\item   965 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96 500
\item   41 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~410
\item   0,016 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,16
\item   5,87 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~587
\item   7,03 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~703
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,393 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,063 93
}\item   936,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,936 1
}\item   3,486 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,348 6
}\item   6,221 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 221
}\item   879,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,879 7
}\item   7,416 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,741 6
}\item   5 049 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,049
}\item   681 ~ \(\times\)  0,1 ~ = ~{\color{red} 68,1
}\item   8 255 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,255
}\item   7,319 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,073 19
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 302 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 930,2
\item   4,136 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,041 36
\item   55,81 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,558 1
\item   97,79 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,779
\item   759 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,59
\item   449 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,449
\item   7 784 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 77,84
\item   8,539 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 539
\item   3 596 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 35,96
\item   382 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,82
\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 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   803,02 ~g~ = {\color{red}  80 302 }~cg
\item   2 641,2 ~dL~ = {\color{red}  26,412 }~daL
\item   672,23 ~mg~ = {\color{red}  6,722 3 }~dg
\item   3 664,1 ~dg~ = {\color{red}  36 641 }~cg
\item   8 504,9 ~hL~ = {\color{red}  85 049 000 }~cL
\item   211,01 ~kL~ = {\color{red}  21 101 }~daL
\item   175,09 ~km~ = {\color{red}  175 090 000 }~mm
\item   562,06 ~L~ = {\color{red}  56 206 }~cL
\item   1 400 ~kL~ = {\color{red}  1 400 000 000 }~mL
\item   6 761,1 ~cm~ = {\color{red}  6,761 1 }~dam
\end{itemize}
\end{multicols}
\end{document}
