\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 139}

\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=139}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0139}
\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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,86  ~ \(\times\)  ~ 100
\item   60,5  ~ \(\times\)  ~ 1 000
\item   8,55  ~ \(\times\)  ~ 10
\item   5,86  ~ \(\times\)  ~ 1 000
\item   51,2  ~ \(\times\)  ~ 100
\item   529  ~ \(\times\)  ~ 1 000
\item   1,99  ~ \(\times\)  ~ 1 000
\item   380  ~ \(\times\)  ~ 10
\item   5,68  ~ \(\times\)  ~ 1 000
\item   33  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,96  ~ : ~ 1 000
\item   87,4  ~ : ~ 1 000
\item   8 514  ~ : ~ 1 000
\item   1,44  ~ : ~ 1 000
\item   7,226  ~ : ~ 1 000
\item   6 426  ~ : ~ 100
\item   58,58  ~ : ~ 1 000
\item   4 025  ~ : ~ 100
\item   66,68  ~ : ~ 1 000
\item   7 744  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,966  ~ \(\times\)  ~ ... ~ = ~ 96,6
\item   911  ~ \(\times\)  ~ ... ~ = ~ 91 100
\item   65,3  ~ \(\times\)  ~ ... ~ = ~ 653
\item   0,224  ~ \(\times\)  ~ ... ~ = ~ 22,4
\item   1,3  ~ \(\times\)  ~ ... ~ = ~ 130
\item   0,038  ~ \(\times\)  ~ ... ~ = ~ 0,38
\item   2,5  ~ \(\times\)  ~ ... ~ = ~ 250
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 0,67
\item   3,31  ~ \(\times\)  ~ ... ~ = ~ 3 310
\item   5,81  ~ \(\times\)  ~ ... ~ = ~ 5 810
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   820  ~ \(\times\)  ~ 0,1
\item   364,2  ~ \(\times\)  ~ 0,01
\item   475,1  ~ \(\times\)  ~ 0,01
\item   5,483  ~ \(\times\)  ~ 0,1
\item   1 902  ~ \(\times\)  ~ 0,1
\item   3,928  ~ \(\times\)  ~ 0,1
\item   46,45  ~ \(\times\)  ~ 0,1
\item   3,098  ~ \(\times\)  ~ 0,001
\item   66,01  ~ \(\times\)  ~ 0,01
\item   7 982  ~ \(\times\)  ~ 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   7,68  ~ \(\times\)  ~ ... ~ = ~  0,007 68
\item   3 020  ~ \(\times\)  ~ ... ~ = ~  302
\item   920,1  ~ \(\times\)  ~ ... ~ = ~  92,01
\item   9 273  ~ \(\times\)  ~ ... ~ = ~  92,73
\item   2 276  ~ \(\times\)  ~ ... ~ = ~  2,276
\item   707,9  ~ \(\times\)  ~ ... ~ = ~  0,707 9
\item   2 562  ~ \(\times\)  ~ ... ~ = ~  2,562
\item   979,7  ~ \(\times\)  ~ ... ~ = ~  97,97
\item   6,328  ~ \(\times\)  ~ ... ~ = ~  0,063 28
\item   5 668  ~ \(\times\)  ~ ... ~ = ~  566,8
\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~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   559,11 ~mg~ = ...~dag
\item   963,91 ~dL~ = ...~mL
\item   9 980,7 ~L~ = ...~hL
\item   246,92 ~dag~ = ...~mg
\item   306,3 ~g~ = ...~kg
\item   125,03 ~dL~ = ...~hL
\item   1 599 ~dag~ = ...~dg
\item   687,36 ~cm~ = ...~m
\item   433,8 ~g~ = ...~hg
\item   557,94 ~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   1 = \(\dfrac{10}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{8100}{100}\) = \(\dfrac{810}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{780}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{540}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,86  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 786}
\item   60,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 60 500}
\item   8,55  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 85,5}
\item   5,86  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 860}
\item   51,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 120}
\item   529  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 529 000}
\item   1,99  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 990}
\item   380  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 800}
\item   5,68  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 680}
\item   33  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 33 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,96 ~ : ~ 1 000 ~ = ~{\color{red} 0,074 96}
\item   87,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,087 4}
\item   8 514 ~ : ~ 1 000 ~ = ~{\color{red} 8,514}
\item   1,44 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 44}
\item   7,226 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 226}
\item   6 426 ~ : ~ 100 ~ = ~{\color{red} 64,26}
\item   58,58 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 58}
\item   4 025 ~ : ~ 100 ~ = ~{\color{red} 40,25}
\item   66,68 ~ : ~ 1 000 ~ = ~{\color{red} 0,066 68}
\item   7 744 ~ : ~ 1 000 ~ = ~{\color{red} 7,744}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,966 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96,6
\item   911 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~91 100
\item   65,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~653
\item   0,224 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22,4
\item   1,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~130
\item   0,038 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,38
\item   2,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~250
\item   0,067 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,67
\item   3,31 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 310
\item   5,81 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 810
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   820 ~ \(\times\)  0,1 ~ = ~{\color{red} 82
}\item   364,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,642
}\item   475,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,751
}\item   5,483 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,548 3
}\item   1 902 ~ \(\times\)  0,1 ~ = ~{\color{red} 190,2
}\item   3,928 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,392 8
}\item   46,45 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,645
}\item   3,098 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 098
}\item   66,01 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,660 1
}\item   7 982 ~ \(\times\)  0,1 ~ = ~{\color{red} 798,2
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,68 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 68
\item   3 020 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 302
\item   920,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 92,01
\item   9 273 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 92,73
\item   2 276 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,276
\item   707,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,707 9
\item   2 562 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,562
\item   979,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 97,97
\item   6,328 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,063 28
\item   5 668 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 566,8
\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}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   559,11 ~mg~ = {\color{red}  0,055 911 }~dag
\item   963,91 ~dL~ = {\color{red}  96 391 }~mL
\item   9 980,7 ~L~ = {\color{red}  99,807 }~hL
\item   246,92 ~dag~ = {\color{red}  2 469 200 }~mg
\item   306,3 ~g~ = {\color{red}  0,306 3 }~kg
\item   125,03 ~dL~ = {\color{red}  0,125 03 }~hL
\item   1 599 ~dag~ = {\color{red}  159 900 }~dg
\item   687,36 ~cm~ = {\color{red}  6,873 6 }~m
\item   433,8 ~g~ = {\color{red}  4,338 }~hg
\item   557,94 ~dag~ = {\color{red}  5 579,4 }~g
\end{itemize}
\end{multicols}
\end{document}
