\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 17}

\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=17}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0017}
\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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{48}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,079  ~ \(\times\)  ~ 1 000
\item   293  ~ \(\times\)  ~ 10
\item   0,263  ~ \(\times\)  ~ 1 000
\item   4,38  ~ \(\times\)  ~ 1 000
\item   8,3  ~ \(\times\)  ~ 1 000
\item   0,875  ~ \(\times\)  ~ 10
\item   573  ~ \(\times\)  ~ 10
\item   84,1  ~ \(\times\)  ~ 10
\item   0,091  ~ \(\times\)  ~ 1 000
\item   83  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 947  ~ : ~ 1 000
\item   12,34  ~ : ~ 100
\item   1,442  ~ : ~ 1 000
\item   2,421  ~ : ~ 1 000
\item   5 612  ~ : ~ 100
\item   6 199  ~ : ~ 1 000
\item   5 911  ~ : ~ 100
\item   6 242  ~ : ~ 100
\item   4 015  ~ : ~ 1 000
\item   360,4  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   377  ~ \(\times\)  ~ ... ~ = ~ 37 700
\item   0,74  ~ \(\times\)  ~ ... ~ = ~ 7,4
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 77
\item   0,055  ~ \(\times\)  ~ ... ~ = ~ 0,55
\item   2,65  ~ \(\times\)  ~ ... ~ = ~ 265
\item   33,5  ~ \(\times\)  ~ ... ~ = ~ 3 350
\item   0,011  ~ \(\times\)  ~ ... ~ = ~ 11
\item   8,1  ~ \(\times\)  ~ ... ~ = ~ 810
\item   18  ~ \(\times\)  ~ ... ~ = ~ 1 800
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 28
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,565  ~ \(\times\)  ~ 0,001
\item   98,5  ~ \(\times\)  ~ 0,01
\item   4 329  ~ \(\times\)  ~ 0,001
\item   8 045  ~ \(\times\)  ~ 0,001
\item   934,4  ~ \(\times\)  ~ 0,01
\item   8,045  ~ \(\times\)  ~ 0,1
\item   33,06  ~ \(\times\)  ~ 0,1
\item   190,9  ~ \(\times\)  ~ 0,1
\item   88,98  ~ \(\times\)  ~ 0,01
\item   5 280  ~ \(\times\)  ~ 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   6 965  ~ \(\times\)  ~ ... ~ = ~  6,965
\item   52,1  ~ \(\times\)  ~ ... ~ = ~  0,052 1
\item   6,714  ~ \(\times\)  ~ ... ~ = ~  0,671 4
\item   8 983  ~ \(\times\)  ~ ... ~ = ~  8,983
\item   406,1  ~ \(\times\)  ~ ... ~ = ~  0,406 1
\item   444,6  ~ \(\times\)  ~ ... ~ = ~  4,446
\item   0,907  ~ \(\times\)  ~ ... ~ = ~  0,000 907
\item   6,536  ~ \(\times\)  ~ ... ~ = ~  0,653 6
\item   9,177  ~ \(\times\)  ~ ... ~ = ~  0,009 177
\item   7 392  ~ \(\times\)  ~ ... ~ = ~  73,92
\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~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 120 ~L~ = ...~daL
\item   8 353,8 ~mL~ = ...~cL
\item   682,44 ~mg~ = ...~kg
\item   419,95 ~km~ = ...~dam
\item   497,18 ~L~ = ...~dL
\item   7 425,1 ~L~ = ...~cL
\item   813,98 ~kg~ = ...~mg
\item   640,54 ~dm~ = ...~cm
\item   7 046,1 ~hg~ = ...~kg
\item   274,17 ~hL~ = ...~mL
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{4900}{100}\) = \(\dfrac{490}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{48}{10}\) = \(\dfrac{480}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{330}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,079  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 79}
\item   293  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 930}
\item   0,263  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 263}
\item   4,38  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 380}
\item   8,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 300}
\item   0,875  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,75}
\item   573  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 730}
\item   84,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 841}
\item   0,091  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 91}
\item   83  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 300}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 947 ~ : ~ 1 000 ~ = ~{\color{red} 8,947}
\item   12,34 ~ : ~ 100 ~ = ~{\color{red} 0,123 4}
\item   1,442 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 442}
\item   2,421 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 421}
\item   5 612 ~ : ~ 100 ~ = ~{\color{red} 56,12}
\item   6 199 ~ : ~ 1 000 ~ = ~{\color{red} 6,199}
\item   5 911 ~ : ~ 100 ~ = ~{\color{red} 59,11}
\item   6 242 ~ : ~ 100 ~ = ~{\color{red} 62,42}
\item   4 015 ~ : ~ 1 000 ~ = ~{\color{red} 4,015}
\item   360,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,360 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   377 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~37 700
\item   0,74 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,4
\item   0,077 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~77
\item   0,055 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,55
\item   2,65 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~265
\item   33,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 350
\item   0,011 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~11
\item   8,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~810
\item   18 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 800
\item   0,028 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~28
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,565 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 565
}\item   98,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,985
}\item   4 329 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,329
}\item   8 045 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,045
}\item   934,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,344
}\item   8,045 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,804 5
}\item   33,06 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,306
}\item   190,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 19,09
}\item   88,98 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,889 8
}\item   5 280 ~ \(\times\)  0,1 ~ = ~{\color{red} 528
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 965 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,965
\item   52,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,052 1
\item   6,714 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,671 4
\item   8 983 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,983
\item   406,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,406 1
\item   444,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,446
\item   0,907 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 907
\item   6,536 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,653 6
\item   9,177 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 177
\item   7 392 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 73,92
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ 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   8 120 ~L~ = {\color{red}  812 }~daL
\item   8 353,8 ~mL~ = {\color{red}  835,38 }~cL
\item   682,44 ~mg~ = {\color{red}  0,000 682 44 }~kg
\item   419,95 ~km~ = {\color{red}  41 995 }~dam
\item   497,18 ~L~ = {\color{red}  4 971,8 }~dL
\item   7 425,1 ~L~ = {\color{red}  742 510 }~cL
\item   813,98 ~kg~ = {\color{red}  813 980 000 }~mg
\item   640,54 ~dm~ = {\color{red}  6 405,4 }~cm
\item   7 046,1 ~hg~ = {\color{red}  704,61 }~kg
\item   274,17 ~hL~ = {\color{red}  27 417 000 }~mL
\end{itemize}
\end{multicols}
\end{document}
