\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 112}

\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=112}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0112}
\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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{95}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{31}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   38  ~ \(\times\)  ~ 1 000
\item   474  ~ \(\times\)  ~ 100
\item   61,8  ~ \(\times\)  ~ 1 000
\item   0,475  ~ \(\times\)  ~ 100
\item   36,8  ~ \(\times\)  ~ 10
\item   0,076  ~ \(\times\)  ~ 1 000
\item   95,5  ~ \(\times\)  ~ 1 000
\item   0,047  ~ \(\times\)  ~ 100
\item   0,043  ~ \(\times\)  ~ 100
\item   269  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   122,2  ~ : ~ 100
\item   6 622  ~ : ~ 1 000
\item   334  ~ : ~ 10
\item   4,281  ~ : ~ 10
\item   4,33  ~ : ~ 1 000
\item   28,99  ~ : ~ 1 000
\item   724,2  ~ : ~ 1 000
\item   173,2  ~ : ~ 1 000
\item   444,6  ~ : ~ 1 000
\item   975,3  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   40,9  ~ \(\times\)  ~ ... ~ = ~ 40 900
\item   72,4  ~ \(\times\)  ~ ... ~ = ~ 72 400
\item   0,79  ~ \(\times\)  ~ ... ~ = ~ 790
\item   0,071  ~ \(\times\)  ~ ... ~ = ~ 0,71
\item   603  ~ \(\times\)  ~ ... ~ = ~ 603 000
\item   331  ~ \(\times\)  ~ ... ~ = ~ 33 100
\item   0,112  ~ \(\times\)  ~ ... ~ = ~ 112
\item   52,6  ~ \(\times\)  ~ ... ~ = ~ 5 260
\item   78  ~ \(\times\)  ~ ... ~ = ~ 78 000
\item   722  ~ \(\times\)  ~ ... ~ = ~ 722 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,49  ~ \(\times\)  ~ 0,01
\item   6,508  ~ \(\times\)  ~ 0,01
\item   837,6  ~ \(\times\)  ~ 0,001
\item   5 188  ~ \(\times\)  ~ 0,1
\item   952,8  ~ \(\times\)  ~ 0,001
\item   6,855  ~ \(\times\)  ~ 0,1
\item   23,56  ~ \(\times\)  ~ 0,01
\item   987  ~ \(\times\)  ~ 0,01
\item   5,429  ~ \(\times\)  ~ 0,01
\item   2 570  ~ \(\times\)  ~ 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   88,3  ~ \(\times\)  ~ ... ~ = ~  0,883
\item   7,72  ~ \(\times\)  ~ ... ~ = ~  0,077 2
\item   0,463  ~ \(\times\)  ~ ... ~ = ~  0,004 63
\item   46,96  ~ \(\times\)  ~ ... ~ = ~  4,696
\item   500,2  ~ \(\times\)  ~ ... ~ = ~  0,500 2
\item   5,22  ~ \(\times\)  ~ ... ~ = ~  0,052 2
\item   6,898  ~ \(\times\)  ~ ... ~ = ~  0,068 98
\item   2,22  ~ \(\times\)  ~ ... ~ = ~  0,222
\item   8,893  ~ \(\times\)  ~ ... ~ = ~  0,889 3
\item   88,54  ~ \(\times\)  ~ ... ~ = ~  0,885 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~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 723 ~dag~ = ...~hg
\item   237,93 ~dL~ = ...~mL
\item   560,05 ~m~ = ...~hm
\item   5 292,8 ~cg~ = ...~g
\item   4 643,7 ~cL~ = ...~kL
\item   5 256,1 ~km~ = ...~dam
\item   745,99 ~km~ = ...~dm
\item   235,32 ~dag~ = ...~g
\item   726,01 ~dL~ = ...~kL
\item   691,28 ~cL~ = ...~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   8 = \(\dfrac{80}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{7000}{100}\) = \(\dfrac{700}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{95}{10}\) = \(\dfrac{950}{100}\)
\item   \(\dfrac{31}{100}\) = \(\dfrac{310}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   38  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 38 000}
\item   474  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 47 400}
\item   61,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 61 800}
\item   0,475  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 47,5}
\item   36,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 368}
\item   0,076  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 76}
\item   95,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 95 500}
\item   0,047  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,7}
\item   0,043  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,3}
\item   269  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 690}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   122,2 ~ : ~ 100 ~ = ~{\color{red} 1,222}
\item   6 622 ~ : ~ 1 000 ~ = ~{\color{red} 6,622}
\item   334 ~ : ~ 10 ~ = ~{\color{red} 33,4}
\item   4,281 ~ : ~ 10 ~ = ~{\color{red} 0,428 1}
\item   4,33 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 33}
\item   28,99 ~ : ~ 1 000 ~ = ~{\color{red} 0,028 99}
\item   724,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,724 2}
\item   173,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,173 2}
\item   444,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,444 6}
\item   975,3 ~ : ~ 100 ~ = ~{\color{red} 9,753}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   40,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~40 900
\item   72,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~72 400
\item   0,79 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~790
\item   0,071 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,71
\item   603 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~603 000
\item   331 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~33 100
\item   0,112 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~112
\item   52,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 260
\item   78 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~78 000
\item   722 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~722 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,49 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,554 9
}\item   6,508 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,065 08
}\item   837,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,837 6
}\item   5 188 ~ \(\times\)  0,1 ~ = ~{\color{red} 518,8
}\item   952,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,952 8
}\item   6,855 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,685 5
}\item   23,56 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,235 6
}\item   987 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,87
}\item   5,429 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,054 29
}\item   2 570 ~ \(\times\)  0,01 ~ = ~{\color{red} 25,7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   88,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,883
\item   7,72 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,077 2
\item   0,463 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,004 63
\item   46,96 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,696
\item   500,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,500 2
\item   5,22 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,052 2
\item   6,898 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,068 98
\item   2,22 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,222
\item   8,893 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,889 3
\item   88,54 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,885 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~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 723 ~dag~ = {\color{red}  672,3 }~hg
\item   237,93 ~dL~ = {\color{red}  23 793 }~mL
\item   560,05 ~m~ = {\color{red}  5,600 5 }~hm
\item   5 292,8 ~cg~ = {\color{red}  52,928 }~g
\item   4 643,7 ~cL~ = {\color{red}  0,046 437 }~kL
\item   5 256,1 ~km~ = {\color{red}  525 610 }~dam
\item   745,99 ~km~ = {\color{red}  7 459 900 }~dm
\item   235,32 ~dag~ = {\color{red}  2 353,2 }~g
\item   726,01 ~dL~ = {\color{red}  0,072 601 }~kL
\item   691,28 ~cL~ = {\color{red}  6 912,8 }~mL
\end{itemize}
\end{multicols}
\end{document}
