\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 224}

\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=224}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0224}
\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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,111  ~ \(\times\)  ~ 1 000
\item   55  ~ \(\times\)  ~ 10
\item   3,44  ~ \(\times\)  ~ 1 000
\item   260  ~ \(\times\)  ~ 10
\item   0,851  ~ \(\times\)  ~ 100
\item   0,208  ~ \(\times\)  ~ 100
\item   0,395  ~ \(\times\)  ~ 100
\item   736  ~ \(\times\)  ~ 1 000
\item   0,181  ~ \(\times\)  ~ 1 000
\item   0,042  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 877  ~ : ~ 10
\item   947  ~ : ~ 100
\item   66,83  ~ : ~ 10
\item   3,138  ~ : ~ 1 000
\item   9,509  ~ : ~ 10
\item   74,22  ~ : ~ 1 000
\item   9 015  ~ : ~ 1 000
\item   659,2  ~ : ~ 100
\item   0,591  ~ : ~ 100
\item   3,91  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,668  ~ \(\times\)  ~ ... ~ = ~ 668
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 0,28
\item   908  ~ \(\times\)  ~ ... ~ = ~ 908 000
\item   0,53  ~ \(\times\)  ~ ... ~ = ~ 5,3
\item   2,11  ~ \(\times\)  ~ ... ~ = ~ 2 110
\item   9,87  ~ \(\times\)  ~ ... ~ = ~ 987
\item   0,005  ~ \(\times\)  ~ ... ~ = ~ 0,05
\item   0,018  ~ \(\times\)  ~ ... ~ = ~ 1,8
\item   1,12  ~ \(\times\)  ~ ... ~ = ~ 1 120
\item   0,859  ~ \(\times\)  ~ ... ~ = ~ 859
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,84  ~ \(\times\)  ~ 0,01
\item   9,592  ~ \(\times\)  ~ 0,01
\item   1,355  ~ \(\times\)  ~ 0,001
\item   4 995  ~ \(\times\)  ~ 0,1
\item   3 572  ~ \(\times\)  ~ 0,1
\item   26,13  ~ \(\times\)  ~ 0,1
\item   4 004  ~ \(\times\)  ~ 0,001
\item   38,79  ~ \(\times\)  ~ 0,01
\item   7,709  ~ \(\times\)  ~ 0,01
\item   27,91  ~ \(\times\)  ~ 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   5,59  ~ \(\times\)  ~ ... ~ = ~  0,005 59
\item   9,279  ~ \(\times\)  ~ ... ~ = ~  0,927 9
\item   72,51  ~ \(\times\)  ~ ... ~ = ~  0,725 1
\item   83,13  ~ \(\times\)  ~ ... ~ = ~  8,313
\item   9 447  ~ \(\times\)  ~ ... ~ = ~  944,7
\item   7 581  ~ \(\times\)  ~ ... ~ = ~  75,81
\item   33,72  ~ \(\times\)  ~ ... ~ = ~  0,033 72
\item   6,174  ~ \(\times\)  ~ ... ~ = ~  0,617 4
\item   9 694  ~ \(\times\)  ~ ... ~ = ~  96,94
\item   431,5  ~ \(\times\)  ~ ... ~ = ~  0,431 5
\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 ~dam~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   215,53 ~g~ = ...~mg
\item   924,27 ~cg~ = ...~kg
\item   987,58 ~m~ = ...~mm
\item   504,47 ~daL~ = ...~L
\item   8 239 ~cg~ = ...~dg
\item   428,94 ~daL~ = ...~mL
\item   957 ~km~ = ...~hm
\item   716,14 ~cm~ = ...~mm
\item   382,13 ~dm~ = ...~km
\item   4 995,3 ~L~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{7000}{100}\) = \(\dfrac{700}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{790}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{400}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,111  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 111}
\item   55  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 550}
\item   3,44  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 440}
\item   260  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 600}
\item   0,851  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 85,1}
\item   0,208  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 20,8}
\item   0,395  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 39,5}
\item   736  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 736 000}
\item   0,181  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 181}
\item   0,042  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 42}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 877 ~ : ~ 10 ~ = ~{\color{red} 487,7}
\item   947 ~ : ~ 100 ~ = ~{\color{red} 9,47}
\item   66,83 ~ : ~ 10 ~ = ~{\color{red} 6,683}
\item   3,138 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 138}
\item   9,509 ~ : ~ 10 ~ = ~{\color{red} 0,950 9}
\item   74,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,074 22}
\item   9 015 ~ : ~ 1 000 ~ = ~{\color{red} 9,015}
\item   659,2 ~ : ~ 100 ~ = ~{\color{red} 6,592}
\item   0,591 ~ : ~ 100 ~ = ~{\color{red} 0,005 91}
\item   3,91 ~ : ~ 10 ~ = ~{\color{red} 0,391}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,668 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~668
\item   0,028 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,28
\item   908 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~908 000
\item   0,53 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,3
\item   2,11 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 110
\item   9,87 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~987
\item   0,005 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,05
\item   0,018 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,8
\item   1,12 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 120
\item   0,859 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~859
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,84 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,048 4
}\item   9,592 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,095 92
}\item   1,355 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 355
}\item   4 995 ~ \(\times\)  0,1 ~ = ~{\color{red} 499,5
}\item   3 572 ~ \(\times\)  0,1 ~ = ~{\color{red} 357,2
}\item   26,13 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,613
}\item   4 004 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,004
}\item   38,79 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,387 9
}\item   7,709 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,077 09
}\item   27,91 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,279 1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,59 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 59
\item   9,279 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,927 9
\item   72,51 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,725 1
\item   83,13 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,313
\item   9 447 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 944,7
\item   7 581 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 75,81
\item   33,72 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,033 72
\item   6,174 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,617 4
\item   9 694 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 96,94
\item   431,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,431 5
\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 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   215,53 ~g~ = {\color{red}  215 530 }~mg
\item   924,27 ~cg~ = {\color{red}  0,009 242 7 }~kg
\item   987,58 ~m~ = {\color{red}  987 580 }~mm
\item   504,47 ~daL~ = {\color{red}  5 044,7 }~L
\item   8 239 ~cg~ = {\color{red}  823,9 }~dg
\item   428,94 ~daL~ = {\color{red}  4 289 400 }~mL
\item   957 ~km~ = {\color{red}  9 570 }~hm
\item   716,14 ~cm~ = {\color{red}  7 161,4 }~mm
\item   382,13 ~dm~ = {\color{red}  0,038 213 }~km
\item   4 995,3 ~L~ = {\color{red}  4,995 3 }~kL
\end{itemize}
\end{multicols}
\end{document}
