\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 385}

\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=385}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0385}
\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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{50}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,955  ~ \(\times\)  ~ 10
\item   0,595  ~ \(\times\)  ~ 100
\item   53,8  ~ \(\times\)  ~ 10
\item   0,786  ~ \(\times\)  ~ 10
\item   171  ~ \(\times\)  ~ 10
\item   71,8  ~ \(\times\)  ~ 100
\item   9,79  ~ \(\times\)  ~ 10
\item   171  ~ \(\times\)  ~ 1 000
\item   27,2  ~ \(\times\)  ~ 10
\item   294  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 775  ~ : ~ 100
\item   740,6  ~ : ~ 100
\item   4 159  ~ : ~ 1 000
\item   908  ~ : ~ 1 000
\item   4 489  ~ : ~ 1 000
\item   7 098  ~ : ~ 100
\item   83,93  ~ : ~ 10
\item   70,45  ~ : ~ 1 000
\item   66,6  ~ : ~ 100
\item   22,6  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,48  ~ \(\times\)  ~ ... ~ = ~ 348
\item   553  ~ \(\times\)  ~ ... ~ = ~ 5 530
\item   0,516  ~ \(\times\)  ~ ... ~ = ~ 5,16
\item   16,1  ~ \(\times\)  ~ ... ~ = ~ 16 100
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 7,7
\item   266  ~ \(\times\)  ~ ... ~ = ~ 26 600
\item   7,2  ~ \(\times\)  ~ ... ~ = ~ 7 200
\item   5,09  ~ \(\times\)  ~ ... ~ = ~ 509
\item   91,3  ~ \(\times\)  ~ ... ~ = ~ 91 300
\item   8,11  ~ \(\times\)  ~ ... ~ = ~ 811
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 010  ~ \(\times\)  ~ 0,1
\item   8 367  ~ \(\times\)  ~ 0,1
\item   3,614  ~ \(\times\)  ~ 0,1
\item   9,347  ~ \(\times\)  ~ 0,1
\item   7 931  ~ \(\times\)  ~ 0,001
\item   5,638  ~ \(\times\)  ~ 0,01
\item   18,6  ~ \(\times\)  ~ 0,01
\item   7,222  ~ \(\times\)  ~ 0,01
\item   3 480  ~ \(\times\)  ~ 0,1
\item   52,2  ~ \(\times\)  ~ 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   6,7  ~ \(\times\)  ~ ... ~ = ~  0,067
\item   389,4  ~ \(\times\)  ~ ... ~ = ~  3,894
\item   0,514  ~ \(\times\)  ~ ... ~ = ~  0,051 4
\item   6 113  ~ \(\times\)  ~ ... ~ = ~  6,113
\item   2,253  ~ \(\times\)  ~ ... ~ = ~  0,022 53
\item   1,23  ~ \(\times\)  ~ ... ~ = ~  0,001 23
\item   360,7  ~ \(\times\)  ~ ... ~ = ~  36,07
\item   656  ~ \(\times\)  ~ ... ~ = ~  65,6
\item   556,8  ~ \(\times\)  ~ ... ~ = ~  0,556 8
\item   7 222  ~ \(\times\)  ~ ... ~ = ~  722,2
\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 ~dam~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   364,74 ~dam~ = ...~m
\item   747,5 ~kg~ = ...~cg
\item   266,97 ~mm~ = ...~dm
\item   558,2 ~hg~ = ...~g
\item   6 382,4 ~dg~ = ...~kg
\item   630,68 ~kL~ = ...~dL
\item   196,34 ~kg~ = ...~mg
\item   780,91 ~hm~ = ...~mm
\item   2 993,2 ~daL~ = ...~L
\item   931 ~dL~ = ...~hL
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{6100}{100}\) = \(\dfrac{610}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{50}{10}\) = \(\dfrac{500}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{130}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,955  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,55}
\item   0,595  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 59,5}
\item   53,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 538}
\item   0,786  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,86}
\item   171  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 710}
\item   71,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 180}
\item   9,79  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 97,9}
\item   171  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 171 000}
\item   27,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 272}
\item   294  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 294 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 775 ~ : ~ 100 ~ = ~{\color{red} 17,75}
\item   740,6 ~ : ~ 100 ~ = ~{\color{red} 7,406}
\item   4 159 ~ : ~ 1 000 ~ = ~{\color{red} 4,159}
\item   908 ~ : ~ 1 000 ~ = ~{\color{red} 0,908}
\item   4 489 ~ : ~ 1 000 ~ = ~{\color{red} 4,489}
\item   7 098 ~ : ~ 100 ~ = ~{\color{red} 70,98}
\item   83,93 ~ : ~ 10 ~ = ~{\color{red} 8,393}
\item   70,45 ~ : ~ 1 000 ~ = ~{\color{red} 0,070 45}
\item   66,6 ~ : ~ 100 ~ = ~{\color{red} 0,666}
\item   22,6 ~ : ~ 10 ~ = ~{\color{red} 2,26}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,48 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~348
\item   553 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 530
\item   0,516 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,16
\item   16,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~16 100
\item   0,077 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,7
\item   266 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~26 600
\item   7,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 200
\item   5,09 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~509
\item   91,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~91 300
\item   8,11 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~811
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 010 ~ \(\times\)  0,1 ~ = ~{\color{red} 801
}\item   8 367 ~ \(\times\)  0,1 ~ = ~{\color{red} 836,7
}\item   3,614 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,361 4
}\item   9,347 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,934 7
}\item   7 931 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,931
}\item   5,638 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,056 38
}\item   18,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,186
}\item   7,222 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,072 22
}\item   3 480 ~ \(\times\)  0,1 ~ = ~{\color{red} 348
}\item   52,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,22
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,067
\item   389,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,894
\item   0,514 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,051 4
\item   6 113 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,113
\item   2,253 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,022 53
\item   1,23 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 23
\item   360,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 36,07
\item   656 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 65,6
\item   556,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,556 8
\item   7 222 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 722,2
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   364,74 ~dam~ = {\color{red}  3 647,4 }~m
\item   747,5 ~kg~ = {\color{red}  74 750 000 }~cg
\item   266,97 ~mm~ = {\color{red}  2,669 7 }~dm
\item   558,2 ~hg~ = {\color{red}  55 820 }~g
\item   6 382,4 ~dg~ = {\color{red}  0,638 24 }~kg
\item   630,68 ~kL~ = {\color{red}  6 306 800 }~dL
\item   196,34 ~kg~ = {\color{red}  196 340 000 }~mg
\item   780,91 ~hm~ = {\color{red}  78 091 000 }~mm
\item   2 993,2 ~daL~ = {\color{red}  29 932 }~L
\item   931 ~dL~ = {\color{red}  0,931 }~hL
\end{itemize}
\end{multicols}
\end{document}
