\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 190}

\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=190}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0190}
\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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,493  ~ \(\times\)  ~ 10
\item   167  ~ \(\times\)  ~ 1 000
\item   0,082  ~ \(\times\)  ~ 10
\item   0,061  ~ \(\times\)  ~ 10
\item   5,37  ~ \(\times\)  ~ 1 000
\item   0,327  ~ \(\times\)  ~ 10
\item   7,39  ~ \(\times\)  ~ 10
\item   403  ~ \(\times\)  ~ 100
\item   0,05  ~ \(\times\)  ~ 100
\item   0,059  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   868,6  ~ : ~ 100
\item   3 497  ~ : ~ 100
\item   968,5  ~ : ~ 100
\item   8,959  ~ : ~ 100
\item   9,427  ~ : ~ 100
\item   40,37  ~ : ~ 10
\item   442,4  ~ : ~ 10
\item   6 203  ~ : ~ 1 000
\item   7 680  ~ : ~ 10
\item   390,9  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,39  ~ \(\times\)  ~ ... ~ = ~ 3 390
\item   5,54  ~ \(\times\)  ~ ... ~ = ~ 554
\item   73,2  ~ \(\times\)  ~ ... ~ = ~ 73 200
\item   0,396  ~ \(\times\)  ~ ... ~ = ~ 39,6
\item   6,78  ~ \(\times\)  ~ ... ~ = ~ 6 780
\item   54,3  ~ \(\times\)  ~ ... ~ = ~ 5 430
\item   4,18  ~ \(\times\)  ~ ... ~ = ~ 418
\item   18,2  ~ \(\times\)  ~ ... ~ = ~ 182
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 43
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 2,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,11  ~ \(\times\)  ~ 0,01
\item   7 739  ~ \(\times\)  ~ 0,001
\item   3,951  ~ \(\times\)  ~ 0,01
\item   9,844  ~ \(\times\)  ~ 0,1
\item   2,839  ~ \(\times\)  ~ 0,01
\item   7,672  ~ \(\times\)  ~ 0,1
\item   5,456  ~ \(\times\)  ~ 0,001
\item   2,54  ~ \(\times\)  ~ 0,01
\item   3 853  ~ \(\times\)  ~ 0,01
\item   0,729  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 897  ~ \(\times\)  ~ ... ~ = ~  2,897
\item   40,89  ~ \(\times\)  ~ ... ~ = ~  4,089
\item   9 402  ~ \(\times\)  ~ ... ~ = ~  9,402
\item   92,75  ~ \(\times\)  ~ ... ~ = ~  0,092 75
\item   4,958  ~ \(\times\)  ~ ... ~ = ~  0,495 8
\item   44,18  ~ \(\times\)  ~ ... ~ = ~  0,044 18
\item   9,05  ~ \(\times\)  ~ ... ~ = ~  0,905
\item   9,441  ~ \(\times\)  ~ ... ~ = ~  0,009 441
\item   450,7  ~ \(\times\)  ~ ... ~ = ~  4,507
\item   706  ~ \(\times\)  ~ ... ~ = ~  0,706
\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~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 093 ~hm~ = ...~dam
\item   385,01 ~dag~ = ...~hg
\item   3 530,6 ~cL~ = ...~mL
\item   7 390,5 ~daL~ = ...~hL
\item   1 671,3 ~kL~ = ...~daL
\item   998,91 ~cL~ = ...~kL
\item   513,02 ~cg~ = ...~hg
\item   4 021,1 ~mL~ = ...~kL
\item   9 703,8 ~cg~ = ...~kg
\item   3 275,7 ~g~ = ...~dg
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{530}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{370}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{390}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,493  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,93}
\item   167  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 167 000}
\item   0,082  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,82}
\item   0,061  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,61}
\item   5,37  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 370}
\item   0,327  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,27}
\item   7,39  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 73,9}
\item   403  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 40 300}
\item   0,05  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5}
\item   0,059  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,59}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   868,6 ~ : ~ 100 ~ = ~{\color{red} 8,686}
\item   3 497 ~ : ~ 100 ~ = ~{\color{red} 34,97}
\item   968,5 ~ : ~ 100 ~ = ~{\color{red} 9,685}
\item   8,959 ~ : ~ 100 ~ = ~{\color{red} 0,089 59}
\item   9,427 ~ : ~ 100 ~ = ~{\color{red} 0,094 27}
\item   40,37 ~ : ~ 10 ~ = ~{\color{red} 4,037}
\item   442,4 ~ : ~ 10 ~ = ~{\color{red} 44,24}
\item   6 203 ~ : ~ 1 000 ~ = ~{\color{red} 6,203}
\item   7 680 ~ : ~ 10 ~ = ~{\color{red} 768}
\item   390,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,390 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,39 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 390
\item   5,54 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~554
\item   73,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~73 200
\item   0,396 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~39,6
\item   6,78 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 780
\item   54,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 430
\item   4,18 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~418
\item   18,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~182
\item   0,043 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43
\item   0,028 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,11 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,891 1
}\item   7 739 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,739
}\item   3,951 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,039 51
}\item   9,844 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,984 4
}\item   2,839 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,028 39
}\item   7,672 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,767 2
}\item   5,456 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 456
}\item   2,54 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,025 4
}\item   3 853 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,53
}\item   0,729 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 729
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 897 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,897
\item   40,89 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,089
\item   9 402 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,402
\item   92,75 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,092 75
\item   4,958 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,495 8
\item   44,18 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,044 18
\item   9,05 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,905
\item   9,441 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 441
\item   450,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,507
\item   706 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,706
\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}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 093 ~hm~ = {\color{red}  60 930 }~dam
\item   385,01 ~dag~ = {\color{red}  38,501 }~hg
\item   3 530,6 ~cL~ = {\color{red}  35 306 }~mL
\item   7 390,5 ~daL~ = {\color{red}  739,05 }~hL
\item   1 671,3 ~kL~ = {\color{red}  167 130 }~daL
\item   998,91 ~cL~ = {\color{red}  0,009 989 1 }~kL
\item   513,02 ~cg~ = {\color{red}  0,051 302 }~hg
\item   4 021,1 ~mL~ = {\color{red}  0,004 021 1 }~kL
\item   9 703,8 ~cg~ = {\color{red}  0,097 038 }~kg
\item   3 275,7 ~g~ = {\color{red}  32 757 }~dg
\end{itemize}
\end{multicols}
\end{document}
