\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 286}

\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=286}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0286}
\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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{21}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{63}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,426  ~ \(\times\)  ~ 10
\item   5,54  ~ \(\times\)  ~ 1 000
\item   86,6  ~ \(\times\)  ~ 100
\item   405  ~ \(\times\)  ~ 10
\item   91  ~ \(\times\)  ~ 100
\item   0,059  ~ \(\times\)  ~ 1 000
\item   891  ~ \(\times\)  ~ 10
\item   94  ~ \(\times\)  ~ 100
\item   596  ~ \(\times\)  ~ 10
\item   0,004  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,28  ~ : ~ 1 000
\item   0,841  ~ : ~ 100
\item   6,918  ~ : ~ 100
\item   75,12  ~ : ~ 100
\item   3,94  ~ : ~ 100
\item   5 441  ~ : ~ 1 000
\item   412  ~ : ~ 100
\item   5,026  ~ : ~ 100
\item   1 764  ~ : ~ 1 000
\item   844,1  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   342  ~ \(\times\)  ~ ... ~ = ~ 34 200
\item   72,8  ~ \(\times\)  ~ ... ~ = ~ 728
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 0,32
\item   184  ~ \(\times\)  ~ ... ~ = ~ 184 000
\item   152  ~ \(\times\)  ~ ... ~ = ~ 15 200
\item   894  ~ \(\times\)  ~ ... ~ = ~ 8 940
\item   83  ~ \(\times\)  ~ ... ~ = ~ 830
\item   63,5  ~ \(\times\)  ~ ... ~ = ~ 63 500
\item   0,915  ~ \(\times\)  ~ ... ~ = ~ 91,5
\item   6  ~ \(\times\)  ~ ... ~ = ~ 600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,541  ~ \(\times\)  ~ 0,01
\item   16,65  ~ \(\times\)  ~ 0,01
\item   1 529  ~ \(\times\)  ~ 0,001
\item   29,29  ~ \(\times\)  ~ 0,1
\item   9,793  ~ \(\times\)  ~ 0,1
\item   374  ~ \(\times\)  ~ 0,01
\item   7 283  ~ \(\times\)  ~ 0,1
\item   8,241  ~ \(\times\)  ~ 0,01
\item   174,8  ~ \(\times\)  ~ 0,1
\item   175,5  ~ \(\times\)  ~ 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   702,7  ~ \(\times\)  ~ ... ~ = ~  0,702 7
\item   4,659  ~ \(\times\)  ~ ... ~ = ~  0,004 659
\item   950,4  ~ \(\times\)  ~ ... ~ = ~  95,04
\item   4 003  ~ \(\times\)  ~ ... ~ = ~  400,3
\item   9,091  ~ \(\times\)  ~ ... ~ = ~  0,909 1
\item   830,7  ~ \(\times\)  ~ ... ~ = ~  8,307
\item   987,5  ~ \(\times\)  ~ ... ~ = ~  0,987 5
\item   530,1  ~ \(\times\)  ~ ... ~ = ~  53,01
\item   376,7  ~ \(\times\)  ~ ... ~ = ~  0,376 7
\item   730,5  ~ \(\times\)  ~ ... ~ = ~  0,730 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 ~km~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   716,88 ~L~ = ...~cL
\item   9 027,1 ~dag~ = ...~kg
\item   2 384,7 ~mL~ = ...~daL
\item   531,26 ~hg~ = ...~dag
\item   217,51 ~g~ = ...~dag
\item   4 359,6 ~dg~ = ...~g
\item   871,6 ~L~ = ...~kL
\item   5 822,5 ~m~ = ...~dam
\item   5 055 ~cm~ = ...~hm
\item   444,88 ~kg~ = ...~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   8 = \(\dfrac{80}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{510}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{21}{10}\) = \(\dfrac{210}{100}\)
\item   \(\dfrac{63}{100}\) = \(\dfrac{630}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,426  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,26}
\item   5,54  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 540}
\item   86,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 660}
\item   405  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 050}
\item   91  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 100}
\item   0,059  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 59}
\item   891  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 910}
\item   94  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 400}
\item   596  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 960}
\item   0,004  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,28 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 28}
\item   0,841 ~ : ~ 100 ~ = ~{\color{red} 0,008 41}
\item   6,918 ~ : ~ 100 ~ = ~{\color{red} 0,069 18}
\item   75,12 ~ : ~ 100 ~ = ~{\color{red} 0,751 2}
\item   3,94 ~ : ~ 100 ~ = ~{\color{red} 0,039 4}
\item   5 441 ~ : ~ 1 000 ~ = ~{\color{red} 5,441}
\item   412 ~ : ~ 100 ~ = ~{\color{red} 4,12}
\item   5,026 ~ : ~ 100 ~ = ~{\color{red} 0,050 26}
\item   1 764 ~ : ~ 1 000 ~ = ~{\color{red} 1,764}
\item   844,1 ~ : ~ 100 ~ = ~{\color{red} 8,441}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   342 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~34 200
\item   72,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~728
\item   0,032 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,32
\item   184 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~184 000
\item   152 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~15 200
\item   894 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 940
\item   83 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~830
\item   63,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~63 500
\item   0,915 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~91,5
\item   6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,541 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,055 41
}\item   16,65 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,166 5
}\item   1 529 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,529
}\item   29,29 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,929
}\item   9,793 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,979 3
}\item   374 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,74
}\item   7 283 ~ \(\times\)  0,1 ~ = ~{\color{red} 728,3
}\item   8,241 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,082 41
}\item   174,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 17,48
}\item   175,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,175 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   702,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,702 7
\item   4,659 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 659
\item   950,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 95,04
\item   4 003 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 400,3
\item   9,091 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,909 1
\item   830,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,307
\item   987,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,987 5
\item   530,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 53,01
\item   376,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,376 7
\item   730,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,730 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 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   716,88 ~L~ = {\color{red}  71 688 }~cL
\item   9 027,1 ~dag~ = {\color{red}  90,271 }~kg
\item   2 384,7 ~mL~ = {\color{red}  0,238 47 }~daL
\item   531,26 ~hg~ = {\color{red}  5 312,6 }~dag
\item   217,51 ~g~ = {\color{red}  21,751 }~dag
\item   4 359,6 ~dg~ = {\color{red}  435,96 }~g
\item   871,6 ~L~ = {\color{red}  0,871 6 }~kL
\item   5 822,5 ~m~ = {\color{red}  582,25 }~dam
\item   5 055 ~cm~ = {\color{red}  0,505 5 }~hm
\item   444,88 ~kg~ = {\color{red}  4 448 800 }~dg
\end{itemize}
\end{multicols}
\end{document}
