\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 3}

\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=3}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0003}
\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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{85}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,008  ~ \(\times\)  ~ 10
\item   0,939  ~ \(\times\)  ~ 100
\item   57,3  ~ \(\times\)  ~ 10
\item   0,743  ~ \(\times\)  ~ 1 000
\item   0,087  ~ \(\times\)  ~ 100
\item   41,5  ~ \(\times\)  ~ 10
\item   65,9  ~ \(\times\)  ~ 1 000
\item   408  ~ \(\times\)  ~ 1 000
\item   804  ~ \(\times\)  ~ 10
\item   0,079  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 036  ~ : ~ 100
\item   7,846  ~ : ~ 1 000
\item   7,095  ~ : ~ 1 000
\item   9,553  ~ : ~ 10
\item   6 089  ~ : ~ 10
\item   2,328  ~ : ~ 10
\item   4,327  ~ : ~ 1 000
\item   5,033  ~ : ~ 1 000
\item   64,23  ~ : ~ 1 000
\item   9,686  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,46  ~ \(\times\)  ~ ... ~ = ~ 2 460
\item   946  ~ \(\times\)  ~ ... ~ = ~ 94 600
\item   62,9  ~ \(\times\)  ~ ... ~ = ~ 62 900
\item   8,9  ~ \(\times\)  ~ ... ~ = ~ 8 900
\item   0,094  ~ \(\times\)  ~ ... ~ = ~ 94
\item   11,5  ~ \(\times\)  ~ ... ~ = ~ 11 500
\item   0,086  ~ \(\times\)  ~ ... ~ = ~ 8,6
\item   300  ~ \(\times\)  ~ ... ~ = ~ 3 000
\item   0,502  ~ \(\times\)  ~ ... ~ = ~ 5,02
\item   361  ~ \(\times\)  ~ ... ~ = ~ 36 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 571  ~ \(\times\)  ~ 0,01
\item   7,099  ~ \(\times\)  ~ 0,1
\item   825  ~ \(\times\)  ~ 0,01
\item   97,08  ~ \(\times\)  ~ 0,001
\item   467,3  ~ \(\times\)  ~ 0,1
\item   5 174  ~ \(\times\)  ~ 0,1
\item   1 872  ~ \(\times\)  ~ 0,1
\item   67,84  ~ \(\times\)  ~ 0,001
\item   441,6  ~ \(\times\)  ~ 0,001
\item   7,96  ~ \(\times\)  ~ 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   600,2  ~ \(\times\)  ~ ... ~ = ~  6,002
\item   6,273  ~ \(\times\)  ~ ... ~ = ~  0,006 273
\item   6 428  ~ \(\times\)  ~ ... ~ = ~  6,428
\item   84,08  ~ \(\times\)  ~ ... ~ = ~  0,840 8
\item   39,94  ~ \(\times\)  ~ ... ~ = ~  0,399 4
\item   43,31  ~ \(\times\)  ~ ... ~ = ~  0,043 31
\item   5 653  ~ \(\times\)  ~ ... ~ = ~  56,53
\item   96,03  ~ \(\times\)  ~ ... ~ = ~  9,603
\item   626,9  ~ \(\times\)  ~ ... ~ = ~  62,69
\item   5,547  ~ \(\times\)  ~ ... ~ = ~  0,055 47
\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~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 633,8 ~hg~ = ...~g
\item   823,95 ~dg~ = ...~cg
\item   927,24 ~dg~ = ...~hg
\item   720,22 ~g~ = ...~hg
\item   935,03 ~km~ = ...~cm
\item   7 436,5 ~cL~ = ...~mL
\item   523,91 ~dm~ = ...~cm
\item   5 284,3 ~mm~ = ...~m
\item   220,24 ~daL~ = ...~mL
\item   8 503,2 ~hL~ = ...~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   4 = \(\dfrac{40}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{5800}{100}\) = \(\dfrac{580}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{910}{100}\)
\item   \(\dfrac{85}{100}\) = \(\dfrac{850}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,008  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,08}
\item   0,939  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 93,9}
\item   57,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 573}
\item   0,743  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 743}
\item   0,087  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,7}
\item   41,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 415}
\item   65,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 65 900}
\item   408  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 408 000}
\item   804  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 040}
\item   0,079  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,79}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 036 ~ : ~ 100 ~ = ~{\color{red} 50,36}
\item   7,846 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 846}
\item   7,095 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 095}
\item   9,553 ~ : ~ 10 ~ = ~{\color{red} 0,955 3}
\item   6 089 ~ : ~ 10 ~ = ~{\color{red} 608,9}
\item   2,328 ~ : ~ 10 ~ = ~{\color{red} 0,232 8}
\item   4,327 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 327}
\item   5,033 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 033}
\item   64,23 ~ : ~ 1 000 ~ = ~{\color{red} 0,064 23}
\item   9,686 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 686}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,46 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 460
\item   946 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~94 600
\item   62,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~62 900
\item   8,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 900
\item   0,094 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~94
\item   11,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~11 500
\item   0,086 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,6
\item   300 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 000
\item   0,502 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,02
\item   361 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~36 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 571 ~ \(\times\)  0,01 ~ = ~{\color{red} 25,71
}\item   7,099 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,709 9
}\item   825 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,25
}\item   97,08 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,097 08
}\item   467,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 46,73
}\item   5 174 ~ \(\times\)  0,1 ~ = ~{\color{red} 517,4
}\item   1 872 ~ \(\times\)  0,1 ~ = ~{\color{red} 187,2
}\item   67,84 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,067 84
}\item   441,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,441 6
}\item   7,96 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,079 6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   600,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,002
\item   6,273 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 273
\item   6 428 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,428
\item   84,08 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,840 8
\item   39,94 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,399 4
\item   43,31 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,043 31
\item   5 653 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 56,53
\item   96,03 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,603
\item   626,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 62,69
\item   5,547 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,055 47
\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}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 633,8 ~hg~ = {\color{red}  963 380 }~g
\item   823,95 ~dg~ = {\color{red}  8 239,5 }~cg
\item   927,24 ~dg~ = {\color{red}  0,927 24 }~hg
\item   720,22 ~g~ = {\color{red}  7,202 2 }~hg
\item   935,03 ~km~ = {\color{red}  93 503 000 }~cm
\item   7 436,5 ~cL~ = {\color{red}  74 365 }~mL
\item   523,91 ~dm~ = {\color{red}  5 239,1 }~cm
\item   5 284,3 ~mm~ = {\color{red}  5,284 3 }~m
\item   220,24 ~daL~ = {\color{red}  2 202 400 }~mL
\item   8 503,2 ~hL~ = {\color{red}  850 320 000 }~mL
\end{itemize}
\end{multicols}
\end{document}
