\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 354}

\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=354}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0354}
\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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{30}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   10  ~ \(\times\)  ~ 100
\item   0,024  ~ \(\times\)  ~ 100
\item   56,7  ~ \(\times\)  ~ 100
\item   8,67  ~ \(\times\)  ~ 100
\item   0,924  ~ \(\times\)  ~ 10
\item   0,03  ~ \(\times\)  ~ 10
\item   8,26  ~ \(\times\)  ~ 1 000
\item   0,514  ~ \(\times\)  ~ 10
\item   0,085  ~ \(\times\)  ~ 100
\item   0,03  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 862  ~ : ~ 10
\item   3 877  ~ : ~ 1 000
\item   88,45  ~ : ~ 100
\item   89,05  ~ : ~ 100
\item   429,4  ~ : ~ 1 000
\item   1 657  ~ : ~ 100
\item   7,08  ~ : ~ 10
\item   9 162  ~ : ~ 1 000
\item   15,77  ~ : ~ 10
\item   10,03  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54  ~ \(\times\)  ~ ... ~ = ~ 5 400
\item   9,77  ~ \(\times\)  ~ ... ~ = ~ 977
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 3,2
\item   527  ~ \(\times\)  ~ ... ~ = ~ 5 270
\item   13,4  ~ \(\times\)  ~ ... ~ = ~ 13 400
\item   7,83  ~ \(\times\)  ~ ... ~ = ~ 78,3
\item   0,511  ~ \(\times\)  ~ ... ~ = ~ 511
\item   465  ~ \(\times\)  ~ ... ~ = ~ 4 650
\item   0,007  ~ \(\times\)  ~ ... ~ = ~ 0,7
\item   52,8  ~ \(\times\)  ~ ... ~ = ~ 52 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 000  ~ \(\times\)  ~ 0,01
\item   315,4  ~ \(\times\)  ~ 0,001
\item   4,665  ~ \(\times\)  ~ 0,1
\item   3,325  ~ \(\times\)  ~ 0,1
\item   72,71  ~ \(\times\)  ~ 0,1
\item   8 000  ~ \(\times\)  ~ 0,001
\item   3,164  ~ \(\times\)  ~ 0,01
\item   344,8  ~ \(\times\)  ~ 0,001
\item   411,6  ~ \(\times\)  ~ 0,001
\item   315,3  ~ \(\times\)  ~ 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   2,826  ~ \(\times\)  ~ ... ~ = ~  0,002 826
\item   457,5  ~ \(\times\)  ~ ... ~ = ~  4,575
\item   255,1  ~ \(\times\)  ~ ... ~ = ~  0,255 1
\item   51,87  ~ \(\times\)  ~ ... ~ = ~  5,187
\item   87,8  ~ \(\times\)  ~ ... ~ = ~  0,878
\item   3 673  ~ \(\times\)  ~ ... ~ = ~  3,673
\item   617,4  ~ \(\times\)  ~ ... ~ = ~  6,174
\item   97,08  ~ \(\times\)  ~ ... ~ = ~  0,097 08
\item   348,9  ~ \(\times\)  ~ ... ~ = ~  3,489
\item   4,037  ~ \(\times\)  ~ ... ~ = ~  0,004 037
\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 ~dm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 913 ~g~ = ...~dag
\item   3 048,4 ~daL~ = ...~mL
\item   7 457,6 ~g~ = ...~dg
\item   408,24 ~km~ = ...~mm
\item   3 704 ~dm~ = ...~km
\item   151,12 ~dL~ = ...~mL
\item   594,34 ~hg~ = ...~dg
\item   7 801,8 ~dL~ = ...~cL
\item   151,64 ~hL~ = ...~L
\item   881,16 ~m~ = ...~cm
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{2200}{100}\) = \(\dfrac{220}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{920}{100}\)
\item   \(\dfrac{30}{100}\) = \(\dfrac{300}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   10  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 000}
\item   0,024  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,4}
\item   56,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 670}
\item   8,67  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 867}
\item   0,924  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,24}
\item   0,03  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,3}
\item   8,26  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 260}
\item   0,514  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,14}
\item   0,085  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,5}
\item   0,03  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 30}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 862 ~ : ~ 10 ~ = ~{\color{red} 286,2}
\item   3 877 ~ : ~ 1 000 ~ = ~{\color{red} 3,877}
\item   88,45 ~ : ~ 100 ~ = ~{\color{red} 0,884 5}
\item   89,05 ~ : ~ 100 ~ = ~{\color{red} 0,890 5}
\item   429,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,429 4}
\item   1 657 ~ : ~ 100 ~ = ~{\color{red} 16,57}
\item   7,08 ~ : ~ 10 ~ = ~{\color{red} 0,708}
\item   9 162 ~ : ~ 1 000 ~ = ~{\color{red} 9,162}
\item   15,77 ~ : ~ 10 ~ = ~{\color{red} 1,577}
\item   10,03 ~ : ~ 100 ~ = ~{\color{red} 0,100 3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 400
\item   9,77 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~977
\item   0,032 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,2
\item   527 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 270
\item   13,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~13 400
\item   7,83 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~78,3
\item   0,511 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~511
\item   465 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 650
\item   0,007 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,7
\item   52,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~52 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 000 ~ \(\times\)  0,01 ~ = ~{\color{red} 80
}\item   315,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,315 4
}\item   4,665 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,466 5
}\item   3,325 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,332 5
}\item   72,71 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,271
}\item   8 000 ~ \(\times\)  0,001 ~ = ~{\color{red} 8
}\item   3,164 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,031 64
}\item   344,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,344 8
}\item   411,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,411 6
}\item   315,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,315 3
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,826 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 826
\item   457,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,575
\item   255,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,255 1
\item   51,87 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,187
\item   87,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,878
\item   3 673 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,673
\item   617,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,174
\item   97,08 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,097 08
\item   348,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,489
\item   4,037 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 037
\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 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 913 ~g~ = {\color{red}  591,3 }~dag
\item   3 048,4 ~daL~ = {\color{red}  30 484 000 }~mL
\item   7 457,6 ~g~ = {\color{red}  74 576 }~dg
\item   408,24 ~km~ = {\color{red}  408 240 000 }~mm
\item   3 704 ~dm~ = {\color{red}  0,370 4 }~km
\item   151,12 ~dL~ = {\color{red}  15 112 }~mL
\item   594,34 ~hg~ = {\color{red}  594 340 }~dg
\item   7 801,8 ~dL~ = {\color{red}  78 018 }~cL
\item   151,64 ~hL~ = {\color{red}  15 164 }~L
\item   881,16 ~m~ = {\color{red}  88 116 }~cm
\end{itemize}
\end{multicols}
\end{document}
