\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 315}

\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=315}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0315}
\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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   667  ~ \(\times\)  ~ 10
\item   1,68  ~ \(\times\)  ~ 10
\item   7  ~ \(\times\)  ~ 10
\item   525  ~ \(\times\)  ~ 10
\item   52,3  ~ \(\times\)  ~ 10
\item   522  ~ \(\times\)  ~ 1 000
\item   0,031  ~ \(\times\)  ~ 100
\item   0,079  ~ \(\times\)  ~ 100
\item   0,046  ~ \(\times\)  ~ 100
\item   0,4  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 837  ~ : ~ 10
\item   337,4  ~ : ~ 10
\item   3 790  ~ : ~ 100
\item   283,7  ~ : ~ 1 000
\item   17,2  ~ : ~ 1 000
\item   4,43  ~ : ~ 100
\item   8,341  ~ : ~ 100
\item   0,243  ~ : ~ 100
\item   9,252  ~ : ~ 100
\item   9,651  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,06  ~ \(\times\)  ~ ... ~ = ~ 20,6
\item   0,093  ~ \(\times\)  ~ ... ~ = ~ 0,93
\item   21,8  ~ \(\times\)  ~ ... ~ = ~ 21 800
\item   4  ~ \(\times\)  ~ ... ~ = ~ 400
\item   2,18  ~ \(\times\)  ~ ... ~ = ~ 2 180
\item   8,56  ~ \(\times\)  ~ ... ~ = ~ 85,6
\item   0,794  ~ \(\times\)  ~ ... ~ = ~ 79,4
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 89
\item   9,7  ~ \(\times\)  ~ ... ~ = ~ 97
\item   5,64  ~ \(\times\)  ~ ... ~ = ~ 56,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   851,2  ~ \(\times\)  ~ 0,01
\item   0,946  ~ \(\times\)  ~ 0,01
\item   24,56  ~ \(\times\)  ~ 0,1
\item   213,2  ~ \(\times\)  ~ 0,001
\item   47,76  ~ \(\times\)  ~ 0,01
\item   32,54  ~ \(\times\)  ~ 0,1
\item   275,5  ~ \(\times\)  ~ 0,01
\item   7,067  ~ \(\times\)  ~ 0,1
\item   127,4  ~ \(\times\)  ~ 0,01
\item   5,016  ~ \(\times\)  ~ 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   0,608  ~ \(\times\)  ~ ... ~ = ~  0,000 608
\item   43,19  ~ \(\times\)  ~ ... ~ = ~  0,043 19
\item   8 510  ~ \(\times\)  ~ ... ~ = ~  85,1
\item   53,31  ~ \(\times\)  ~ ... ~ = ~  0,533 1
\item   3 305  ~ \(\times\)  ~ ... ~ = ~  33,05
\item   386,2  ~ \(\times\)  ~ ... ~ = ~  0,386 2
\item   6 369  ~ \(\times\)  ~ ... ~ = ~  6,369
\item   911  ~ \(\times\)  ~ ... ~ = ~  0,911
\item   3,283  ~ \(\times\)  ~ ... ~ = ~  0,032 83
\item   3,752  ~ \(\times\)  ~ ... ~ = ~  0,037 52
\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 ~cm~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 040 ~mm~ = ...~dam
\item   891,63 ~daL~ = ...~kL
\item   173,39 ~hg~ = ...~dg
\item   9 346,8 ~dL~ = ...~mL
\item   4 976,1 ~dL~ = ...~daL
\item   955,97 ~cm~ = ...~m
\item   9 690,1 ~dm~ = ...~mm
\item   5 365,6 ~kg~ = ...~g
\item   271,61 ~hg~ = ...~kg
\item   607,49 ~mL~ = ...~cL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{530}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{580}{100}\)
\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   667  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 670}
\item   1,68  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 16,8}
\item   7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 70}
\item   525  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 250}
\item   52,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 523}
\item   522  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 522 000}
\item   0,031  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,1}
\item   0,079  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,9}
\item   0,046  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,6}
\item   0,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 400}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 837 ~ : ~ 10 ~ = ~{\color{red} 383,7}
\item   337,4 ~ : ~ 10 ~ = ~{\color{red} 33,74}
\item   3 790 ~ : ~ 100 ~ = ~{\color{red} 37,9}
\item   283,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,283 7}
\item   17,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,017 2}
\item   4,43 ~ : ~ 100 ~ = ~{\color{red} 0,044 3}
\item   8,341 ~ : ~ 100 ~ = ~{\color{red} 0,083 41}
\item   0,243 ~ : ~ 100 ~ = ~{\color{red} 0,002 43}
\item   9,252 ~ : ~ 100 ~ = ~{\color{red} 0,092 52}
\item   9,651 ~ : ~ 10 ~ = ~{\color{red} 0,965 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,06 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~20,6
\item   0,093 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,93
\item   21,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~21 800
\item   4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~400
\item   2,18 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 180
\item   8,56 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~85,6
\item   0,794 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~79,4
\item   0,089 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~89
\item   9,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~97
\item   5,64 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~56,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   851,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,512
}\item   0,946 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,009 46
}\item   24,56 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,456
}\item   213,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,213 2
}\item   47,76 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,477 6
}\item   32,54 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,254
}\item   275,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,755
}\item   7,067 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,706 7
}\item   127,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,274
}\item   5,016 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 016
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,608 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 608
\item   43,19 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,043 19
\item   8 510 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 85,1
\item   53,31 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,533 1
\item   3 305 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 33,05
\item   386,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,386 2
\item   6 369 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,369
\item   911 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,911
\item   3,283 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,032 83
\item   3,752 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,037 52
\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 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 040 ~mm~ = {\color{red}  0,704 }~dam
\item   891,63 ~daL~ = {\color{red}  8,916 3 }~kL
\item   173,39 ~hg~ = {\color{red}  173 390 }~dg
\item   9 346,8 ~dL~ = {\color{red}  934 680 }~mL
\item   4 976,1 ~dL~ = {\color{red}  49,761 }~daL
\item   955,97 ~cm~ = {\color{red}  9,559 7 }~m
\item   9 690,1 ~dm~ = {\color{red}  969 010 }~mm
\item   5 365,6 ~kg~ = {\color{red}  5 365 600 }~g
\item   271,61 ~hg~ = {\color{red}  27,161 }~kg
\item   607,49 ~mL~ = {\color{red}  60,749 }~cL
\end{itemize}
\end{multicols}
\end{document}
