\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 257}

\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=257}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0257}
\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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,5  ~ \(\times\)  ~ 10
\item   639  ~ \(\times\)  ~ 1 000
\item   0,048  ~ \(\times\)  ~ 10
\item   89,2  ~ \(\times\)  ~ 100
\item   0,074  ~ \(\times\)  ~ 100
\item   93,9  ~ \(\times\)  ~ 10
\item   0,004  ~ \(\times\)  ~ 10
\item   0,063  ~ \(\times\)  ~ 1 000
\item   90  ~ \(\times\)  ~ 10
\item   40,4  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   810,9  ~ : ~ 10
\item   2 331  ~ : ~ 1 000
\item   229,4  ~ : ~ 1 000
\item   64,3  ~ : ~ 10
\item   30,57  ~ : ~ 1 000
\item   79,7  ~ : ~ 1 000
\item   4 889  ~ : ~ 10
\item   933,8  ~ : ~ 10
\item   0,969  ~ : ~ 1 000
\item   62,38  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   268  ~ \(\times\)  ~ ... ~ = ~ 268 000
\item   5,16  ~ \(\times\)  ~ ... ~ = ~ 51,6
\item   27,3  ~ \(\times\)  ~ ... ~ = ~ 2 730
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 0,84
\item   0,509  ~ \(\times\)  ~ ... ~ = ~ 509
\item   64  ~ \(\times\)  ~ ... ~ = ~ 640
\item   318  ~ \(\times\)  ~ ... ~ = ~ 31 800
\item   1,98  ~ \(\times\)  ~ ... ~ = ~ 19,8
\item   0,852  ~ \(\times\)  ~ ... ~ = ~ 85,2
\item   0,22  ~ \(\times\)  ~ ... ~ = ~ 220
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 433  ~ \(\times\)  ~ 0,001
\item   158,6  ~ \(\times\)  ~ 0,1
\item   12,99  ~ \(\times\)  ~ 0,01
\item   8 687  ~ \(\times\)  ~ 0,001
\item   229,7  ~ \(\times\)  ~ 0,01
\item   9,302  ~ \(\times\)  ~ 0,01
\item   8,466  ~ \(\times\)  ~ 0,001
\item   1,067  ~ \(\times\)  ~ 0,001
\item   342,3  ~ \(\times\)  ~ 0,01
\item   26,47  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 406  ~ \(\times\)  ~ ... ~ = ~  5,406
\item   601,9  ~ \(\times\)  ~ ... ~ = ~  60,19
\item   7,438  ~ \(\times\)  ~ ... ~ = ~  0,743 8
\item   6 553  ~ \(\times\)  ~ ... ~ = ~  655,3
\item   8,69  ~ \(\times\)  ~ ... ~ = ~  0,869
\item   614,8  ~ \(\times\)  ~ ... ~ = ~  0,614 8
\item   6 773  ~ \(\times\)  ~ ... ~ = ~  677,3
\item   9 578  ~ \(\times\)  ~ ... ~ = ~  9,578
\item   8,017  ~ \(\times\)  ~ ... ~ = ~  0,008 017
\item   7 161  ~ \(\times\)  ~ ... ~ = ~  71,61
\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~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   247,13 ~cL~ = ...~hL
\item   986,38 ~L~ = ...~mL
\item   339,86 ~cg~ = ...~dg
\item   852,91 ~cm~ = ...~km
\item   7 510,9 ~g~ = ...~kg
\item   614,55 ~cg~ = ...~g
\item   933,26 ~cL~ = ...~L
\item   255,36 ~kg~ = ...~mg
\item   9 512,3 ~km~ = ...~mm
\item   6 889,3 ~mm~ = ...~m
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{230}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{790}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{790}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 545}
\item   639  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 639 000}
\item   0,048  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,48}
\item   89,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 920}
\item   0,074  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,4}
\item   93,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 939}
\item   0,004  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,04}
\item   0,063  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 63}
\item   90  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 900}
\item   40,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 040}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   810,9 ~ : ~ 10 ~ = ~{\color{red} 81,09}
\item   2 331 ~ : ~ 1 000 ~ = ~{\color{red} 2,331}
\item   229,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,229 4}
\item   64,3 ~ : ~ 10 ~ = ~{\color{red} 6,43}
\item   30,57 ~ : ~ 1 000 ~ = ~{\color{red} 0,030 57}
\item   79,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,079 7}
\item   4 889 ~ : ~ 10 ~ = ~{\color{red} 488,9}
\item   933,8 ~ : ~ 10 ~ = ~{\color{red} 93,38}
\item   0,969 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 969}
\item   62,38 ~ : ~ 1 000 ~ = ~{\color{red} 0,062 38}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   268 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~268 000
\item   5,16 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~51,6
\item   27,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 730
\item   0,084 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,84
\item   0,509 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~509
\item   64 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~640
\item   318 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~31 800
\item   1,98 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~19,8
\item   0,852 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~85,2
\item   0,22 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~220
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 433 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,433
}\item   158,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 15,86
}\item   12,99 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,129 9
}\item   8 687 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,687
}\item   229,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,297
}\item   9,302 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,093 02
}\item   8,466 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 466
}\item   1,067 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 067
}\item   342,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,423
}\item   26,47 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,647
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 406 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,406
\item   601,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 60,19
\item   7,438 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,743 8
\item   6 553 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 655,3
\item   8,69 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,869
\item   614,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,614 8
\item   6 773 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 677,3
\item   9 578 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,578
\item   8,017 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 017
\item   7 161 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 71,61
\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~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   247,13 ~cL~ = {\color{red}  0,024 713 }~hL
\item   986,38 ~L~ = {\color{red}  986 380 }~mL
\item   339,86 ~cg~ = {\color{red}  33,986 }~dg
\item   852,91 ~cm~ = {\color{red}  0,008 529 1 }~km
\item   7 510,9 ~g~ = {\color{red}  7,510 9 }~kg
\item   614,55 ~cg~ = {\color{red}  6,145 5 }~g
\item   933,26 ~cL~ = {\color{red}  9,332 6 }~L
\item   255,36 ~kg~ = {\color{red}  255 360 000 }~mg
\item   9 512,3 ~km~ = {\color{red}  9 512 300 000 }~mm
\item   6 889,3 ~mm~ = {\color{red}  6,889 3 }~m
\end{itemize}
\end{multicols}
\end{document}
