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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 180}

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\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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,013  ~ \(\times\)  ~ 1 000
\item   46,9  ~ \(\times\)  ~ 1 000
\item   4,6  ~ \(\times\)  ~ 10
\item   14  ~ \(\times\)  ~ 10
\item   207  ~ \(\times\)  ~ 10
\item   0,885  ~ \(\times\)  ~ 1 000
\item   494  ~ \(\times\)  ~ 100
\item   350  ~ \(\times\)  ~ 10
\item   70  ~ \(\times\)  ~ 100
\item   6,42  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,38  ~ : ~ 100
\item   5 039  ~ : ~ 10
\item   602,3  ~ : ~ 10
\item   5 799  ~ : ~ 1 000
\item   712,8  ~ : ~ 10
\item   62,8  ~ : ~ 1 000
\item   7,093  ~ : ~ 100
\item   3,563  ~ : ~ 100
\item   66,07  ~ : ~ 100
\item   8 001  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,73  ~ \(\times\)  ~ ... ~ = ~ 4 730
\item   6,83  ~ \(\times\)  ~ ... ~ = ~ 683
\item   74  ~ \(\times\)  ~ ... ~ = ~ 7 400
\item   50,1  ~ \(\times\)  ~ ... ~ = ~ 50 100
\item   2,89  ~ \(\times\)  ~ ... ~ = ~ 289
\item   0,865  ~ \(\times\)  ~ ... ~ = ~ 8,65
\item   653  ~ \(\times\)  ~ ... ~ = ~ 6 530
\item   4,68  ~ \(\times\)  ~ ... ~ = ~ 4 680
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 6,3
\item   0,087  ~ \(\times\)  ~ ... ~ = ~ 0,87
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   883,4  ~ \(\times\)  ~ 0,1
\item   7,838  ~ \(\times\)  ~ 0,01
\item   8,94  ~ \(\times\)  ~ 0,1
\item   3 284  ~ \(\times\)  ~ 0,01
\item   3 796  ~ \(\times\)  ~ 0,01
\item   18,42  ~ \(\times\)  ~ 0,1
\item   964,1  ~ \(\times\)  ~ 0,01
\item   243,7  ~ \(\times\)  ~ 0,01
\item   1 803  ~ \(\times\)  ~ 0,1
\item   47,33  ~ \(\times\)  ~ 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   91,84  ~ \(\times\)  ~ ... ~ = ~  0,918 4
\item   59,8  ~ \(\times\)  ~ ... ~ = ~  0,598
\item   63,39  ~ \(\times\)  ~ ... ~ = ~  0,633 9
\item   4 644  ~ \(\times\)  ~ ... ~ = ~  464,4
\item   8,071  ~ \(\times\)  ~ ... ~ = ~  0,008 071
\item   642,2  ~ \(\times\)  ~ ... ~ = ~  64,22
\item   723,8  ~ \(\times\)  ~ ... ~ = ~  0,723 8
\item   8 983  ~ \(\times\)  ~ ... ~ = ~  898,3
\item   58,88  ~ \(\times\)  ~ ... ~ = ~  0,058 88
\item   9 522  ~ \(\times\)  ~ ... ~ = ~  9,522
\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 ~hm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 782,4 ~dg~ = ...~kg
\item   5 069,5 ~mm~ = ...~dm
\item   942,16 ~hm~ = ...~km
\item   9 626 ~dL~ = ...~kL
\item   1 991,2 ~dL~ = ...~mL
\item   335,65 ~mg~ = ...~dag
\item   5 315,4 ~m~ = ...~hm
\item   5 579,1 ~kg~ = ...~mg
\item   386,19 ~cL~ = ...~kL
\item   4 677,3 ~cm~ = ...~km
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{970}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{900}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{440}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,013  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 13}
\item   46,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 46 900}
\item   4,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 46}
\item   14  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 140}
\item   207  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 070}
\item   0,885  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 885}
\item   494  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 49 400}
\item   350  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 500}
\item   70  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 000}
\item   6,42  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 420}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,38 ~ : ~ 100 ~ = ~{\color{red} 0,083 8}
\item   5 039 ~ : ~ 10 ~ = ~{\color{red} 503,9}
\item   602,3 ~ : ~ 10 ~ = ~{\color{red} 60,23}
\item   5 799 ~ : ~ 1 000 ~ = ~{\color{red} 5,799}
\item   712,8 ~ : ~ 10 ~ = ~{\color{red} 71,28}
\item   62,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,062 8}
\item   7,093 ~ : ~ 100 ~ = ~{\color{red} 0,070 93}
\item   3,563 ~ : ~ 100 ~ = ~{\color{red} 0,035 63}
\item   66,07 ~ : ~ 100 ~ = ~{\color{red} 0,660 7}
\item   8 001 ~ : ~ 1 000 ~ = ~{\color{red} 8,001}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,73 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 730
\item   6,83 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~683
\item   74 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 400
\item   50,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~50 100
\item   2,89 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~289
\item   0,865 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,65
\item   653 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 530
\item   4,68 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 680
\item   0,063 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,3
\item   0,087 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,87
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   883,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 88,34
}\item   7,838 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,078 38
}\item   8,94 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,894
}\item   3 284 ~ \(\times\)  0,01 ~ = ~{\color{red} 32,84
}\item   3 796 ~ \(\times\)  0,01 ~ = ~{\color{red} 37,96
}\item   18,42 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,842
}\item   964,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,641
}\item   243,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,437
}\item   1 803 ~ \(\times\)  0,1 ~ = ~{\color{red} 180,3
}\item   47,33 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,473 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   91,84 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,918 4
\item   59,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,598
\item   63,39 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,633 9
\item   4 644 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 464,4
\item   8,071 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 071
\item   642,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 64,22
\item   723,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,723 8
\item   8 983 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 898,3
\item   58,88 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,058 88
\item   9 522 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,522
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 782,4 ~dg~ = {\color{red}  0,978 24 }~kg
\item   5 069,5 ~mm~ = {\color{red}  50,695 }~dm
\item   942,16 ~hm~ = {\color{red}  94,216 }~km
\item   9 626 ~dL~ = {\color{red}  0,962 6 }~kL
\item   1 991,2 ~dL~ = {\color{red}  199 120 }~mL
\item   335,65 ~mg~ = {\color{red}  0,033 565 }~dag
\item   5 315,4 ~m~ = {\color{red}  53,154 }~hm
\item   5 579,1 ~kg~ = {\color{red}  5 579 100 000 }~mg
\item   386,19 ~cL~ = {\color{red}  0,003 861 9 }~kL
\item   4 677,3 ~cm~ = {\color{red}  0,046 773 }~km
\end{itemize}
\end{multicols}
\end{document}
