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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 78}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{65}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{15}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68  ~ \(\times\)  ~ 1 000
\item   41,9  ~ \(\times\)  ~ 1 000
\item   0,491  ~ \(\times\)  ~ 1 000
\item   1,8  ~ \(\times\)  ~ 1 000
\item   1,87  ~ \(\times\)  ~ 100
\item   0,354  ~ \(\times\)  ~ 1 000
\item   87  ~ \(\times\)  ~ 10
\item   8,07  ~ \(\times\)  ~ 100
\item   6,4  ~ \(\times\)  ~ 10
\item   20,8  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   487,5  ~ : ~ 1 000
\item   87,01  ~ : ~ 1 000
\item   2,844  ~ : ~ 1 000
\item   1 459  ~ : ~ 10
\item   76,12  ~ : ~ 10
\item   7 183  ~ : ~ 100
\item   680  ~ : ~ 1 000
\item   2 246  ~ : ~ 1 000
\item   62,35  ~ : ~ 1 000
\item   91,17  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 70
\item   834  ~ \(\times\)  ~ ... ~ = ~ 8 340
\item   41,5  ~ \(\times\)  ~ ... ~ = ~ 415
\item   32  ~ \(\times\)  ~ ... ~ = ~ 3 200
\item   0,746  ~ \(\times\)  ~ ... ~ = ~ 7,46
\item   0,95  ~ \(\times\)  ~ ... ~ = ~ 9,5
\item   0,47  ~ \(\times\)  ~ ... ~ = ~ 470
\item   0,412  ~ \(\times\)  ~ ... ~ = ~ 4,12
\item   7,8  ~ \(\times\)  ~ ... ~ = ~ 78
\item   0,85  ~ \(\times\)  ~ ... ~ = ~ 85
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,038  ~ \(\times\)  ~ 0,1
\item   156,4  ~ \(\times\)  ~ 0,001
\item   5,4  ~ \(\times\)  ~ 0,01
\item   371,3  ~ \(\times\)  ~ 0,01
\item   497,6  ~ \(\times\)  ~ 0,1
\item   793,5  ~ \(\times\)  ~ 0,1
\item   9 364  ~ \(\times\)  ~ 0,001
\item   6 739  ~ \(\times\)  ~ 0,01
\item   7,02  ~ \(\times\)  ~ 0,01
\item   3,931  ~ \(\times\)  ~ 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   6 544  ~ \(\times\)  ~ ... ~ = ~  65,44
\item   28,77  ~ \(\times\)  ~ ... ~ = ~  0,287 7
\item   0,949  ~ \(\times\)  ~ ... ~ = ~  0,000 949
\item   57,96  ~ \(\times\)  ~ ... ~ = ~  0,579 6
\item   824,8  ~ \(\times\)  ~ ... ~ = ~  0,824 8
\item   2,46  ~ \(\times\)  ~ ... ~ = ~  0,024 6
\item   7,854  ~ \(\times\)  ~ ... ~ = ~  0,785 4
\item   904,2  ~ \(\times\)  ~ ... ~ = ~  0,904 2
\item   1,32  ~ \(\times\)  ~ ... ~ = ~  0,001 32
\item   88,68  ~ \(\times\)  ~ ... ~ = ~  0,088 68
\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 ~m~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 788,2 ~dm~ = ...~m
\item   876,09 ~daL~ = ...~kL
\item   6 815,6 ~cm~ = ...~dam
\item   806,97 ~dam~ = ...~cm
\item   3 330,4 ~cm~ = ...~dm
\item   5 390,2 ~dam~ = ...~dm
\item   5 241,9 ~kg~ = ...~dag
\item   2 430,4 ~cL~ = ...~kL
\item   7 810,1 ~m~ = ...~dm
\item   402,56 ~hm~ = ...~mm
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{4900}{100}\) = \(\dfrac{490}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{65}{10}\) = \(\dfrac{650}{100}\)
\item   \(\dfrac{15}{100}\) = \(\dfrac{150}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 68 000}
\item   41,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 41 900}
\item   0,491  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 491}
\item   1,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 800}
\item   1,87  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 187}
\item   0,354  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 354}
\item   87  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 870}
\item   8,07  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 807}
\item   6,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 64}
\item   20,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 080}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   487,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,487 5}
\item   87,01 ~ : ~ 1 000 ~ = ~{\color{red} 0,087 01}
\item   2,844 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 844}
\item   1 459 ~ : ~ 10 ~ = ~{\color{red} 145,9}
\item   76,12 ~ : ~ 10 ~ = ~{\color{red} 7,612}
\item   7 183 ~ : ~ 100 ~ = ~{\color{red} 71,83}
\item   680 ~ : ~ 1 000 ~ = ~{\color{red} 0,68}
\item   2 246 ~ : ~ 1 000 ~ = ~{\color{red} 2,246}
\item   62,35 ~ : ~ 1 000 ~ = ~{\color{red} 0,062 35}
\item   91,17 ~ : ~ 10 ~ = ~{\color{red} 9,117}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,07 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~70
\item   834 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 340
\item   41,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~415
\item   32 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 200
\item   0,746 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,46
\item   0,95 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,5
\item   0,47 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~470
\item   0,412 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,12
\item   7,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~78
\item   0,85 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~85
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,038 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,403 8
}\item   156,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,156 4
}\item   5,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,054
}\item   371,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,713
}\item   497,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 49,76
}\item   793,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 79,35
}\item   9 364 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,364
}\item   6 739 ~ \(\times\)  0,01 ~ = ~{\color{red} 67,39
}\item   7,02 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,070 2
}\item   3,931 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,393 1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 544 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 65,44
\item   28,77 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,287 7
\item   0,949 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 949
\item   57,96 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,579 6
\item   824,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,824 8
\item   2,46 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,024 6
\item   7,854 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,785 4
\item   904,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,904 2
\item   1,32 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 32
\item   88,68 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,088 68
\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 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 788,2 ~dm~ = {\color{red}  278,82 }~m
\item   876,09 ~daL~ = {\color{red}  8,760 9 }~kL
\item   6 815,6 ~cm~ = {\color{red}  6,815 6 }~dam
\item   806,97 ~dam~ = {\color{red}  806 970 }~cm
\item   3 330,4 ~cm~ = {\color{red}  333,04 }~dm
\item   5 390,2 ~dam~ = {\color{red}  539 020 }~dm
\item   5 241,9 ~kg~ = {\color{red}  524 190 }~dag
\item   2 430,4 ~cL~ = {\color{red}  0,024 304 }~kL
\item   7 810,1 ~m~ = {\color{red}  78 101 }~dm
\item   402,56 ~hm~ = {\color{red}  40 256 000 }~mm
\end{itemize}
\end{multicols}
\end{document}
