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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 380}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{67}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,024  ~ \(\times\)  ~ 10
\item   0,063  ~ \(\times\)  ~ 100
\item   0,954  ~ \(\times\)  ~ 1 000
\item   0,075  ~ \(\times\)  ~ 100
\item   4,01  ~ \(\times\)  ~ 1 000
\item   0,058  ~ \(\times\)  ~ 10
\item   0,095  ~ \(\times\)  ~ 1 000
\item   88,8  ~ \(\times\)  ~ 1 000
\item   0,257  ~ \(\times\)  ~ 100
\item   89,4  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,189  ~ : ~ 1 000
\item   1 936  ~ : ~ 1 000
\item   58,38  ~ : ~ 10
\item   65,84  ~ : ~ 1 000
\item   1,937  ~ : ~ 10
\item   7,78  ~ : ~ 1 000
\item   16,57  ~ : ~ 1 000
\item   397,3  ~ : ~ 1 000
\item   3,013  ~ : ~ 1 000
\item   3 598  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,7  ~ \(\times\)  ~ ... ~ = ~ 667
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 6,4
\item   8,13  ~ \(\times\)  ~ ... ~ = ~ 8 130
\item   8,59  ~ \(\times\)  ~ ... ~ = ~ 859
\item   126  ~ \(\times\)  ~ ... ~ = ~ 126 000
\item   536  ~ \(\times\)  ~ ... ~ = ~ 5 360
\item   0,174  ~ \(\times\)  ~ ... ~ = ~ 17,4
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   6,26  ~ \(\times\)  ~ ... ~ = ~ 62,6
\item   848  ~ \(\times\)  ~ ... ~ = ~ 8 480
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,22  ~ \(\times\)  ~ 0,01
\item   3 308  ~ \(\times\)  ~ 0,01
\item   2,228  ~ \(\times\)  ~ 0,001
\item   88,76  ~ \(\times\)  ~ 0,01
\item   965,9  ~ \(\times\)  ~ 0,1
\item   3 223  ~ \(\times\)  ~ 0,1
\item   9,75  ~ \(\times\)  ~ 0,1
\item   32,55  ~ \(\times\)  ~ 0,01
\item   93,8  ~ \(\times\)  ~ 0,01
\item   38,12  ~ \(\times\)  ~ 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   803  ~ \(\times\)  ~ ... ~ = ~  8,03
\item   3 550  ~ \(\times\)  ~ ... ~ = ~  3,55
\item   4 050  ~ \(\times\)  ~ ... ~ = ~  405
\item   241,3  ~ \(\times\)  ~ ... ~ = ~  24,13
\item   423,7  ~ \(\times\)  ~ ... ~ = ~  0,423 7
\item   8,61  ~ \(\times\)  ~ ... ~ = ~  0,861
\item   3,758  ~ \(\times\)  ~ ... ~ = ~  0,003 758
\item   1 025  ~ \(\times\)  ~ ... ~ = ~  10,25
\item   77,57  ~ \(\times\)  ~ ... ~ = ~  0,775 7
\item   455,6  ~ \(\times\)  ~ ... ~ = ~  0,455 6
\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~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 512,3 ~mg~ = ...~dag
\item   676,93 ~L~ = ...~mL
\item   476,38 ~dm~ = ...~hm
\item   724,1 ~L~ = ...~dL
\item   929,42 ~cg~ = ...~hg
\item   600,91 ~cL~ = ...~kL
\item   4 530,9 ~dm~ = ...~mm
\item   703,96 ~dam~ = ...~cm
\item   6 401,3 ~mL~ = ...~cL
\item   455,02 ~cm~ = ...~dam
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{8300}{100}\) = \(\dfrac{830}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{810}{100}\)
\item   \(\dfrac{67}{100}\) = \(\dfrac{670}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,024  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,24}
\item   0,063  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,3}
\item   0,954  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 954}
\item   0,075  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,5}
\item   4,01  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 010}
\item   0,058  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,58}
\item   0,095  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 95}
\item   88,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 88 800}
\item   0,257  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 25,7}
\item   89,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 894}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,189 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 189}
\item   1 936 ~ : ~ 1 000 ~ = ~{\color{red} 1,936}
\item   58,38 ~ : ~ 10 ~ = ~{\color{red} 5,838}
\item   65,84 ~ : ~ 1 000 ~ = ~{\color{red} 0,065 84}
\item   1,937 ~ : ~ 10 ~ = ~{\color{red} 0,193 7}
\item   7,78 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 78}
\item   16,57 ~ : ~ 1 000 ~ = ~{\color{red} 0,016 57}
\item   397,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,397 3}
\item   3,013 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 013}
\item   3 598 ~ : ~ 100 ~ = ~{\color{red} 35,98}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~667
\item   0,064 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,4
\item   8,13 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 130
\item   8,59 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~859
\item   126 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~126 000
\item   536 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 360
\item   0,174 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~17,4
\item   0,004 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,4
\item   6,26 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~62,6
\item   848 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 480
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,22 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,692 2
}\item   3 308 ~ \(\times\)  0,01 ~ = ~{\color{red} 33,08
}\item   2,228 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 228
}\item   88,76 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,887 6
}\item   965,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 96,59
}\item   3 223 ~ \(\times\)  0,1 ~ = ~{\color{red} 322,3
}\item   9,75 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,975
}\item   32,55 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,325 5
}\item   93,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,938
}\item   38,12 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,812
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   803 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,03
\item   3 550 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,55
\item   4 050 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 405
\item   241,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 24,13
\item   423,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,423 7
\item   8,61 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,861
\item   3,758 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 758
\item   1 025 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 10,25
\item   77,57 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,775 7
\item   455,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,455 6
\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~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 512,3 ~mg~ = {\color{red}  0,551 23 }~dag
\item   676,93 ~L~ = {\color{red}  676 930 }~mL
\item   476,38 ~dm~ = {\color{red}  0,476 38 }~hm
\item   724,1 ~L~ = {\color{red}  7 241 }~dL
\item   929,42 ~cg~ = {\color{red}  0,092 942 }~hg
\item   600,91 ~cL~ = {\color{red}  0,006 009 1 }~kL
\item   4 530,9 ~dm~ = {\color{red}  453 090 }~mm
\item   703,96 ~dam~ = {\color{red}  703 960 }~cm
\item   6 401,3 ~mL~ = {\color{red}  640,13 }~cL
\item   455,02 ~cm~ = {\color{red}  0,455 02 }~dam
\end{itemize}
\end{multicols}
\end{document}
