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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 225}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   91,2  ~ \(\times\)  ~ 10
\item   64,1  ~ \(\times\)  ~ 10
\item   5,6  ~ \(\times\)  ~ 1 000
\item   25,5  ~ \(\times\)  ~ 1 000
\item   3,07  ~ \(\times\)  ~ 10
\item   0,445  ~ \(\times\)  ~ 1 000
\item   0,015  ~ \(\times\)  ~ 10
\item   0,312  ~ \(\times\)  ~ 1 000
\item   38,8  ~ \(\times\)  ~ 100
\item   0,065  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   517,6  ~ : ~ 1 000
\item   14,55  ~ : ~ 1 000
\item   9,87  ~ : ~ 10
\item   4,82  ~ : ~ 10
\item   98,41  ~ : ~ 1 000
\item   47,21  ~ : ~ 100
\item   7 015  ~ : ~ 10
\item   371,4  ~ : ~ 10
\item   9,67  ~ : ~ 10
\item   1 285  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,05  ~ \(\times\)  ~ ... ~ = ~ 0,5
\item   804  ~ \(\times\)  ~ ... ~ = ~ 804 000
\item   0,822  ~ \(\times\)  ~ ... ~ = ~ 822
\item   86,5  ~ \(\times\)  ~ ... ~ = ~ 86 500
\item   0,563  ~ \(\times\)  ~ ... ~ = ~ 56,3
\item   351  ~ \(\times\)  ~ ... ~ = ~ 35 100
\item   0,831  ~ \(\times\)  ~ ... ~ = ~ 831
\item   299  ~ \(\times\)  ~ ... ~ = ~ 2 990
\item   41,1  ~ \(\times\)  ~ ... ~ = ~ 411
\item   0,892  ~ \(\times\)  ~ ... ~ = ~ 89,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64,48  ~ \(\times\)  ~ 0,1
\item   6 986  ~ \(\times\)  ~ 0,01
\item   37,15  ~ \(\times\)  ~ 0,001
\item   4 541  ~ \(\times\)  ~ 0,1
\item   492  ~ \(\times\)  ~ 0,1
\item   977,8  ~ \(\times\)  ~ 0,1
\item   9,375  ~ \(\times\)  ~ 0,01
\item   777,8  ~ \(\times\)  ~ 0,001
\item   6 762  ~ \(\times\)  ~ 0,1
\item   716,7  ~ \(\times\)  ~ 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   540,9  ~ \(\times\)  ~ ... ~ = ~  54,09
\item   6,351  ~ \(\times\)  ~ ... ~ = ~  0,006 351
\item   7 023  ~ \(\times\)  ~ ... ~ = ~  70,23
\item   9,325  ~ \(\times\)  ~ ... ~ = ~  0,932 5
\item   103,8  ~ \(\times\)  ~ ... ~ = ~  10,38
\item   795  ~ \(\times\)  ~ ... ~ = ~  0,795
\item   5 576  ~ \(\times\)  ~ ... ~ = ~  55,76
\item   2 319  ~ \(\times\)  ~ ... ~ = ~  231,9
\item   85,8  ~ \(\times\)  ~ ... ~ = ~  0,858
\item   2,342  ~ \(\times\)  ~ ... ~ = ~  0,234 2
\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~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   830,6 ~L~ = ...~mL
\item   2 961,9 ~dg~ = ...~mg
\item   3 142,2 ~hg~ = ...~cg
\item   386,79 ~L~ = ...~cL
\item   5 915,8 ~dm~ = ...~dam
\item   975,2 ~hm~ = ...~dam
\item   3 889,2 ~hg~ = ...~dag
\item   977,48 ~hL~ = ...~L
\item   2 533,9 ~kL~ = ...~cL
\item   425,86 ~mg~ = ...~dg
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{990}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{580}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   91,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 912}
\item   64,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 641}
\item   5,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 600}
\item   25,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 25 500}
\item   3,07  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 30,7}
\item   0,445  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 445}
\item   0,015  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,15}
\item   0,312  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 312}
\item   38,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 880}
\item   0,065  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   517,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,517 6}
\item   14,55 ~ : ~ 1 000 ~ = ~{\color{red} 0,014 55}
\item   9,87 ~ : ~ 10 ~ = ~{\color{red} 0,987}
\item   4,82 ~ : ~ 10 ~ = ~{\color{red} 0,482}
\item   98,41 ~ : ~ 1 000 ~ = ~{\color{red} 0,098 41}
\item   47,21 ~ : ~ 100 ~ = ~{\color{red} 0,472 1}
\item   7 015 ~ : ~ 10 ~ = ~{\color{red} 701,5}
\item   371,4 ~ : ~ 10 ~ = ~{\color{red} 37,14}
\item   9,67 ~ : ~ 10 ~ = ~{\color{red} 0,967}
\item   1 285 ~ : ~ 10 ~ = ~{\color{red} 128,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,05 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,5
\item   804 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~804 000
\item   0,822 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~822
\item   86,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~86 500
\item   0,563 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~56,3
\item   351 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~35 100
\item   0,831 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~831
\item   299 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 990
\item   41,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~411
\item   0,892 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~89,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64,48 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,448
}\item   6 986 ~ \(\times\)  0,01 ~ = ~{\color{red} 69,86
}\item   37,15 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,037 15
}\item   4 541 ~ \(\times\)  0,1 ~ = ~{\color{red} 454,1
}\item   492 ~ \(\times\)  0,1 ~ = ~{\color{red} 49,2
}\item   977,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 97,78
}\item   9,375 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,093 75
}\item   777,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,777 8
}\item   6 762 ~ \(\times\)  0,1 ~ = ~{\color{red} 676,2
}\item   716,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,716 7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   540,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 54,09
\item   6,351 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 351
\item   7 023 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 70,23
\item   9,325 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,932 5
\item   103,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 10,38
\item   795 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,795
\item   5 576 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 55,76
\item   2 319 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 231,9
\item   85,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,858
\item   2,342 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,234 2
\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~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   830,6 ~L~ = {\color{red}  830 600 }~mL
\item   2 961,9 ~dg~ = {\color{red}  296 190 }~mg
\item   3 142,2 ~hg~ = {\color{red}  31 422 000 }~cg
\item   386,79 ~L~ = {\color{red}  38 679 }~cL
\item   5 915,8 ~dm~ = {\color{red}  59,158 }~dam
\item   975,2 ~hm~ = {\color{red}  9 752 }~dam
\item   3 889,2 ~hg~ = {\color{red}  38 892 }~dag
\item   977,48 ~hL~ = {\color{red}  97 748 }~L
\item   2 533,9 ~kL~ = {\color{red}  253 390 000 }~cL
\item   425,86 ~mg~ = {\color{red}  4,258 6 }~dg
\end{itemize}
\end{multicols}
\end{document}
