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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 108}

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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   \(\dfrac{9500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{59}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   209  ~ \(\times\)  ~ 100
\item   22,8  ~ \(\times\)  ~ 10
\item   7,37  ~ \(\times\)  ~ 10
\item   12,3  ~ \(\times\)  ~ 10
\item   0,096  ~ \(\times\)  ~ 100
\item   0,011  ~ \(\times\)  ~ 100
\item   0,683  ~ \(\times\)  ~ 10
\item   0,065  ~ \(\times\)  ~ 1 000
\item   943  ~ \(\times\)  ~ 1 000
\item   0,075  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,55  ~ : ~ 1 000
\item   553,7  ~ : ~ 10
\item   8,476  ~ : ~ 10
\item   482  ~ : ~ 100
\item   9 338  ~ : ~ 100
\item   31,56  ~ : ~ 10
\item   7 289  ~ : ~ 100
\item   308,9  ~ : ~ 1 000
\item   604,5  ~ : ~ 10
\item   3,872  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   204  ~ \(\times\)  ~ ... ~ = ~ 204 000
\item   66,6  ~ \(\times\)  ~ ... ~ = ~ 666
\item   0,076  ~ \(\times\)  ~ ... ~ = ~ 0,76
\item   0,092  ~ \(\times\)  ~ ... ~ = ~ 0,92
\item   3,57  ~ \(\times\)  ~ ... ~ = ~ 35,7
\item   0,82  ~ \(\times\)  ~ ... ~ = ~ 8,2
\item   412  ~ \(\times\)  ~ ... ~ = ~ 41 200
\item   0,735  ~ \(\times\)  ~ ... ~ = ~ 73,5
\item   8,1  ~ \(\times\)  ~ ... ~ = ~ 8 100
\item   0,562  ~ \(\times\)  ~ ... ~ = ~ 5,62
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,89  ~ \(\times\)  ~ 0,1
\item   6,463  ~ \(\times\)  ~ 0,1
\item   311,7  ~ \(\times\)  ~ 0,1
\item   927,1  ~ \(\times\)  ~ 0,01
\item   3 992  ~ \(\times\)  ~ 0,01
\item   13,32  ~ \(\times\)  ~ 0,001
\item   6 262  ~ \(\times\)  ~ 0,01
\item   126  ~ \(\times\)  ~ 0,1
\item   8 520  ~ \(\times\)  ~ 0,1
\item   9 279  ~ \(\times\)  ~ 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   6,199  ~ \(\times\)  ~ ... ~ = ~  0,061 99
\item   7,193  ~ \(\times\)  ~ ... ~ = ~  0,007 193
\item   5 411  ~ \(\times\)  ~ ... ~ = ~  5,411
\item   2,75  ~ \(\times\)  ~ ... ~ = ~  0,275
\item   785,4  ~ \(\times\)  ~ ... ~ = ~  0,785 4
\item   6 915  ~ \(\times\)  ~ ... ~ = ~  6,915
\item   7 949  ~ \(\times\)  ~ ... ~ = ~  794,9
\item   816,6  ~ \(\times\)  ~ ... ~ = ~  0,816 6
\item   1,337  ~ \(\times\)  ~ ... ~ = ~  0,013 37
\item   8 910  ~ \(\times\)  ~ ... ~ = ~  89,1
\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 ~dam~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   434,22 ~cL~ = ...~L
\item   8 175,1 ~m~ = ...~km
\item   8 543,4 ~dL~ = ...~daL
\item   500,18 ~km~ = ...~dam
\item   298,55 ~hL~ = ...~cL
\item   652,92 ~hg~ = ...~cg
\item   700,95 ~cL~ = ...~daL
\item   278,66 ~mL~ = ...~daL
\item   649,09 ~cg~ = ...~kg
\item   6 725,1 ~dL~ = ...~mL
\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   \(\dfrac{9500}{100}\) = \(\dfrac{950}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{460}{100}\)
\item   \(\dfrac{59}{100}\) = \(\dfrac{590}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   209  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 20 900}
\item   22,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 228}
\item   7,37  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 73,7}
\item   12,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 123}
\item   0,096  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,6}
\item   0,011  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,1}
\item   0,683  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,83}
\item   0,065  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 65}
\item   943  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 943 000}
\item   0,075  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,55 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 55}
\item   553,7 ~ : ~ 10 ~ = ~{\color{red} 55,37}
\item   8,476 ~ : ~ 10 ~ = ~{\color{red} 0,847 6}
\item   482 ~ : ~ 100 ~ = ~{\color{red} 4,82}
\item   9 338 ~ : ~ 100 ~ = ~{\color{red} 93,38}
\item   31,56 ~ : ~ 10 ~ = ~{\color{red} 3,156}
\item   7 289 ~ : ~ 100 ~ = ~{\color{red} 72,89}
\item   308,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,308 9}
\item   604,5 ~ : ~ 10 ~ = ~{\color{red} 60,45}
\item   3,872 ~ : ~ 100 ~ = ~{\color{red} 0,038 72}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   204 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~204 000
\item   66,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~666
\item   0,076 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,76
\item   0,092 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,92
\item   3,57 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~35,7
\item   0,82 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,2
\item   412 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~41 200
\item   0,735 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~73,5
\item   8,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 100
\item   0,562 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,62
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,89 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,489
}\item   6,463 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,646 3
}\item   311,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 31,17
}\item   927,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,271
}\item   3 992 ~ \(\times\)  0,01 ~ = ~{\color{red} 39,92
}\item   13,32 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,013 32
}\item   6 262 ~ \(\times\)  0,01 ~ = ~{\color{red} 62,62
}\item   126 ~ \(\times\)  0,1 ~ = ~{\color{red} 12,6
}\item   8 520 ~ \(\times\)  0,1 ~ = ~{\color{red} 852
}\item   9 279 ~ \(\times\)  0,1 ~ = ~{\color{red} 927,9
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,199 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,061 99
\item   7,193 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 193
\item   5 411 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,411
\item   2,75 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,275
\item   785,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,785 4
\item   6 915 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,915
\item   7 949 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 794,9
\item   816,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,816 6
\item   1,337 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,013 37
\item   8 910 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 89,1
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   434,22 ~cL~ = {\color{red}  4,342 2 }~L
\item   8 175,1 ~m~ = {\color{red}  8,175 1 }~km
\item   8 543,4 ~dL~ = {\color{red}  85,434 }~daL
\item   500,18 ~km~ = {\color{red}  50 018 }~dam
\item   298,55 ~hL~ = {\color{red}  2 985 500 }~cL
\item   652,92 ~hg~ = {\color{red}  6 529 200 }~cg
\item   700,95 ~cL~ = {\color{red}  0,700 95 }~daL
\item   278,66 ~mL~ = {\color{red}  0,027 866 }~daL
\item   649,09 ~cg~ = {\color{red}  0,006 490 9 }~kg
\item   6 725,1 ~dL~ = {\color{red}  672 510 }~mL
\end{itemize}
\end{multicols}
\end{document}
