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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 209}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{93}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,9  ~ \(\times\)  ~ 10
\item   38,3  ~ \(\times\)  ~ 1 000
\item   0,238  ~ \(\times\)  ~ 100
\item   18,5  ~ \(\times\)  ~ 100
\item   0,078  ~ \(\times\)  ~ 100
\item   8,73  ~ \(\times\)  ~ 10
\item   3,7  ~ \(\times\)  ~ 10
\item   0,588  ~ \(\times\)  ~ 1 000
\item   342  ~ \(\times\)  ~ 1 000
\item   6,65  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 595  ~ : ~ 100
\item   177  ~ : ~ 1 000
\item   653  ~ : ~ 1 000
\item   576,6  ~ : ~ 1 000
\item   6 339  ~ : ~ 100
\item   8 912  ~ : ~ 100
\item   76,41  ~ : ~ 1 000
\item   56,69  ~ : ~ 10
\item   498,6  ~ : ~ 10
\item   0,815  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,08  ~ \(\times\)  ~ ... ~ = ~ 908
\item   0,029  ~ \(\times\)  ~ ... ~ = ~ 0,29
\item   0,209  ~ \(\times\)  ~ ... ~ = ~ 20,9
\item   0,78  ~ \(\times\)  ~ ... ~ = ~ 7,8
\item   0,514  ~ \(\times\)  ~ ... ~ = ~ 5,14
\item   652  ~ \(\times\)  ~ ... ~ = ~ 65 200
\item   0,092  ~ \(\times\)  ~ ... ~ = ~ 9,2
\item   65,5  ~ \(\times\)  ~ ... ~ = ~ 65 500
\item   301  ~ \(\times\)  ~ ... ~ = ~ 30 100
\item   0,273  ~ \(\times\)  ~ ... ~ = ~ 2,73
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   968,1  ~ \(\times\)  ~ 0,01
\item   2 211  ~ \(\times\)  ~ 0,001
\item   35,32  ~ \(\times\)  ~ 0,1
\item   6,19  ~ \(\times\)  ~ 0,001
\item   412,6  ~ \(\times\)  ~ 0,1
\item   869,3  ~ \(\times\)  ~ 0,001
\item   90  ~ \(\times\)  ~ 0,01
\item   8,348  ~ \(\times\)  ~ 0,1
\item   539,6  ~ \(\times\)  ~ 0,1
\item   47,53  ~ \(\times\)  ~ 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   4,493  ~ \(\times\)  ~ ... ~ = ~  0,449 3
\item   873  ~ \(\times\)  ~ ... ~ = ~  87,3
\item   5,31  ~ \(\times\)  ~ ... ~ = ~  0,005 31
\item   165,9  ~ \(\times\)  ~ ... ~ = ~  16,59
\item   1,54  ~ \(\times\)  ~ ... ~ = ~  0,001 54
\item   2 367  ~ \(\times\)  ~ ... ~ = ~  236,7
\item   4 122  ~ \(\times\)  ~ ... ~ = ~  412,2
\item   0,527  ~ \(\times\)  ~ ... ~ = ~  0,000 527
\item   2 300  ~ \(\times\)  ~ ... ~ = ~  230
\item   759,2  ~ \(\times\)  ~ ... ~ = ~  0,759 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 ~dam~ = ...~dm
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 865,9 ~mm~ = ...~dm
\item   6 243,7 ~hg~ = ...~g
\item   382,74 ~mg~ = ...~dag
\item   562,56 ~dam~ = ...~dm
\item   196,95 ~dm~ = ...~hm
\item   8 512,7 ~kL~ = ...~hL
\item   437,74 ~dam~ = ...~km
\item   5 321 ~hg~ = ...~dg
\item   668,65 ~mm~ = ...~cm
\item   299,05 ~kg~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{320}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{220}{100}\)
\item   \(\dfrac{93}{100}\) = \(\dfrac{930}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 699}
\item   38,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 38 300}
\item   0,238  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 23,8}
\item   18,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 850}
\item   0,078  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,8}
\item   8,73  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 87,3}
\item   3,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 37}
\item   0,588  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 588}
\item   342  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 342 000}
\item   6,65  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 66,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 595 ~ : ~ 100 ~ = ~{\color{red} 85,95}
\item   177 ~ : ~ 1 000 ~ = ~{\color{red} 0,177}
\item   653 ~ : ~ 1 000 ~ = ~{\color{red} 0,653}
\item   576,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,576 6}
\item   6 339 ~ : ~ 100 ~ = ~{\color{red} 63,39}
\item   8 912 ~ : ~ 100 ~ = ~{\color{red} 89,12}
\item   76,41 ~ : ~ 1 000 ~ = ~{\color{red} 0,076 41}
\item   56,69 ~ : ~ 10 ~ = ~{\color{red} 5,669}
\item   498,6 ~ : ~ 10 ~ = ~{\color{red} 49,86}
\item   0,815 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 815}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,08 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~908
\item   0,029 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,29
\item   0,209 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~20,9
\item   0,78 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,8
\item   0,514 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,14
\item   652 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~65 200
\item   0,092 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,2
\item   65,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~65 500
\item   301 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30 100
\item   0,273 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,73
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   968,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,681
}\item   2 211 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,211
}\item   35,32 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,532
}\item   6,19 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 19
}\item   412,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 41,26
}\item   869,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,869 3
}\item   90 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,9
}\item   8,348 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,834 8
}\item   539,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 53,96
}\item   47,53 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,753
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,493 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,449 3
\item   873 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 87,3
\item   5,31 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 31
\item   165,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 16,59
\item   1,54 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 54
\item   2 367 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 236,7
\item   4 122 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 412,2
\item   0,527 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 527
\item   2 300 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 230
\item   759,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,759 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 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 865,9 ~mm~ = {\color{red}  18,659 }~dm
\item   6 243,7 ~hg~ = {\color{red}  624 370 }~g
\item   382,74 ~mg~ = {\color{red}  0,038 274 }~dag
\item   562,56 ~dam~ = {\color{red}  56 256 }~dm
\item   196,95 ~dm~ = {\color{red}  0,196 95 }~hm
\item   8 512,7 ~kL~ = {\color{red}  85 127 }~hL
\item   437,74 ~dam~ = {\color{red}  4,377 4 }~km
\item   5 321 ~hg~ = {\color{red}  5 321 000 }~dg
\item   668,65 ~mm~ = {\color{red}  66,865 }~cm
\item   299,05 ~kg~ = {\color{red}  299 050 000 }~mg
\end{itemize}
\end{multicols}
\end{document}
