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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 171}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{86}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   95,4  ~ \(\times\)  ~ 100
\item   3,27  ~ \(\times\)  ~ 10
\item   18,7  ~ \(\times\)  ~ 10
\item   79,1  ~ \(\times\)  ~ 10
\item   0,086  ~ \(\times\)  ~ 1 000
\item   26,3  ~ \(\times\)  ~ 10
\item   194  ~ \(\times\)  ~ 1 000
\item   6,27  ~ \(\times\)  ~ 10
\item   6,02  ~ \(\times\)  ~ 100
\item   809  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   791,2  ~ : ~ 1 000
\item   2,239  ~ : ~ 1 000
\item   7 207  ~ : ~ 100
\item   2 669  ~ : ~ 10
\item   6,04  ~ : ~ 1 000
\item   6 134  ~ : ~ 1 000
\item   32,87  ~ : ~ 10
\item   8,826  ~ : ~ 1 000
\item   68,15  ~ : ~ 1 000
\item   741,1  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,082  ~ \(\times\)  ~ ... ~ = ~ 82
\item   0,181  ~ \(\times\)  ~ ... ~ = ~ 18,1
\item   3,37  ~ \(\times\)  ~ ... ~ = ~ 337
\item   0,025  ~ \(\times\)  ~ ... ~ = ~ 0,25
\item   723  ~ \(\times\)  ~ ... ~ = ~ 72 300
\item   555  ~ \(\times\)  ~ ... ~ = ~ 55 500
\item   6,3  ~ \(\times\)  ~ ... ~ = ~ 6 300
\item   59,7  ~ \(\times\)  ~ ... ~ = ~ 597
\item   0,08  ~ \(\times\)  ~ ... ~ = ~ 0,8
\item   0,051  ~ \(\times\)  ~ ... ~ = ~ 51
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,115  ~ \(\times\)  ~ 0,1
\item   3,092  ~ \(\times\)  ~ 0,001
\item   8 112  ~ \(\times\)  ~ 0,01
\item   8,46  ~ \(\times\)  ~ 0,01
\item   6 792  ~ \(\times\)  ~ 0,001
\item   2 146  ~ \(\times\)  ~ 0,1
\item   83,06  ~ \(\times\)  ~ 0,1
\item   5,842  ~ \(\times\)  ~ 0,001
\item   2,898  ~ \(\times\)  ~ 0,1
\item   2,507  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   419  ~ \(\times\)  ~ ... ~ = ~  0,419
\item   952,6  ~ \(\times\)  ~ ... ~ = ~  95,26
\item   3,341  ~ \(\times\)  ~ ... ~ = ~  0,033 41
\item   237,1  ~ \(\times\)  ~ ... ~ = ~  2,371
\item   1 930  ~ \(\times\)  ~ ... ~ = ~  19,3
\item   1 264  ~ \(\times\)  ~ ... ~ = ~  1,264
\item   48,4  ~ \(\times\)  ~ ... ~ = ~  0,484
\item   3,892  ~ \(\times\)  ~ ... ~ = ~  0,038 92
\item   2 377  ~ \(\times\)  ~ ... ~ = ~  2,377
\item   20,14  ~ \(\times\)  ~ ... ~ = ~  2,014
\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~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 029,7 ~hL~ = ...~dL
\item   9 088,9 ~dm~ = ...~dam
\item   541,56 ~L~ = ...~hL
\item   2 955,2 ~daL~ = ...~dL
\item   600,99 ~mL~ = ...~kL
\item   4 353,1 ~hL~ = ...~L
\item   8 675,9 ~mm~ = ...~dm
\item   245,5 ~cm~ = ...~dm
\item   6 750,1 ~dam~ = ...~mm
\item   826,36 ~cg~ = ...~hg
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{86}{10}\) = \(\dfrac{860}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{700}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   95,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 540}
\item   3,27  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 32,7}
\item   18,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 187}
\item   79,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 791}
\item   0,086  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 86}
\item   26,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 263}
\item   194  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 194 000}
\item   6,27  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 62,7}
\item   6,02  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 602}
\item   809  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 809 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   791,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,791 2}
\item   2,239 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 239}
\item   7 207 ~ : ~ 100 ~ = ~{\color{red} 72,07}
\item   2 669 ~ : ~ 10 ~ = ~{\color{red} 266,9}
\item   6,04 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 04}
\item   6 134 ~ : ~ 1 000 ~ = ~{\color{red} 6,134}
\item   32,87 ~ : ~ 10 ~ = ~{\color{red} 3,287}
\item   8,826 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 826}
\item   68,15 ~ : ~ 1 000 ~ = ~{\color{red} 0,068 15}
\item   741,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,741 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,082 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~82
\item   0,181 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~18,1
\item   3,37 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~337
\item   0,025 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,25
\item   723 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~72 300
\item   555 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~55 500
\item   6,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 300
\item   59,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~597
\item   0,08 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,8
\item   0,051 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~51
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,115 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,411 5
}\item   3,092 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 092
}\item   8 112 ~ \(\times\)  0,01 ~ = ~{\color{red} 81,12
}\item   8,46 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,084 6
}\item   6 792 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,792
}\item   2 146 ~ \(\times\)  0,1 ~ = ~{\color{red} 214,6
}\item   83,06 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,306
}\item   5,842 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 842
}\item   2,898 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,289 8
}\item   2,507 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,025 07
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   419 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,419
\item   952,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 95,26
\item   3,341 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,033 41
\item   237,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,371
\item   1 930 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 19,3
\item   1 264 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,264
\item   48,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,484
\item   3,892 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,038 92
\item   2 377 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,377
\item   20,14 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,014
\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~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 029,7 ~hL~ = {\color{red}  5 029 700 }~dL
\item   9 088,9 ~dm~ = {\color{red}  90,889 }~dam
\item   541,56 ~L~ = {\color{red}  5,415 6 }~hL
\item   2 955,2 ~daL~ = {\color{red}  295 520 }~dL
\item   600,99 ~mL~ = {\color{red}  0,000 600 99 }~kL
\item   4 353,1 ~hL~ = {\color{red}  435 310 }~L
\item   8 675,9 ~mm~ = {\color{red}  86,759 }~dm
\item   245,5 ~cm~ = {\color{red}  24,55 }~dm
\item   6 750,1 ~dam~ = {\color{red}  67 501 000 }~mm
\item   826,36 ~cg~ = {\color{red}  0,082 636 }~hg
\end{itemize}
\end{multicols}
\end{document}
