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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 119}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{66}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{24}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,09  ~ \(\times\)  ~ 1 000
\item   25,8  ~ \(\times\)  ~ 100
\item   9,72  ~ \(\times\)  ~ 10
\item   0,049  ~ \(\times\)  ~ 10
\item   4,24  ~ \(\times\)  ~ 100
\item   776  ~ \(\times\)  ~ 1 000
\item   6,83  ~ \(\times\)  ~ 10
\item   0,142  ~ \(\times\)  ~ 10
\item   0,084  ~ \(\times\)  ~ 1 000
\item   0,752  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 867  ~ : ~ 10
\item   3,579  ~ : ~ 100
\item   785  ~ : ~ 10
\item   20,5  ~ : ~ 1 000
\item   191,3  ~ : ~ 1 000
\item   27  ~ : ~ 100
\item   5,755  ~ : ~ 1 000
\item   615,7  ~ : ~ 1 000
\item   912,8  ~ : ~ 1 000
\item   3,978  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,162  ~ \(\times\)  ~ ... ~ = ~ 16,2
\item   560  ~ \(\times\)  ~ ... ~ = ~ 5 600
\item   0,47  ~ \(\times\)  ~ ... ~ = ~ 4,7
\item   0,45  ~ \(\times\)  ~ ... ~ = ~ 450
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 0,27
\item   3,44  ~ \(\times\)  ~ ... ~ = ~ 344
\item   97,4  ~ \(\times\)  ~ ... ~ = ~ 9 740
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 0,88
\item   0,674  ~ \(\times\)  ~ ... ~ = ~ 674
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   16,15  ~ \(\times\)  ~ 0,1
\item   444  ~ \(\times\)  ~ 0,1
\item   923,9  ~ \(\times\)  ~ 0,001
\item   1 152  ~ \(\times\)  ~ 0,01
\item   278,1  ~ \(\times\)  ~ 0,1
\item   878,6  ~ \(\times\)  ~ 0,1
\item   251,4  ~ \(\times\)  ~ 0,1
\item   4,117  ~ \(\times\)  ~ 0,001
\item   4,487  ~ \(\times\)  ~ 0,1
\item   76,26  ~ \(\times\)  ~ 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   979,6  ~ \(\times\)  ~ ... ~ = ~  0,979 6
\item   3,17  ~ \(\times\)  ~ ... ~ = ~  0,317
\item   387,4  ~ \(\times\)  ~ ... ~ = ~  38,74
\item   4 424  ~ \(\times\)  ~ ... ~ = ~  442,4
\item   8 141  ~ \(\times\)  ~ ... ~ = ~  814,1
\item   78,29  ~ \(\times\)  ~ ... ~ = ~  7,829
\item   4 952  ~ \(\times\)  ~ ... ~ = ~  49,52
\item   1,06  ~ \(\times\)  ~ ... ~ = ~  0,010 6
\item   26,02  ~ \(\times\)  ~ ... ~ = ~  0,026 02
\item   5 940  ~ \(\times\)  ~ ... ~ = ~  59,4
\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 ~hm~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   317,12 ~hm~ = ...~dam
\item   479,77 ~daL~ = ...~dL
\item   750,09 ~hg~ = ...~dg
\item   6 320,2 ~mm~ = ...~dam
\item   914,29 ~hm~ = ...~cm
\item   3 931,7 ~dm~ = ...~hm
\item   1 582,6 ~cL~ = ...~daL
\item   3 036,2 ~mL~ = ...~daL
\item   931,08 ~hL~ = ...~kL
\item   723,79 ~daL~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{790}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{66}{10}\) = \(\dfrac{660}{100}\)
\item   \(\dfrac{24}{100}\) = \(\dfrac{240}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,09  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 90}
\item   25,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 580}
\item   9,72  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 97,2}
\item   0,049  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,49}
\item   4,24  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 424}
\item   776  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 776 000}
\item   6,83  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 68,3}
\item   0,142  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,42}
\item   0,084  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84}
\item   0,752  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 75,2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 867 ~ : ~ 10 ~ = ~{\color{red} 186,7}
\item   3,579 ~ : ~ 100 ~ = ~{\color{red} 0,035 79}
\item   785 ~ : ~ 10 ~ = ~{\color{red} 78,5}
\item   20,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,020 5}
\item   191,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,191 3}
\item   27 ~ : ~ 100 ~ = ~{\color{red} 0,27}
\item   5,755 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 755}
\item   615,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,615 7}
\item   912,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,912 8}
\item   3,978 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 978}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,162 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~16,2
\item   560 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 600
\item   0,47 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,7
\item   0,45 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~450
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\item   0,027 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,27
\item   3,44 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~344
\item   97,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 740
\item   0,088 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,88
\item   0,674 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~674
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   16,15 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,615
}\item   444 ~ \(\times\)  0,1 ~ = ~{\color{red} 44,4
}\item   923,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,923 9
}\item   1 152 ~ \(\times\)  0,01 ~ = ~{\color{red} 11,52
}\item   278,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 27,81
}\item   878,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 87,86
}\item   251,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 25,14
}\item   4,117 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 117
}\item   4,487 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,448 7
}\item   76,26 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,076 26
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   979,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,979 6
\item   3,17 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,317
\item   387,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 38,74
\item   4 424 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 442,4
\item   8 141 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 814,1
\item   78,29 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,829
\item   4 952 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 49,52
\item   1,06 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,010 6
\item   26,02 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,026 02
\item   5 940 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 59,4
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   317,12 ~hm~ = {\color{red}  3 171,2 }~dam
\item   479,77 ~daL~ = {\color{red}  47 977 }~dL
\item   750,09 ~hg~ = {\color{red}  750 090 }~dg
\item   6 320,2 ~mm~ = {\color{red}  0,632 02 }~dam
\item   914,29 ~hm~ = {\color{red}  9 142 900 }~cm
\item   3 931,7 ~dm~ = {\color{red}  3,931 7 }~hm
\item   1 582,6 ~cL~ = {\color{red}  1,582 6 }~daL
\item   3 036,2 ~mL~ = {\color{red}  0,303 62 }~daL
\item   931,08 ~hL~ = {\color{red}  93,108 }~kL
\item   723,79 ~daL~ = {\color{red}  7,237 9 }~kL
\end{itemize}
\end{multicols}
\end{document}
