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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 381}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   29,9  ~ \(\times\)  ~ 1 000
\item   0,064  ~ \(\times\)  ~ 1 000
\item   0,098  ~ \(\times\)  ~ 100
\item   65,4  ~ \(\times\)  ~ 100
\item   66,6  ~ \(\times\)  ~ 100
\item   225  ~ \(\times\)  ~ 10
\item   0,625  ~ \(\times\)  ~ 1 000
\item   0,018  ~ \(\times\)  ~ 10
\item   8,17  ~ \(\times\)  ~ 100
\item   73,3  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,629  ~ : ~ 1 000
\item   6,692  ~ : ~ 1 000
\item   91,6  ~ : ~ 100
\item   93,4  ~ : ~ 100
\item   84,06  ~ : ~ 100
\item   7 739  ~ : ~ 1 000
\item   4,524  ~ : ~ 1 000
\item   1,688  ~ : ~ 100
\item   77,28  ~ : ~ 1 000
\item   58,3  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,9  ~ \(\times\)  ~ ... ~ = ~ 669
\item   839  ~ \(\times\)  ~ ... ~ = ~ 83 900
\item   6,93  ~ \(\times\)  ~ ... ~ = ~ 69,3
\item   5,49  ~ \(\times\)  ~ ... ~ = ~ 54,9
\item   0,086  ~ \(\times\)  ~ ... ~ = ~ 86
\item   8,18  ~ \(\times\)  ~ ... ~ = ~ 81,8
\item   191  ~ \(\times\)  ~ ... ~ = ~ 1 910
\item   30,1  ~ \(\times\)  ~ ... ~ = ~ 3 010
\item   1,03  ~ \(\times\)  ~ ... ~ = ~ 1 030
\item   0,072  ~ \(\times\)  ~ ... ~ = ~ 72
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,571  ~ \(\times\)  ~ 0,001
\item   15,3  ~ \(\times\)  ~ 0,01
\item   2,55  ~ \(\times\)  ~ 0,1
\item   0,658  ~ \(\times\)  ~ 0,001
\item   89,2  ~ \(\times\)  ~ 0,1
\item   6 077  ~ \(\times\)  ~ 0,1
\item   8 149  ~ \(\times\)  ~ 0,01
\item   5 993  ~ \(\times\)  ~ 0,1
\item   1,52  ~ \(\times\)  ~ 0,1
\item   1 230  ~ \(\times\)  ~ 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   5,13  ~ \(\times\)  ~ ... ~ = ~  0,513
\item   642  ~ \(\times\)  ~ ... ~ = ~  6,42
\item   65,11  ~ \(\times\)  ~ ... ~ = ~  6,511
\item   6,55  ~ \(\times\)  ~ ... ~ = ~  0,655
\item   5 295  ~ \(\times\)  ~ ... ~ = ~  529,5
\item   322,6  ~ \(\times\)  ~ ... ~ = ~  0,322 6
\item   84,71  ~ \(\times\)  ~ ... ~ = ~  8,471
\item   5,81  ~ \(\times\)  ~ ... ~ = ~  0,058 1
\item   3,945  ~ \(\times\)  ~ ... ~ = ~  0,394 5
\item   75,16  ~ \(\times\)  ~ ... ~ = ~  7,516
\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~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   842,49 ~km~ = ...~mm
\item   508,21 ~m~ = ...~km
\item   578,01 ~cL~ = ...~kL
\item   158,97 ~cm~ = ...~m
\item   5 419,2 ~dam~ = ...~dm
\item   9 597,7 ~dg~ = ...~kg
\item   215,77 ~dag~ = ...~kg
\item   925,36 ~hL~ = ...~mL
\item   115,21 ~hL~ = ...~kL
\item   599,63 ~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   8 = \(\dfrac{80}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{8400}{100}\) = \(\dfrac{840}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{360}{100}\)
\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   29,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 29 900}
\item   0,064  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 64}
\item   0,098  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,8}
\item   65,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 540}
\item   66,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 660}
\item   225  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 250}
\item   0,625  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 625}
\item   0,018  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,18}
\item   8,17  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 817}
\item   73,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 330}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,629 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 629}
\item   6,692 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 692}
\item   91,6 ~ : ~ 100 ~ = ~{\color{red} 0,916}
\item   93,4 ~ : ~ 100 ~ = ~{\color{red} 0,934}
\item   84,06 ~ : ~ 100 ~ = ~{\color{red} 0,840 6}
\item   7 739 ~ : ~ 1 000 ~ = ~{\color{red} 7,739}
\item   4,524 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 524}
\item   1,688 ~ : ~ 100 ~ = ~{\color{red} 0,016 88}
\item   77,28 ~ : ~ 1 000 ~ = ~{\color{red} 0,077 28}
\item   58,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~669
\item   839 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~83 900
\item   6,93 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~69,3
\item   5,49 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~54,9
\item   0,086 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~86
\item   8,18 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~81,8
\item   191 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 910
\item   30,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 010
\item   1,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 030
\item   0,072 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~72
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,571 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 571
}\item   15,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,153
}\item   2,55 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,255
}\item   0,658 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 658
}\item   89,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,92
}\item   6 077 ~ \(\times\)  0,1 ~ = ~{\color{red} 607,7
}\item   8 149 ~ \(\times\)  0,01 ~ = ~{\color{red} 81,49
}\item   5 993 ~ \(\times\)  0,1 ~ = ~{\color{red} 599,3
}\item   1,52 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,152
}\item   1 230 ~ \(\times\)  0,1 ~ = ~{\color{red} 123
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,13 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,513
\item   642 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,42
\item   65,11 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,511
\item   6,55 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,655
\item   5 295 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 529,5
\item   322,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,322 6
\item   84,71 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,471
\item   5,81 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,058 1
\item   3,945 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,394 5
\item   75,16 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,516
\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~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   842,49 ~km~ = {\color{red}  842 490 000 }~mm
\item   508,21 ~m~ = {\color{red}  0,508 21 }~km
\item   578,01 ~cL~ = {\color{red}  0,005 780 1 }~kL
\item   158,97 ~cm~ = {\color{red}  1,589 7 }~m
\item   5 419,2 ~dam~ = {\color{red}  541 920 }~dm
\item   9 597,7 ~dg~ = {\color{red}  0,959 77 }~kg
\item   215,77 ~dag~ = {\color{red}  2,157 7 }~kg
\item   925,36 ~hL~ = {\color{red}  92 536 000 }~mL
\item   115,21 ~hL~ = {\color{red}  11,521 }~kL
\item   599,63 ~dL~ = {\color{red}  59 963 }~mL
\end{itemize}
\end{multicols}
\end{document}
