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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 186}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{24}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   707  ~ \(\times\)  ~ 10
\item   2,11  ~ \(\times\)  ~ 1 000
\item   0,136  ~ \(\times\)  ~ 100
\item   0,051  ~ \(\times\)  ~ 100
\item   0,49  ~ \(\times\)  ~ 10
\item   0,08  ~ \(\times\)  ~ 10
\item   5,36  ~ \(\times\)  ~ 1 000
\item   0,89  ~ \(\times\)  ~ 10
\item   750  ~ \(\times\)  ~ 10
\item   52,2  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   706  ~ : ~ 1 000
\item   91,11  ~ : ~ 10
\item   4 077  ~ : ~ 10
\item   67,52  ~ : ~ 10
\item   65,57  ~ : ~ 10
\item   7,786  ~ : ~ 1 000
\item   562,2  ~ : ~ 10
\item   6 273  ~ : ~ 100
\item   385,6  ~ : ~ 100
\item   695,9  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,85  ~ \(\times\)  ~ ... ~ = ~ 2 850
\item   0,303  ~ \(\times\)  ~ ... ~ = ~ 303
\item   83,3  ~ \(\times\)  ~ ... ~ = ~ 83 300
\item   68  ~ \(\times\)  ~ ... ~ = ~ 6 800
\item   0,317  ~ \(\times\)  ~ ... ~ = ~ 31,7
\item   82  ~ \(\times\)  ~ ... ~ = ~ 82 000
\item   70,6  ~ \(\times\)  ~ ... ~ = ~ 7 060
\item   0,306  ~ \(\times\)  ~ ... ~ = ~ 30,6
\item   0,012  ~ \(\times\)  ~ ... ~ = ~ 0,12
\item   0,09  ~ \(\times\)  ~ ... ~ = ~ 90
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   126,7  ~ \(\times\)  ~ 0,1
\item   2 516  ~ \(\times\)  ~ 0,001
\item   4,96  ~ \(\times\)  ~ 0,1
\item   954  ~ \(\times\)  ~ 0,1
\item   9,828  ~ \(\times\)  ~ 0,001
\item   354,1  ~ \(\times\)  ~ 0,001
\item   86,29  ~ \(\times\)  ~ 0,1
\item   79,9  ~ \(\times\)  ~ 0,001
\item   79,58  ~ \(\times\)  ~ 0,001
\item   655,4  ~ \(\times\)  ~ 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   1 502  ~ \(\times\)  ~ ... ~ = ~  15,02
\item   8,656  ~ \(\times\)  ~ ... ~ = ~  0,086 56
\item   7,08  ~ \(\times\)  ~ ... ~ = ~  0,007 08
\item   408,3  ~ \(\times\)  ~ ... ~ = ~  4,083
\item   5 253  ~ \(\times\)  ~ ... ~ = ~  525,3
\item   8,268  ~ \(\times\)  ~ ... ~ = ~  0,826 8
\item   8 387  ~ \(\times\)  ~ ... ~ = ~  83,87
\item   2 508  ~ \(\times\)  ~ ... ~ = ~  250,8
\item   5,85  ~ \(\times\)  ~ ... ~ = ~  0,005 85
\item   4 314  ~ \(\times\)  ~ ... ~ = ~  4,314
\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 ~km~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 287,7 ~cg~ = ...~dag
\item   6 972 ~mg~ = ...~kg
\item   840,08 ~dL~ = ...~hL
\item   397,96 ~dL~ = ...~mL
\item   9 428,7 ~cm~ = ...~dm
\item   5 195 ~daL~ = ...~mL
\item   381,88 ~cL~ = ...~mL
\item   157,32 ~mm~ = ...~km
\item   547,33 ~mL~ = ...~dL
\item   682,38 ~km~ = ...~mm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{8100}{100}\) = \(\dfrac{810}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{24}{10}\) = \(\dfrac{240}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   707  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 070}
\item   2,11  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 110}
\item   0,136  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 13,6}
\item   0,051  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,1}
\item   0,49  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,9}
\item   0,08  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,8}
\item   5,36  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 360}
\item   0,89  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,9}
\item   750  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 500}
\item   52,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 522}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   706 ~ : ~ 1 000 ~ = ~{\color{red} 0,706}
\item   91,11 ~ : ~ 10 ~ = ~{\color{red} 9,111}
\item   4 077 ~ : ~ 10 ~ = ~{\color{red} 407,7}
\item   67,52 ~ : ~ 10 ~ = ~{\color{red} 6,752}
\item   65,57 ~ : ~ 10 ~ = ~{\color{red} 6,557}
\item   7,786 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 786}
\item   562,2 ~ : ~ 10 ~ = ~{\color{red} 56,22}
\item   6 273 ~ : ~ 100 ~ = ~{\color{red} 62,73}
\item   385,6 ~ : ~ 100 ~ = ~{\color{red} 3,856}
\item   695,9 ~ : ~ 10 ~ = ~{\color{red} 69,59}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,85 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 850
\item   0,303 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~303
\item   83,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~83 300
\item   68 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 800
\item   0,317 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~31,7
\item   82 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~82 000
\item   70,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 060
\item   0,306 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30,6
\item   0,012 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,12
\item   0,09 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~90
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   126,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 12,67
}\item   2 516 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,516
}\item   4,96 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,496
}\item   954 ~ \(\times\)  0,1 ~ = ~{\color{red} 95,4
}\item   9,828 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 828
}\item   354,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,354 1
}\item   86,29 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,629
}\item   79,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,079 9
}\item   79,58 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,079 58
}\item   655,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,655 4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 502 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 15,02
\item   8,656 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,086 56
\item   7,08 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 08
\item   408,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,083
\item   5 253 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 525,3
\item   8,268 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,826 8
\item   8 387 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 83,87
\item   2 508 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 250,8
\item   5,85 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 85
\item   4 314 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,314
\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 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 287,7 ~cg~ = {\color{red}  4,287 7 }~dag
\item   6 972 ~mg~ = {\color{red}  0,006 972 }~kg
\item   840,08 ~dL~ = {\color{red}  0,840 08 }~hL
\item   397,96 ~dL~ = {\color{red}  39 796 }~mL
\item   9 428,7 ~cm~ = {\color{red}  942,87 }~dm
\item   5 195 ~daL~ = {\color{red}  51 950 000 }~mL
\item   381,88 ~cL~ = {\color{red}  3 818,8 }~mL
\item   157,32 ~mm~ = {\color{red}  0,000 157 32 }~km
\item   547,33 ~mL~ = {\color{red}  5,473 3 }~dL
\item   682,38 ~km~ = {\color{red}  682 380 000 }~mm
\end{itemize}
\end{multicols}
\end{document}
