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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 386}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{64}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{17}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   547  ~ \(\times\)  ~ 10
\item   2,69  ~ \(\times\)  ~ 1 000
\item   59,7  ~ \(\times\)  ~ 1 000
\item   0,309  ~ \(\times\)  ~ 100
\item   0,165  ~ \(\times\)  ~ 10
\item   547  ~ \(\times\)  ~ 1 000
\item   0,009  ~ \(\times\)  ~ 10
\item   68,6  ~ \(\times\)  ~ 10
\item   80,7  ~ \(\times\)  ~ 100
\item   267  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   860,4  ~ : ~ 1 000
\item   118,7  ~ : ~ 10
\item   62,56  ~ : ~ 10
\item   0,835  ~ : ~ 1 000
\item   83,58  ~ : ~ 10
\item   9 038  ~ : ~ 100
\item   6 101  ~ : ~ 1 000
\item   2,003  ~ : ~ 1 000
\item   8 564  ~ : ~ 100
\item   7,826  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,164  ~ \(\times\)  ~ ... ~ = ~ 1,64
\item   9,6  ~ \(\times\)  ~ ... ~ = ~ 96
\item   0,66  ~ \(\times\)  ~ ... ~ = ~ 660
\item   0,031  ~ \(\times\)  ~ ... ~ = ~ 0,31
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 60
\item   377  ~ \(\times\)  ~ ... ~ = ~ 377 000
\item   0,053  ~ \(\times\)  ~ ... ~ = ~ 5,3
\item   9,46  ~ \(\times\)  ~ ... ~ = ~ 946
\item   0,905  ~ \(\times\)  ~ ... ~ = ~ 905
\item   0,065  ~ \(\times\)  ~ ... ~ = ~ 0,65
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,43  ~ \(\times\)  ~ 0,1
\item   378,5  ~ \(\times\)  ~ 0,001
\item   318,7  ~ \(\times\)  ~ 0,1
\item   57,71  ~ \(\times\)  ~ 0,1
\item   8,082  ~ \(\times\)  ~ 0,01
\item   1,592  ~ \(\times\)  ~ 0,01
\item   6,171  ~ \(\times\)  ~ 0,01
\item   42,71  ~ \(\times\)  ~ 0,001
\item   150,7  ~ \(\times\)  ~ 0,01
\item   24,45  ~ \(\times\)  ~ 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   391,7  ~ \(\times\)  ~ ... ~ = ~  3,917
\item   36,08  ~ \(\times\)  ~ ... ~ = ~  3,608
\item   782,3  ~ \(\times\)  ~ ... ~ = ~  7,823
\item   7,059  ~ \(\times\)  ~ ... ~ = ~  0,007 059
\item   6 637  ~ \(\times\)  ~ ... ~ = ~  663,7
\item   90,54  ~ \(\times\)  ~ ... ~ = ~  0,905 4
\item   9 333  ~ \(\times\)  ~ ... ~ = ~  933,3
\item   1 144  ~ \(\times\)  ~ ... ~ = ~  114,4
\item   93,58  ~ \(\times\)  ~ ... ~ = ~  0,935 8
\item   8 304  ~ \(\times\)  ~ ... ~ = ~  8,304
\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 ~dm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   590,15 ~dg~ = ...~cg
\item   286,11 ~dag~ = ...~hg
\item   6 010,6 ~g~ = ...~hg
\item   1 613 ~mL~ = ...~hL
\item   7 000,2 ~mg~ = ...~g
\item   550,34 ~km~ = ...~dm
\item   170,82 ~dL~ = ...~mL
\item   908,66 ~cg~ = ...~hg
\item   940,03 ~hm~ = ...~km
\item   922,13 ~mg~ = ...~dg
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{790}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{64}{10}\) = \(\dfrac{640}{100}\)
\item   \(\dfrac{17}{100}\) = \(\dfrac{170}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   547  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 470}
\item   2,69  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 690}
\item   59,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 59 700}
\item   0,309  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 30,9}
\item   0,165  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,65}
\item   547  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 547 000}
\item   0,009  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,09}
\item   68,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 686}
\item   80,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 070}
\item   267  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 26 700}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   860,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,860 4}
\item   118,7 ~ : ~ 10 ~ = ~{\color{red} 11,87}
\item   62,56 ~ : ~ 10 ~ = ~{\color{red} 6,256}
\item   0,835 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 835}
\item   83,58 ~ : ~ 10 ~ = ~{\color{red} 8,358}
\item   9 038 ~ : ~ 100 ~ = ~{\color{red} 90,38}
\item   6 101 ~ : ~ 1 000 ~ = ~{\color{red} 6,101}
\item   2,003 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 003}
\item   8 564 ~ : ~ 100 ~ = ~{\color{red} 85,64}
\item   7,826 ~ : ~ 100 ~ = ~{\color{red} 0,078 26}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,164 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,64
\item   9,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~96
\item   0,66 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~660
\item   0,031 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,31
\item   0,06 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~60
\item   377 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~377 000
\item   0,053 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,3
\item   9,46 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~946
\item   0,905 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~905
\item   0,065 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,65
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,43 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,443
}\item   378,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,378 5
}\item   318,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 31,87
}\item   57,71 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,771
}\item   8,082 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,080 82
}\item   1,592 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,015 92
}\item   6,171 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,061 71
}\item   42,71 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,042 71
}\item   150,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,507
}\item   24,45 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,244 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   391,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,917
\item   36,08 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,608
\item   782,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,823
\item   7,059 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 059
\item   6 637 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 663,7
\item   90,54 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,905 4
\item   9 333 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 933,3
\item   1 144 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 114,4
\item   93,58 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,935 8
\item   8 304 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,304
\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 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ 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   590,15 ~dg~ = {\color{red}  5 901,5 }~cg
\item   286,11 ~dag~ = {\color{red}  28,611 }~hg
\item   6 010,6 ~g~ = {\color{red}  60,106 }~hg
\item   1 613 ~mL~ = {\color{red}  0,016 13 }~hL
\item   7 000,2 ~mg~ = {\color{red}  7,000 2 }~g
\item   550,34 ~km~ = {\color{red}  5 503 400 }~dm
\item   170,82 ~dL~ = {\color{red}  17 082 }~mL
\item   908,66 ~cg~ = {\color{red}  0,090 866 }~hg
\item   940,03 ~hm~ = {\color{red}  94,003 }~km
\item   922,13 ~mg~ = {\color{red}  9,221 3 }~dg
\end{itemize}
\end{multicols}
\end{document}
