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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 76}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   43,7  ~ \(\times\)  ~ 100
\item   0,317  ~ \(\times\)  ~ 100
\item   245  ~ \(\times\)  ~ 100
\item   8,76  ~ \(\times\)  ~ 10
\item   0,035  ~ \(\times\)  ~ 10
\item   0,016  ~ \(\times\)  ~ 1 000
\item   0,093  ~ \(\times\)  ~ 100
\item   76,9  ~ \(\times\)  ~ 100
\item   0,564  ~ \(\times\)  ~ 10
\item   0,074  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   173,6  ~ : ~ 1 000
\item   15,37  ~ : ~ 1 000
\item   9 571  ~ : ~ 1 000
\item   8 514  ~ : ~ 10
\item   42,5  ~ : ~ 100
\item   828,3  ~ : ~ 1 000
\item   6,774  ~ : ~ 1 000
\item   726,1  ~ : ~ 10
\item   9,425  ~ : ~ 100
\item   3,378  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,378  ~ \(\times\)  ~ ... ~ = ~ 3,78
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 0,58
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 63
\item   3,1  ~ \(\times\)  ~ ... ~ = ~ 3 100
\item   0,014  ~ \(\times\)  ~ ... ~ = ~ 14
\item   0,003  ~ \(\times\)  ~ ... ~ = ~ 0,03
\item   0,01  ~ \(\times\)  ~ ... ~ = ~ 10
\item   0,406  ~ \(\times\)  ~ ... ~ = ~ 40,6
\item   759  ~ \(\times\)  ~ ... ~ = ~ 759 000
\item   162  ~ \(\times\)  ~ ... ~ = ~ 162 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,994  ~ \(\times\)  ~ 0,1
\item   3 691  ~ \(\times\)  ~ 0,001
\item   5,096  ~ \(\times\)  ~ 0,001
\item   1 542  ~ \(\times\)  ~ 0,1
\item   53,6  ~ \(\times\)  ~ 0,1
\item   1,736  ~ \(\times\)  ~ 0,001
\item   2 115  ~ \(\times\)  ~ 0,01
\item   7,047  ~ \(\times\)  ~ 0,01
\item   74,31  ~ \(\times\)  ~ 0,001
\item   6 224  ~ \(\times\)  ~ 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   6 500  ~ \(\times\)  ~ ... ~ = ~  650
\item   5 250  ~ \(\times\)  ~ ... ~ = ~  5,25
\item   3,93  ~ \(\times\)  ~ ... ~ = ~  0,393
\item   68,29  ~ \(\times\)  ~ ... ~ = ~  0,068 29
\item   505,9  ~ \(\times\)  ~ ... ~ = ~  0,505 9
\item   5,052  ~ \(\times\)  ~ ... ~ = ~  0,005 052
\item   18,8  ~ \(\times\)  ~ ... ~ = ~  0,018 8
\item   8,268  ~ \(\times\)  ~ ... ~ = ~  0,008 268
\item   819,4  ~ \(\times\)  ~ ... ~ = ~  81,94
\item   67,93  ~ \(\times\)  ~ ... ~ = ~  0,067 93
\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 ~cm~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   652,69 ~dam~ = ...~cm
\item   1 840,9 ~mg~ = ...~kg
\item   8 724,5 ~cm~ = ...~dm
\item   770,77 ~m~ = ...~dam
\item   5 698,5 ~m~ = ...~mm
\item   1 166,8 ~mg~ = ...~dag
\item   1 403,3 ~hL~ = ...~dL
\item   5 074,3 ~kL~ = ...~daL
\item   868,3 ~cm~ = ...~km
\item   2 902,9 ~hg~ = ...~dag
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{6000}{100}\) = \(\dfrac{600}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{490}{100}\)
\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   43,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 370}
\item   0,317  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 31,7}
\item   245  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 24 500}
\item   8,76  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 87,6}
\item   0,035  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,35}
\item   0,016  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 16}
\item   0,093  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,3}
\item   76,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 690}
\item   0,564  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,64}
\item   0,074  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,74}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   173,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,173 6}
\item   15,37 ~ : ~ 1 000 ~ = ~{\color{red} 0,015 37}
\item   9 571 ~ : ~ 1 000 ~ = ~{\color{red} 9,571}
\item   8 514 ~ : ~ 10 ~ = ~{\color{red} 851,4}
\item   42,5 ~ : ~ 100 ~ = ~{\color{red} 0,425}
\item   828,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,828 3}
\item   6,774 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 774}
\item   726,1 ~ : ~ 10 ~ = ~{\color{red} 72,61}
\item   9,425 ~ : ~ 100 ~ = ~{\color{red} 0,094 25}
\item   3,378 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 378}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,378 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,78
\item   0,058 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,58
\item   0,063 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~63
\item   3,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 100
\item   0,014 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14
\item   0,003 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,03
\item   0,01 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~10
\item   0,406 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~40,6
\item   759 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~759 000
\item   162 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~162 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,994 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,099 4
}\item   3 691 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,691
}\item   5,096 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 096
}\item   1 542 ~ \(\times\)  0,1 ~ = ~{\color{red} 154,2
}\item   53,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,36
}\item   1,736 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 736
}\item   2 115 ~ \(\times\)  0,01 ~ = ~{\color{red} 21,15
}\item   7,047 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,070 47
}\item   74,31 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,074 31
}\item   6 224 ~ \(\times\)  0,01 ~ = ~{\color{red} 62,24
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 500 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 650
\item   5 250 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,25
\item   3,93 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,393
\item   68,29 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,068 29
\item   505,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,505 9
\item   5,052 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 052
\item   18,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,018 8
\item   8,268 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 268
\item   819,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 81,94
\item   67,93 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,067 93
\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 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   652,69 ~dam~ = {\color{red}  652 690 }~cm
\item   1 840,9 ~mg~ = {\color{red}  0,001 840 9 }~kg
\item   8 724,5 ~cm~ = {\color{red}  872,45 }~dm
\item   770,77 ~m~ = {\color{red}  77,077 }~dam
\item   5 698,5 ~m~ = {\color{red}  5 698 500 }~mm
\item   1 166,8 ~mg~ = {\color{red}  0,116 68 }~dag
\item   1 403,3 ~hL~ = {\color{red}  1 403 300 }~dL
\item   5 074,3 ~kL~ = {\color{red}  507 430 }~daL
\item   868,3 ~cm~ = {\color{red}  0,008 683 }~km
\item   2 902,9 ~hg~ = {\color{red}  29 029 }~dag
\end{itemize}
\end{multicols}
\end{document}
