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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 288}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{17}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   448  ~ \(\times\)  ~ 100
\item   0,644  ~ \(\times\)  ~ 10
\item   0,959  ~ \(\times\)  ~ 10
\item   5,05  ~ \(\times\)  ~ 1 000
\item   785  ~ \(\times\)  ~ 100
\item   33,2  ~ \(\times\)  ~ 100
\item   6,23  ~ \(\times\)  ~ 10
\item   0,948  ~ \(\times\)  ~ 100
\item   0,687  ~ \(\times\)  ~ 10
\item   0,022  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 109  ~ : ~ 1 000
\item   4 864  ~ : ~ 10
\item   230,8  ~ : ~ 100
\item   807  ~ : ~ 10
\item   5,841  ~ : ~ 1 000
\item   9,695  ~ : ~ 100
\item   81,43  ~ : ~ 10
\item   80,9  ~ : ~ 10
\item   350,7  ~ : ~ 100
\item   6 147  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,56  ~ \(\times\)  ~ ... ~ = ~ 656
\item   863  ~ \(\times\)  ~ ... ~ = ~ 8 630
\item   801  ~ \(\times\)  ~ ... ~ = ~ 80 100
\item   0,489  ~ \(\times\)  ~ ... ~ = ~ 48,9
\item   0,066  ~ \(\times\)  ~ ... ~ = ~ 0,66
\item   0,75  ~ \(\times\)  ~ ... ~ = ~ 75
\item   813  ~ \(\times\)  ~ ... ~ = ~ 81 300
\item   91,4  ~ \(\times\)  ~ ... ~ = ~ 914
\item   385  ~ \(\times\)  ~ ... ~ = ~ 38 500
\item   9,29  ~ \(\times\)  ~ ... ~ = ~ 9 290
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,418  ~ \(\times\)  ~ 0,001
\item   7 659  ~ \(\times\)  ~ 0,1
\item   894,2  ~ \(\times\)  ~ 0,1
\item   37,2  ~ \(\times\)  ~ 0,01
\item   4,834  ~ \(\times\)  ~ 0,001
\item   2 159  ~ \(\times\)  ~ 0,01
\item   53,76  ~ \(\times\)  ~ 0,01
\item   34,51  ~ \(\times\)  ~ 0,1
\item   66,12  ~ \(\times\)  ~ 0,01
\item   10,14  ~ \(\times\)  ~ 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   4 945  ~ \(\times\)  ~ ... ~ = ~  4,945
\item   7,504  ~ \(\times\)  ~ ... ~ = ~  0,750 4
\item   299  ~ \(\times\)  ~ ... ~ = ~  2,99
\item   124  ~ \(\times\)  ~ ... ~ = ~  0,124
\item   6 704  ~ \(\times\)  ~ ... ~ = ~  67,04
\item   965,7  ~ \(\times\)  ~ ... ~ = ~  96,57
\item   906,3  ~ \(\times\)  ~ ... ~ = ~  0,906 3
\item   791,2  ~ \(\times\)  ~ ... ~ = ~  79,12
\item   2 983  ~ \(\times\)  ~ ... ~ = ~  2,983
\item   8,88  ~ \(\times\)  ~ ... ~ = ~  0,008 88
\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~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~dam~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   173,32 ~dag~ = ...~hg
\item   4 971,3 ~hm~ = ...~dam
\item   409,8 ~dag~ = ...~kg
\item   947,75 ~daL~ = ...~dL
\item   496,75 ~hL~ = ...~dL
\item   952,11 ~dm~ = ...~hm
\item   151,21 ~hg~ = ...~dag
\item   5 406,9 ~hm~ = ...~dm
\item   685,95 ~mg~ = ...~cg
\item   8 711,2 ~dam~ = ...~m
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{720}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{17}{10}\) = \(\dfrac{170}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{760}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   448  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 44 800}
\item   0,644  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,44}
\item   0,959  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,59}
\item   5,05  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 050}
\item   785  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 78 500}
\item   33,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 320}
\item   6,23  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 62,3}
\item   0,948  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 94,8}
\item   0,687  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,87}
\item   0,022  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,22}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 109 ~ : ~ 1 000 ~ = ~{\color{red} 8,109}
\item   4 864 ~ : ~ 10 ~ = ~{\color{red} 486,4}
\item   230,8 ~ : ~ 100 ~ = ~{\color{red} 2,308}
\item   807 ~ : ~ 10 ~ = ~{\color{red} 80,7}
\item   5,841 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 841}
\item   9,695 ~ : ~ 100 ~ = ~{\color{red} 0,096 95}
\item   81,43 ~ : ~ 10 ~ = ~{\color{red} 8,143}
\item   80,9 ~ : ~ 10 ~ = ~{\color{red} 8,09}
\item   350,7 ~ : ~ 100 ~ = ~{\color{red} 3,507}
\item   6 147 ~ : ~ 100 ~ = ~{\color{red} 61,47}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,56 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~656
\item   863 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 630
\item   801 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~80 100
\item   0,489 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~48,9
\item   0,066 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,66
\item   0,75 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~75
\item   813 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~81 300
\item   91,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~914
\item   385 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~38 500
\item   9,29 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 290
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,418 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 418
}\item   7 659 ~ \(\times\)  0,1 ~ = ~{\color{red} 765,9
}\item   894,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 89,42
}\item   37,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,372
}\item   4,834 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 834
}\item   2 159 ~ \(\times\)  0,01 ~ = ~{\color{red} 21,59
}\item   53,76 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,537 6
}\item   34,51 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,451
}\item   66,12 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,661 2
}\item   10,14 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,014
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 945 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,945
\item   7,504 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,750 4
\item   299 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,99
\item   124 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,124
\item   6 704 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 67,04
\item   965,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 96,57
\item   906,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,906 3
\item   791,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 79,12
\item   2 983 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,983
\item   8,88 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 88
\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}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   173,32 ~dag~ = {\color{red}  17,332 }~hg
\item   4 971,3 ~hm~ = {\color{red}  49 713 }~dam
\item   409,8 ~dag~ = {\color{red}  4,098 }~kg
\item   947,75 ~daL~ = {\color{red}  94 775 }~dL
\item   496,75 ~hL~ = {\color{red}  496 750 }~dL
\item   952,11 ~dm~ = {\color{red}  0,952 11 }~hm
\item   151,21 ~hg~ = {\color{red}  1 512,1 }~dag
\item   5 406,9 ~hm~ = {\color{red}  5 406 900 }~dm
\item   685,95 ~mg~ = {\color{red}  68,595 }~cg
\item   8 711,2 ~dam~ = {\color{red}  87 112 }~m
\end{itemize}
\end{multicols}
\end{document}
