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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 109}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{18}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,2  ~ \(\times\)  ~ 1 000
\item   5,18  ~ \(\times\)  ~ 1 000
\item   0,095  ~ \(\times\)  ~ 10
\item   81,7  ~ \(\times\)  ~ 100
\item   5,27  ~ \(\times\)  ~ 100
\item   86,8  ~ \(\times\)  ~ 100
\item   0,091  ~ \(\times\)  ~ 1 000
\item   333  ~ \(\times\)  ~ 1 000
\item   186  ~ \(\times\)  ~ 1 000
\item   0,035  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   235  ~ : ~ 100
\item   740,1  ~ : ~ 100
\item   604,9  ~ : ~ 10
\item   770  ~ : ~ 100
\item   6,475  ~ : ~ 10
\item   446,3  ~ : ~ 100
\item   8 720  ~ : ~ 1 000
\item   9,03  ~ : ~ 100
\item   5,869  ~ : ~ 10
\item   1,088  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,99  ~ \(\times\)  ~ ... ~ = ~ 49,9
\item   0,378  ~ \(\times\)  ~ ... ~ = ~ 3,78
\item   6,35  ~ \(\times\)  ~ ... ~ = ~ 635
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 27
\item   4,36  ~ \(\times\)  ~ ... ~ = ~ 4 360
\item   95  ~ \(\times\)  ~ ... ~ = ~ 95 000
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 84
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 0,68
\item   355  ~ \(\times\)  ~ ... ~ = ~ 3 550
\item   60,1  ~ \(\times\)  ~ ... ~ = ~ 601
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   44  ~ \(\times\)  ~ 0,001
\item   24,52  ~ \(\times\)  ~ 0,1
\item   450,1  ~ \(\times\)  ~ 0,01
\item   7,103  ~ \(\times\)  ~ 0,001
\item   7,418  ~ \(\times\)  ~ 0,1
\item   16,79  ~ \(\times\)  ~ 0,001
\item   7 209  ~ \(\times\)  ~ 0,1
\item   1 367  ~ \(\times\)  ~ 0,1
\item   2,238  ~ \(\times\)  ~ 0,01
\item   1 767  ~ \(\times\)  ~ 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   0,264  ~ \(\times\)  ~ ... ~ = ~  0,026 4
\item   206,3  ~ \(\times\)  ~ ... ~ = ~  20,63
\item   196,9  ~ \(\times\)  ~ ... ~ = ~  19,69
\item   7,801  ~ \(\times\)  ~ ... ~ = ~  0,007 801
\item   28,71  ~ \(\times\)  ~ ... ~ = ~  2,871
\item   424  ~ \(\times\)  ~ ... ~ = ~  42,4
\item   1 016  ~ \(\times\)  ~ ... ~ = ~  10,16
\item   104,2  ~ \(\times\)  ~ ... ~ = ~  1,042
\item   3 518  ~ \(\times\)  ~ ... ~ = ~  3,518
\item   38,67  ~ \(\times\)  ~ ... ~ = ~  3,867
\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 ~dam~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   842,75 ~mm~ = ...~dam
\item   5 610,4 ~hL~ = ...~daL
\item   1 888,7 ~dag~ = ...~hg
\item   445,17 ~cg~ = ...~dg
\item   577,02 ~km~ = ...~m
\item   336,94 ~mm~ = ...~hm
\item   326,6 ~kL~ = ...~L
\item   8 911,7 ~dam~ = ...~m
\item   3 623,4 ~dm~ = ...~hm
\item   178,73 ~cm~ = ...~hm
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{6900}{100}\) = \(\dfrac{690}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{810}{100}\)
\item   \(\dfrac{18}{100}\) = \(\dfrac{180}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 11 200}
\item   5,18  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 180}
\item   0,095  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,95}
\item   81,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 170}
\item   5,27  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 527}
\item   86,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 680}
\item   0,091  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 91}
\item   333  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 333 000}
\item   186  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 186 000}
\item   0,035  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,35}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   235 ~ : ~ 100 ~ = ~{\color{red} 2,35}
\item   740,1 ~ : ~ 100 ~ = ~{\color{red} 7,401}
\item   604,9 ~ : ~ 10 ~ = ~{\color{red} 60,49}
\item   770 ~ : ~ 100 ~ = ~{\color{red} 7,7}
\item   6,475 ~ : ~ 10 ~ = ~{\color{red} 0,647 5}
\item   446,3 ~ : ~ 100 ~ = ~{\color{red} 4,463}
\item   8 720 ~ : ~ 1 000 ~ = ~{\color{red} 8,72}
\item   9,03 ~ : ~ 100 ~ = ~{\color{red} 0,090 3}
\item   5,869 ~ : ~ 10 ~ = ~{\color{red} 0,586 9}
\item   1,088 ~ : ~ 10 ~ = ~{\color{red} 0,108 8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,99 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~49,9
\item   0,378 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,78
\item   6,35 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~635
\item   0,027 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27
\item   4,36 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 360
\item   95 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~95 000
\item   0,084 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~84
\item   0,068 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,68
\item   355 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 550
\item   60,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~601
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   44 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,044
}\item   24,52 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,452
}\item   450,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,501
}\item   7,103 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 103
}\item   7,418 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,741 8
}\item   16,79 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,016 79
}\item   7 209 ~ \(\times\)  0,1 ~ = ~{\color{red} 720,9
}\item   1 367 ~ \(\times\)  0,1 ~ = ~{\color{red} 136,7
}\item   2,238 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,022 38
}\item   1 767 ~ \(\times\)  0,1 ~ = ~{\color{red} 176,7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,264 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,026 4
\item   206,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 20,63
\item   196,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 19,69
\item   7,801 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 801
\item   28,71 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,871
\item   424 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 42,4
\item   1 016 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 10,16
\item   104,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,042
\item   3 518 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,518
\item   38,67 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,867
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   842,75 ~mm~ = {\color{red}  0,084 275 }~dam
\item   5 610,4 ~hL~ = {\color{red}  56 104 }~daL
\item   1 888,7 ~dag~ = {\color{red}  188,87 }~hg
\item   445,17 ~cg~ = {\color{red}  44,517 }~dg
\item   577,02 ~km~ = {\color{red}  577 020 }~m
\item   336,94 ~mm~ = {\color{red}  0,003 369 4 }~hm
\item   326,6 ~kL~ = {\color{red}  326 600 }~L
\item   8 911,7 ~dam~ = {\color{red}  89 117 }~m
\item   3 623,4 ~dm~ = {\color{red}  3,623 4 }~hm
\item   178,73 ~cm~ = {\color{red}  0,017 873 }~hm
\end{itemize}
\end{multicols}
\end{document}
