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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 309}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   21,7  ~ \(\times\)  ~ 1 000
\item   0,774  ~ \(\times\)  ~ 10
\item   1,95  ~ \(\times\)  ~ 100
\item   0,001  ~ \(\times\)  ~ 10
\item   0,013  ~ \(\times\)  ~ 1 000
\item   0,003  ~ \(\times\)  ~ 1 000
\item   773  ~ \(\times\)  ~ 100
\item   0,32  ~ \(\times\)  ~ 10
\item   0,026  ~ \(\times\)  ~ 10
\item   171  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,642  ~ : ~ 1 000
\item   640  ~ : ~ 100
\item   8,742  ~ : ~ 10
\item   6,028  ~ : ~ 10
\item   5 294  ~ : ~ 1 000
\item   31,56  ~ : ~ 100
\item   17,83  ~ : ~ 10
\item   564  ~ : ~ 100
\item   6 948  ~ : ~ 1 000
\item   0,939  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,33  ~ \(\times\)  ~ ... ~ = ~ 83,3
\item   94,7  ~ \(\times\)  ~ ... ~ = ~ 94 700
\item   6,84  ~ \(\times\)  ~ ... ~ = ~ 684
\item   1,12  ~ \(\times\)  ~ ... ~ = ~ 112
\item   32  ~ \(\times\)  ~ ... ~ = ~ 32 000
\item   225  ~ \(\times\)  ~ ... ~ = ~ 22 500
\item   9  ~ \(\times\)  ~ ... ~ = ~ 9 000
\item   0,675  ~ \(\times\)  ~ ... ~ = ~ 67,5
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 0,68
\item   917  ~ \(\times\)  ~ ... ~ = ~ 9 170
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   523,6  ~ \(\times\)  ~ 0,01
\item   87,75  ~ \(\times\)  ~ 0,1
\item   63,11  ~ \(\times\)  ~ 0,1
\item   1,912  ~ \(\times\)  ~ 0,1
\item   889,8  ~ \(\times\)  ~ 0,01
\item   14,4  ~ \(\times\)  ~ 0,01
\item   3,788  ~ \(\times\)  ~ 0,01
\item   6 105  ~ \(\times\)  ~ 0,001
\item   1 408  ~ \(\times\)  ~ 0,1
\item   6,112  ~ \(\times\)  ~ 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   8,276  ~ \(\times\)  ~ ... ~ = ~  0,082 76
\item   7 270  ~ \(\times\)  ~ ... ~ = ~  727
\item   2 028  ~ \(\times\)  ~ ... ~ = ~  202,8
\item   1 028  ~ \(\times\)  ~ ... ~ = ~  102,8
\item   1,952  ~ \(\times\)  ~ ... ~ = ~  0,001 952
\item   8 567  ~ \(\times\)  ~ ... ~ = ~  856,7
\item   3 938  ~ \(\times\)  ~ ... ~ = ~  3,938
\item   4,081  ~ \(\times\)  ~ ... ~ = ~  0,004 081
\item   672,3  ~ \(\times\)  ~ ... ~ = ~  6,723
\item   644,8  ~ \(\times\)  ~ ... ~ = ~  64,48
\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~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   829,46 ~mg~ = ...~kg
\item   7 968,6 ~mm~ = ...~m
\item   809,43 ~kg~ = ...~cg
\item   697,89 ~cg~ = ...~kg
\item   815,89 ~cg~ = ...~g
\item   2 277,8 ~g~ = ...~kg
\item   288,03 ~dam~ = ...~hm
\item   682,51 ~dm~ = ...~m
\item   9 959,3 ~dam~ = ...~dm
\item   4 623,3 ~mm~ = ...~cm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{110}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{360}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{410}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   21,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 21 700}
\item   0,774  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,74}
\item   1,95  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 195}
\item   0,001  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,01}
\item   0,013  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 13}
\item   0,003  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3}
\item   773  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 77 300}
\item   0,32  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,2}
\item   0,026  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,26}
\item   171  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 710}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,642 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 642}
\item   640 ~ : ~ 100 ~ = ~{\color{red} 6,4}
\item   8,742 ~ : ~ 10 ~ = ~{\color{red} 0,874 2}
\item   6,028 ~ : ~ 10 ~ = ~{\color{red} 0,602 8}
\item   5 294 ~ : ~ 1 000 ~ = ~{\color{red} 5,294}
\item   31,56 ~ : ~ 100 ~ = ~{\color{red} 0,315 6}
\item   17,83 ~ : ~ 10 ~ = ~{\color{red} 1,783}
\item   564 ~ : ~ 100 ~ = ~{\color{red} 5,64}
\item   6 948 ~ : ~ 1 000 ~ = ~{\color{red} 6,948}
\item   0,939 ~ : ~ 10 ~ = ~{\color{red} 0,093 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,33 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~83,3
\item   94,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~94 700
\item   6,84 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~684
\item   1,12 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~112
\item   32 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~32 000
\item   225 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22 500
\item   9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 000
\item   0,675 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~67,5
\item   0,068 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,68
\item   917 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 170
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   523,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,236
}\item   87,75 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,775
}\item   63,11 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,311
}\item   1,912 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,191 2
}\item   889,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,898
}\item   14,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,144
}\item   3,788 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,037 88
}\item   6 105 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,105
}\item   1 408 ~ \(\times\)  0,1 ~ = ~{\color{red} 140,8
}\item   6,112 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,061 12
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,276 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,082 76
\item   7 270 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 727
\item   2 028 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 202,8
\item   1 028 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 102,8
\item   1,952 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 952
\item   8 567 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 856,7
\item   3 938 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,938
\item   4,081 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 081
\item   672,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,723
\item   644,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 64,48
\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~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\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   829,46 ~mg~ = {\color{red}  0,000 829 46 }~kg
\item   7 968,6 ~mm~ = {\color{red}  7,968 6 }~m
\item   809,43 ~kg~ = {\color{red}  80 943 000 }~cg
\item   697,89 ~cg~ = {\color{red}  0,006 978 9 }~kg
\item   815,89 ~cg~ = {\color{red}  8,158 9 }~g
\item   2 277,8 ~g~ = {\color{red}  2,277 8 }~kg
\item   288,03 ~dam~ = {\color{red}  28,803 }~hm
\item   682,51 ~dm~ = {\color{red}  68,251 }~m
\item   9 959,3 ~dam~ = {\color{red}  995 930 }~dm
\item   4 623,3 ~mm~ = {\color{red}  462,33 }~cm
\end{itemize}
\end{multicols}
\end{document}
