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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 269}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03  ~ \(\times\)  ~ 10
\item   87,4  ~ \(\times\)  ~ 1 000
\item   1,11  ~ \(\times\)  ~ 100
\item   59  ~ \(\times\)  ~ 1 000
\item   0,072  ~ \(\times\)  ~ 100
\item   358  ~ \(\times\)  ~ 1 000
\item   271  ~ \(\times\)  ~ 10
\item   8,44  ~ \(\times\)  ~ 100
\item   0,202  ~ \(\times\)  ~ 10
\item   8,45  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,42  ~ : ~ 100
\item   18,59  ~ : ~ 10
\item   97,6  ~ : ~ 100
\item   833  ~ : ~ 100
\item   260,9  ~ : ~ 100
\item   826,5  ~ : ~ 1 000
\item   4,53  ~ : ~ 1 000
\item   17  ~ : ~ 1 000
\item   8,992  ~ : ~ 100
\item   425  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,32  ~ \(\times\)  ~ ... ~ = ~ 6 320
\item   0,072  ~ \(\times\)  ~ ... ~ = ~ 7,2
\item   27,6  ~ \(\times\)  ~ ... ~ = ~ 27 600
\item   5,15  ~ \(\times\)  ~ ... ~ = ~ 51,5
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 4
\item   914  ~ \(\times\)  ~ ... ~ = ~ 9 140
\item   0,485  ~ \(\times\)  ~ ... ~ = ~ 48,5
\item   3,3  ~ \(\times\)  ~ ... ~ = ~ 330
\item   0,053  ~ \(\times\)  ~ ... ~ = ~ 0,53
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 6,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,57  ~ \(\times\)  ~ 0,1
\item   78,13  ~ \(\times\)  ~ 0,01
\item   0,285  ~ \(\times\)  ~ 0,001
\item   921,2  ~ \(\times\)  ~ 0,001
\item   84,86  ~ \(\times\)  ~ 0,01
\item   868,5  ~ \(\times\)  ~ 0,001
\item   17,49  ~ \(\times\)  ~ 0,1
\item   0,649  ~ \(\times\)  ~ 0,001
\item   7,947  ~ \(\times\)  ~ 0,01
\item   3 953  ~ \(\times\)  ~ 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   2,525  ~ \(\times\)  ~ ... ~ = ~  0,002 525
\item   7,6  ~ \(\times\)  ~ ... ~ = ~  0,007 6
\item   4,992  ~ \(\times\)  ~ ... ~ = ~  0,049 92
\item   6 425  ~ \(\times\)  ~ ... ~ = ~  642,5
\item   304,8  ~ \(\times\)  ~ ... ~ = ~  0,304 8
\item   703,2  ~ \(\times\)  ~ ... ~ = ~  0,703 2
\item   61,93  ~ \(\times\)  ~ ... ~ = ~  6,193
\item   679,7  ~ \(\times\)  ~ ... ~ = ~  6,797
\item   1 539  ~ \(\times\)  ~ ... ~ = ~  1,539
\item   160,4  ~ \(\times\)  ~ ... ~ = ~  16,04
\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~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 295,6 ~daL~ = ...~kL
\item   2 754,7 ~cm~ = ...~m
\item   4 561,5 ~cL~ = ...~L
\item   9 222,7 ~daL~ = ...~L
\item   7 801,3 ~L~ = ...~dL
\item   787,57 ~cm~ = ...~mm
\item   605,27 ~dm~ = ...~mm
\item   7 187,7 ~dL~ = ...~kL
\item   235 ~hL~ = ...~mL
\item   9 741,9 ~cg~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{190}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{540}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,3}
\item   87,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 87 400}
\item   1,11  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 111}
\item   59  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 59 000}
\item   0,072  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,2}
\item   358  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 358 000}
\item   271  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 710}
\item   8,44  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 844}
\item   0,202  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,02}
\item   8,45  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 845}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,42 ~ : ~ 100 ~ = ~{\color{red} 0,024 2}
\item   18,59 ~ : ~ 10 ~ = ~{\color{red} 1,859}
\item   97,6 ~ : ~ 100 ~ = ~{\color{red} 0,976}
\item   833 ~ : ~ 100 ~ = ~{\color{red} 8,33}
\item   260,9 ~ : ~ 100 ~ = ~{\color{red} 2,609}
\item   826,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,826 5}
\item   4,53 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 53}
\item   17 ~ : ~ 1 000 ~ = ~{\color{red} 0,017}
\item   8,992 ~ : ~ 100 ~ = ~{\color{red} 0,089 92}
\item   425 ~ : ~ 1 000 ~ = ~{\color{red} 0,425}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,32 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 320
\item   0,072 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,2
\item   27,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27 600
\item   5,15 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~51,5
\item   0,004 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4
\item   914 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 140
\item   0,485 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~48,5
\item   3,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~330
\item   0,053 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,53
\item   0,069 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,57 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,157
}\item   78,13 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,781 3
}\item   0,285 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 285
}\item   921,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,921 2
}\item   84,86 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,848 6
}\item   868,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,868 5
}\item   17,49 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,749
}\item   0,649 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 649
}\item   7,947 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,079 47
}\item   3 953 ~ \(\times\)  0,1 ~ = ~{\color{red} 395,3
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,525 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 525
\item   7,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 6
\item   4,992 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,049 92
\item   6 425 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 642,5
\item   304,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,304 8
\item   703,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,703 2
\item   61,93 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,193
\item   679,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,797
\item   1 539 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,539
\item   160,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 16,04
\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~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 295,6 ~daL~ = {\color{red}  72,956 }~kL
\item   2 754,7 ~cm~ = {\color{red}  27,547 }~m
\item   4 561,5 ~cL~ = {\color{red}  45,615 }~L
\item   9 222,7 ~daL~ = {\color{red}  92 227 }~L
\item   7 801,3 ~L~ = {\color{red}  78 013 }~dL
\item   787,57 ~cm~ = {\color{red}  7 875,7 }~mm
\item   605,27 ~dm~ = {\color{red}  60 527 }~mm
\item   7 187,7 ~dL~ = {\color{red}  0,718 77 }~kL
\item   235 ~hL~ = {\color{red}  23 500 000 }~mL
\item   9 741,9 ~cg~ = {\color{red}  97 419 }~mg
\end{itemize}
\end{multicols}
\end{document}
