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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 272}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{54}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,072  ~ \(\times\)  ~ 100
\item   0,056  ~ \(\times\)  ~ 10
\item   0,097  ~ \(\times\)  ~ 100
\item   84,6  ~ \(\times\)  ~ 100
\item   809  ~ \(\times\)  ~ 10
\item   2,09  ~ \(\times\)  ~ 10
\item   91,1  ~ \(\times\)  ~ 1 000
\item   62,8  ~ \(\times\)  ~ 1 000
\item   0,054  ~ \(\times\)  ~ 1 000
\item   75,2  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,151  ~ : ~ 100
\item   684,2  ~ : ~ 1 000
\item   2 606  ~ : ~ 1 000
\item   640,5  ~ : ~ 100
\item   5,546  ~ : ~ 10
\item   7,533  ~ : ~ 100
\item   5 742  ~ : ~ 100
\item   3 711  ~ : ~ 1 000
\item   9 171  ~ : ~ 1 000
\item   0,499  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03  ~ \(\times\)  ~ ... ~ = ~ 30
\item   16,1  ~ \(\times\)  ~ ... ~ = ~ 1 610
\item   508  ~ \(\times\)  ~ ... ~ = ~ 5 080
\item   0,41  ~ \(\times\)  ~ ... ~ = ~ 4,1
\item   4,29  ~ \(\times\)  ~ ... ~ = ~ 429
\item   0,42  ~ \(\times\)  ~ ... ~ = ~ 4,2
\item   0,03  ~ \(\times\)  ~ ... ~ = ~ 30
\item   91  ~ \(\times\)  ~ ... ~ = ~ 910
\item   0,658  ~ \(\times\)  ~ ... ~ = ~ 658
\item   0,025  ~ \(\times\)  ~ ... ~ = ~ 25
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   957,5  ~ \(\times\)  ~ 0,01
\item   7,06  ~ \(\times\)  ~ 0,1
\item   82,26  ~ \(\times\)  ~ 0,001
\item   580,2  ~ \(\times\)  ~ 0,1
\item   4 092  ~ \(\times\)  ~ 0,001
\item   447,2  ~ \(\times\)  ~ 0,001
\item   57,14  ~ \(\times\)  ~ 0,01
\item   3,372  ~ \(\times\)  ~ 0,001
\item   92,7  ~ \(\times\)  ~ 0,001
\item   5 426  ~ \(\times\)  ~ 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   6,783  ~ \(\times\)  ~ ... ~ = ~  0,678 3
\item   55,17  ~ \(\times\)  ~ ... ~ = ~  0,055 17
\item   6,884  ~ \(\times\)  ~ ... ~ = ~  0,006 884
\item   78,76  ~ \(\times\)  ~ ... ~ = ~  0,787 6
\item   29,67  ~ \(\times\)  ~ ... ~ = ~  0,296 7
\item   70,26  ~ \(\times\)  ~ ... ~ = ~  7,026
\item   285,9  ~ \(\times\)  ~ ... ~ = ~  28,59
\item   20,26  ~ \(\times\)  ~ ... ~ = ~  0,020 26
\item   9,447  ~ \(\times\)  ~ ... ~ = ~  0,944 7
\item   623  ~ \(\times\)  ~ ... ~ = ~  62,3
\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 ~m~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   547,26 ~dam~ = ...~hm
\item   920,92 ~g~ = ...~dg
\item   9 918,7 ~hg~ = ...~dg
\item   1 342,9 ~cg~ = ...~g
\item   629,66 ~hm~ = ...~m
\item   470,88 ~hg~ = ...~kg
\item   602,21 ~kg~ = ...~dg
\item   9 432,5 ~dm~ = ...~cm
\item   3 235,1 ~cL~ = ...~kL
\item   812,6 ~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   8 = \(\dfrac{80}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{190}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{54}{10}\) = \(\dfrac{540}{100}\)
\item   \(\dfrac{58}{100}\) = \(\dfrac{580}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,072  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,2}
\item   0,056  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,56}
\item   0,097  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,7}
\item   84,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 460}
\item   809  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 090}
\item   2,09  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 20,9}
\item   91,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 91 100}
\item   62,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 62 800}
\item   0,054  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 54}
\item   75,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 520}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,151 ~ : ~ 100 ~ = ~{\color{red} 0,011 51}
\item   684,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,684 2}
\item   2 606 ~ : ~ 1 000 ~ = ~{\color{red} 2,606}
\item   640,5 ~ : ~ 100 ~ = ~{\color{red} 6,405}
\item   5,546 ~ : ~ 10 ~ = ~{\color{red} 0,554 6}
\item   7,533 ~ : ~ 100 ~ = ~{\color{red} 0,075 33}
\item   5 742 ~ : ~ 100 ~ = ~{\color{red} 57,42}
\item   3 711 ~ : ~ 1 000 ~ = ~{\color{red} 3,711}
\item   9 171 ~ : ~ 1 000 ~ = ~{\color{red} 9,171}
\item   0,499 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 499}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~30
\item   16,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 610
\item   508 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 080
\item   0,41 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,1
\item   4,29 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~429
\item   0,42 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,2
\item   0,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~30
\item   91 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~910
\item   0,658 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~658
\item   0,025 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~25
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   957,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,575
}\item   7,06 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,706
}\item   82,26 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,082 26
}\item   580,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 58,02
}\item   4 092 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,092
}\item   447,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,447 2
}\item   57,14 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,571 4
}\item   3,372 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 372
}\item   92,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,092 7
}\item   5 426 ~ \(\times\)  0,1 ~ = ~{\color{red} 542,6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,783 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,678 3
\item   55,17 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,055 17
\item   6,884 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 884
\item   78,76 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,787 6
\item   29,67 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,296 7
\item   70,26 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,026
\item   285,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 28,59
\item   20,26 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,020 26
\item   9,447 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,944 7
\item   623 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 62,3
\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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   547,26 ~dam~ = {\color{red}  54,726 }~hm
\item   920,92 ~g~ = {\color{red}  9 209,2 }~dg
\item   9 918,7 ~hg~ = {\color{red}  9 918 700 }~dg
\item   1 342,9 ~cg~ = {\color{red}  13,429 }~g
\item   629,66 ~hm~ = {\color{red}  62 966 }~m
\item   470,88 ~hg~ = {\color{red}  47,088 }~kg
\item   602,21 ~kg~ = {\color{red}  6 022 100 }~dg
\item   9 432,5 ~dm~ = {\color{red}  94 325 }~cm
\item   3 235,1 ~cL~ = {\color{red}  0,032 351 }~kL
\item   812,6 ~cm~ = {\color{red}  0,081 26 }~hm
\end{itemize}
\end{multicols}
\end{document}
