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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 86}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{75}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,319  ~ \(\times\)  ~ 10
\item   0,091  ~ \(\times\)  ~ 10
\item   0,848  ~ \(\times\)  ~ 100
\item   0,001  ~ \(\times\)  ~ 10
\item   2,22  ~ \(\times\)  ~ 10
\item   81  ~ \(\times\)  ~ 100
\item   300  ~ \(\times\)  ~ 100
\item   412  ~ \(\times\)  ~ 100
\item   50  ~ \(\times\)  ~ 100
\item   0,389  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   632,3  ~ : ~ 10
\item   0,782  ~ : ~ 100
\item   53,02  ~ : ~ 100
\item   6,457  ~ : ~ 100
\item   97,91  ~ : ~ 10
\item   8,186  ~ : ~ 100
\item   1 006  ~ : ~ 1 000
\item   33,1  ~ : ~ 10
\item   6,319  ~ : ~ 10
\item   8 924  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64  ~ \(\times\)  ~ ... ~ = ~ 6 400
\item   47,5  ~ \(\times\)  ~ ... ~ = ~ 4 750
\item   833  ~ \(\times\)  ~ ... ~ = ~ 833 000
\item   32,4  ~ \(\times\)  ~ ... ~ = ~ 3 240
\item   0,757  ~ \(\times\)  ~ ... ~ = ~ 75,7
\item   74,4  ~ \(\times\)  ~ ... ~ = ~ 74 400
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 62
\item   0,748  ~ \(\times\)  ~ ... ~ = ~ 748
\item   54,6  ~ \(\times\)  ~ ... ~ = ~ 5 460
\item   0,48  ~ \(\times\)  ~ ... ~ = ~ 480
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,98  ~ \(\times\)  ~ 0,01
\item   3,15  ~ \(\times\)  ~ 0,01
\item   606,4  ~ \(\times\)  ~ 0,01
\item   48,49  ~ \(\times\)  ~ 0,001
\item   7,22  ~ \(\times\)  ~ 0,01
\item   7 084  ~ \(\times\)  ~ 0,1
\item   323,6  ~ \(\times\)  ~ 0,1
\item   6 802  ~ \(\times\)  ~ 0,01
\item   0,965  ~ \(\times\)  ~ 0,001
\item   6,894  ~ \(\times\)  ~ 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   950,3  ~ \(\times\)  ~ ... ~ = ~  0,950 3
\item   455,9  ~ \(\times\)  ~ ... ~ = ~  4,559
\item   9,75  ~ \(\times\)  ~ ... ~ = ~  0,097 5
\item   255,4  ~ \(\times\)  ~ ... ~ = ~  25,54
\item   95,34  ~ \(\times\)  ~ ... ~ = ~  9,534
\item   6 083  ~ \(\times\)  ~ ... ~ = ~  60,83
\item   9 228  ~ \(\times\)  ~ ... ~ = ~  922,8
\item   1 787  ~ \(\times\)  ~ ... ~ = ~  17,87
\item   43,3  ~ \(\times\)  ~ ... ~ = ~  4,33
\item   434,9  ~ \(\times\)  ~ ... ~ = ~  43,49
\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~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   606,25 ~dag~ = ...~g
\item   897,52 ~kL~ = ...~hL
\item   594,65 ~dL~ = ...~hL
\item   8 997,3 ~dm~ = ...~mm
\item   428,52 ~dm~ = ...~m
\item   787,97 ~mL~ = ...~daL
\item   497,42 ~cm~ = ...~dam
\item   7 134,1 ~dL~ = ...~L
\item   350,59 ~cm~ = ...~mm
\item   330,66 ~kg~ = ...~cg
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{1200}{100}\) = \(\dfrac{120}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{75}{10}\) = \(\dfrac{750}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{910}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,319  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,19}
\item   0,091  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,91}
\item   0,848  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 84,8}
\item   0,001  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,01}
\item   2,22  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 22,2}
\item   81  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 100}
\item   300  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 30 000}
\item   412  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 41 200}
\item   50  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 000}
\item   0,389  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 38,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   632,3 ~ : ~ 10 ~ = ~{\color{red} 63,23}
\item   0,782 ~ : ~ 100 ~ = ~{\color{red} 0,007 82}
\item   53,02 ~ : ~ 100 ~ = ~{\color{red} 0,530 2}
\item   6,457 ~ : ~ 100 ~ = ~{\color{red} 0,064 57}
\item   97,91 ~ : ~ 10 ~ = ~{\color{red} 9,791}
\item   8,186 ~ : ~ 100 ~ = ~{\color{red} 0,081 86}
\item   1 006 ~ : ~ 1 000 ~ = ~{\color{red} 1,006}
\item   33,1 ~ : ~ 10 ~ = ~{\color{red} 3,31}
\item   6,319 ~ : ~ 10 ~ = ~{\color{red} 0,631 9}
\item   8 924 ~ : ~ 1 000 ~ = ~{\color{red} 8,924}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 400
\item   47,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 750
\item   833 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~833 000
\item   32,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 240
\item   0,757 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~75,7
\item   74,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~74 400
\item   0,062 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~62
\item   0,748 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~748
\item   54,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 460
\item   0,48 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~480
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,98 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,159 8
}\item   3,15 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,031 5
}\item   606,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,064
}\item   48,49 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,048 49
}\item   7,22 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,072 2
}\item   7 084 ~ \(\times\)  0,1 ~ = ~{\color{red} 708,4
}\item   323,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 32,36
}\item   6 802 ~ \(\times\)  0,01 ~ = ~{\color{red} 68,02
}\item   0,965 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 965
}\item   6,894 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,068 94
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   950,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,950 3
\item   455,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,559
\item   9,75 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,097 5
\item   255,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 25,54
\item   95,34 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,534
\item   6 083 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 60,83
\item   9 228 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 922,8
\item   1 787 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 17,87
\item   43,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,33
\item   434,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 43,49
\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~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\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   606,25 ~dag~ = {\color{red}  6 062,5 }~g
\item   897,52 ~kL~ = {\color{red}  8 975,2 }~hL
\item   594,65 ~dL~ = {\color{red}  0,594 65 }~hL
\item   8 997,3 ~dm~ = {\color{red}  899 730 }~mm
\item   428,52 ~dm~ = {\color{red}  42,852 }~m
\item   787,97 ~mL~ = {\color{red}  0,078 797 }~daL
\item   497,42 ~cm~ = {\color{red}  0,497 42 }~dam
\item   7 134,1 ~dL~ = {\color{red}  713,41 }~L
\item   350,59 ~cm~ = {\color{red}  3 505,9 }~mm
\item   330,66 ~kg~ = {\color{red}  33 066 000 }~cg
\end{itemize}
\end{multicols}
\end{document}
