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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 145}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{95}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{52}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,759  ~ \(\times\)  ~ 1 000
\item   5,32  ~ \(\times\)  ~ 10
\item   27,9  ~ \(\times\)  ~ 10
\item   6,31  ~ \(\times\)  ~ 1 000
\item   464  ~ \(\times\)  ~ 1 000
\item   2,82  ~ \(\times\)  ~ 100
\item   41,8  ~ \(\times\)  ~ 1 000
\item   339  ~ \(\times\)  ~ 1 000
\item   511  ~ \(\times\)  ~ 10
\item   0,006  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,806  ~ : ~ 1 000
\item   7,194  ~ : ~ 1 000
\item   89,73  ~ : ~ 1 000
\item   72,66  ~ : ~ 100
\item   32,7  ~ : ~ 100
\item   4,915  ~ : ~ 10
\item   511,8  ~ : ~ 1 000
\item   4 303  ~ : ~ 100
\item   659,4  ~ : ~ 10
\item   3,797  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 6,2
\item   5,32  ~ \(\times\)  ~ ... ~ = ~ 5 320
\item   3  ~ \(\times\)  ~ ... ~ = ~ 300
\item   2,25  ~ \(\times\)  ~ ... ~ = ~ 2 250
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 0,27
\item   43,7  ~ \(\times\)  ~ ... ~ = ~ 437
\item   624  ~ \(\times\)  ~ ... ~ = ~ 6 240
\item   0,33  ~ \(\times\)  ~ ... ~ = ~ 3,3
\item   414  ~ \(\times\)  ~ ... ~ = ~ 414 000
\item   0,025  ~ \(\times\)  ~ ... ~ = ~ 0,25
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   38,86  ~ \(\times\)  ~ 0,1
\item   4,194  ~ \(\times\)  ~ 0,1
\item   7 005  ~ \(\times\)  ~ 0,01
\item   314,9  ~ \(\times\)  ~ 0,01
\item   4 739  ~ \(\times\)  ~ 0,001
\item   522,5  ~ \(\times\)  ~ 0,1
\item   7,782  ~ \(\times\)  ~ 0,001
\item   298  ~ \(\times\)  ~ 0,001
\item   6 189  ~ \(\times\)  ~ 0,01
\item   0,968  ~ \(\times\)  ~ 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   3,479  ~ \(\times\)  ~ ... ~ = ~  0,034 79
\item   19,75  ~ \(\times\)  ~ ... ~ = ~  1,975
\item   9 259  ~ \(\times\)  ~ ... ~ = ~  925,9
\item   38,31  ~ \(\times\)  ~ ... ~ = ~  3,831
\item   581,8  ~ \(\times\)  ~ ... ~ = ~  5,818
\item   1,951  ~ \(\times\)  ~ ... ~ = ~  0,019 51
\item   329,9  ~ \(\times\)  ~ ... ~ = ~  3,299
\item   65,72  ~ \(\times\)  ~ ... ~ = ~  0,065 72
\item   4 900  ~ \(\times\)  ~ ... ~ = ~  490
\item   279,5  ~ \(\times\)  ~ ... ~ = ~  27,95
\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 ~cm~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   495,95 ~m~ = ...~km
\item   509,33 ~hL~ = ...~L
\item   7 233,6 ~mg~ = ...~kg
\item   2 050,5 ~mg~ = ...~dag
\item   8 964,5 ~mm~ = ...~m
\item   4 911,9 ~dL~ = ...~daL
\item   117,91 ~g~ = ...~kg
\item   912,11 ~dm~ = ...~cm
\item   3 471,9 ~dag~ = ...~mg
\item   258,96 ~L~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{6700}{100}\) = \(\dfrac{670}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{95}{10}\) = \(\dfrac{950}{100}\)
\item   \(\dfrac{52}{100}\) = \(\dfrac{520}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,759  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 759}
\item   5,32  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 53,2}
\item   27,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 279}
\item   6,31  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 310}
\item   464  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 464 000}
\item   2,82  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 282}
\item   41,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 41 800}
\item   339  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 339 000}
\item   511  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 110}
\item   0,006  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,06}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,806 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 806}
\item   7,194 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 194}
\item   89,73 ~ : ~ 1 000 ~ = ~{\color{red} 0,089 73}
\item   72,66 ~ : ~ 100 ~ = ~{\color{red} 0,726 6}
\item   32,7 ~ : ~ 100 ~ = ~{\color{red} 0,327}
\item   4,915 ~ : ~ 10 ~ = ~{\color{red} 0,491 5}
\item   511,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,511 8}
\item   4 303 ~ : ~ 100 ~ = ~{\color{red} 43,03}
\item   659,4 ~ : ~ 10 ~ = ~{\color{red} 65,94}
\item   3,797 ~ : ~ 100 ~ = ~{\color{red} 0,037 97}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,062 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,2
\item   5,32 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 320
\item   3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~300
\item   2,25 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 250
\item   0,027 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,27
\item   43,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~437
\item   624 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 240
\item   0,33 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,3
\item   414 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~414 000
\item   0,025 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,25
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   38,86 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,886
}\item   4,194 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,419 4
}\item   7 005 ~ \(\times\)  0,01 ~ = ~{\color{red} 70,05
}\item   314,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,149
}\item   4 739 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,739
}\item   522,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 52,25
}\item   7,782 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 782
}\item   298 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,298
}\item   6 189 ~ \(\times\)  0,01 ~ = ~{\color{red} 61,89
}\item   0,968 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,009 68
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,479 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,034 79
\item   19,75 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,975
\item   9 259 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 925,9
\item   38,31 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,831
\item   581,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,818
\item   1,951 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,019 51
\item   329,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,299
\item   65,72 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,065 72
\item   4 900 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 490
\item   279,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 27,95
\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 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   495,95 ~m~ = {\color{red}  0,495 95 }~km
\item   509,33 ~hL~ = {\color{red}  50 933 }~L
\item   7 233,6 ~mg~ = {\color{red}  0,007 233 6 }~kg
\item   2 050,5 ~mg~ = {\color{red}  0,205 05 }~dag
\item   8 964,5 ~mm~ = {\color{red}  8,964 5 }~m
\item   4 911,9 ~dL~ = {\color{red}  49,119 }~daL
\item   117,91 ~g~ = {\color{red}  0,117 91 }~kg
\item   912,11 ~dm~ = {\color{red}  9 121,1 }~cm
\item   3 471,9 ~dag~ = {\color{red}  34 719 000 }~mg
\item   258,96 ~L~ = {\color{red}  0,258 96 }~kL
\end{itemize}
\end{multicols}
\end{document}
