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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 199}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{12}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,072  ~ \(\times\)  ~ 100
\item   27  ~ \(\times\)  ~ 1 000
\item   0,036  ~ \(\times\)  ~ 100
\item   0,004  ~ \(\times\)  ~ 1 000
\item   0,815  ~ \(\times\)  ~ 100
\item   52,6  ~ \(\times\)  ~ 100
\item   0,016  ~ \(\times\)  ~ 1 000
\item   0,088  ~ \(\times\)  ~ 100
\item   0,914  ~ \(\times\)  ~ 1 000
\item   0,334  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,394  ~ : ~ 10
\item   50,17  ~ : ~ 100
\item   1 591  ~ : ~ 10
\item   910,4  ~ : ~ 10
\item   7 111  ~ : ~ 1 000
\item   1 689  ~ : ~ 1 000
\item   7 891  ~ : ~ 1 000
\item   3,2  ~ : ~ 10
\item   2 397  ~ : ~ 100
\item   171,2  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,073  ~ \(\times\)  ~ ... ~ = ~ 73
\item   0,527  ~ \(\times\)  ~ ... ~ = ~ 52,7
\item   0,016  ~ \(\times\)  ~ ... ~ = ~ 1,6
\item   0,402  ~ \(\times\)  ~ ... ~ = ~ 40,2
\item   0,056  ~ \(\times\)  ~ ... ~ = ~ 0,56
\item   887  ~ \(\times\)  ~ ... ~ = ~ 88 700
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 6,4
\item   9,75  ~ \(\times\)  ~ ... ~ = ~ 975
\item   0,023  ~ \(\times\)  ~ ... ~ = ~ 2,3
\item   0,45  ~ \(\times\)  ~ ... ~ = ~ 450
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   493,1  ~ \(\times\)  ~ 0,01
\item   37,27  ~ \(\times\)  ~ 0,01
\item   726,1  ~ \(\times\)  ~ 0,01
\item   0,435  ~ \(\times\)  ~ 0,1
\item   22,64  ~ \(\times\)  ~ 0,01
\item   520,4  ~ \(\times\)  ~ 0,001
\item   5,725  ~ \(\times\)  ~ 0,001
\item   0,721  ~ \(\times\)  ~ 0,1
\item   599,6  ~ \(\times\)  ~ 0,1
\item   477,5  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 234  ~ \(\times\)  ~ ... ~ = ~  32,34
\item   463,9  ~ \(\times\)  ~ ... ~ = ~  46,39
\item   9,569  ~ \(\times\)  ~ ... ~ = ~  0,009 569
\item   0,251  ~ \(\times\)  ~ ... ~ = ~  0,000 251
\item   83,64  ~ \(\times\)  ~ ... ~ = ~  8,364
\item   2 402  ~ \(\times\)  ~ ... ~ = ~  240,2
\item   4,013  ~ \(\times\)  ~ ... ~ = ~  0,040 13
\item   8,37  ~ \(\times\)  ~ ... ~ = ~  0,837
\item   5 377  ~ \(\times\)  ~ ... ~ = ~  53,77
\item   5,632  ~ \(\times\)  ~ ... ~ = ~  0,563 2
\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 ~hm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 761,9 ~cm~ = ...~hm
\item   389,9 ~cL~ = ...~dL
\item   2 860,2 ~mg~ = ...~hg
\item   8 256,1 ~kg~ = ...~dag
\item   230,94 ~hL~ = ...~cL
\item   7 070,9 ~dag~ = ...~kg
\item   812,14 ~kL~ = ...~hL
\item   7 209,6 ~cm~ = ...~km
\item   774,17 ~dm~ = ...~cm
\item   8 839,4 ~hm~ = ...~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   6 = \(\dfrac{60}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{460}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{12}{10}\) = \(\dfrac{120}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{720}{1\,000}\)
\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   27  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 27 000}
\item   0,036  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,6}
\item   0,004  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4}
\item   0,815  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 81,5}
\item   52,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 260}
\item   0,016  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 16}
\item   0,088  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,8}
\item   0,914  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 914}
\item   0,334  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 33,4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,394 ~ : ~ 10 ~ = ~{\color{red} 0,039 4}
\item   50,17 ~ : ~ 100 ~ = ~{\color{red} 0,501 7}
\item   1 591 ~ : ~ 10 ~ = ~{\color{red} 159,1}
\item   910,4 ~ : ~ 10 ~ = ~{\color{red} 91,04}
\item   7 111 ~ : ~ 1 000 ~ = ~{\color{red} 7,111}
\item   1 689 ~ : ~ 1 000 ~ = ~{\color{red} 1,689}
\item   7 891 ~ : ~ 1 000 ~ = ~{\color{red} 7,891}
\item   3,2 ~ : ~ 10 ~ = ~{\color{red} 0,32}
\item   2 397 ~ : ~ 100 ~ = ~{\color{red} 23,97}
\item   171,2 ~ : ~ 10 ~ = ~{\color{red} 17,12}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,073 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~73
\item   0,527 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~52,7
\item   0,016 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,6
\item   0,402 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~40,2
\item   0,056 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,56
\item   887 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88 700
\item   0,064 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,4
\item   9,75 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~975
\item   0,023 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,3
\item   0,45 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~450
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   493,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,931
}\item   37,27 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,372 7
}\item   726,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,261
}\item   0,435 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,043 5
}\item   22,64 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,226 4
}\item   520,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,520 4
}\item   5,725 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 725
}\item   0,721 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,072 1
}\item   599,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 59,96
}\item   477,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,477 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 234 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 32,34
\item   463,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 46,39
\item   9,569 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 569
\item   0,251 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 251
\item   83,64 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,364
\item   2 402 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 240,2
\item   4,013 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,040 13
\item   8,37 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,837
\item   5 377 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 53,77
\item   5,632 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,563 2
\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 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 761,9 ~cm~ = {\color{red}  0,676 19 }~hm
\item   389,9 ~cL~ = {\color{red}  38,99 }~dL
\item   2 860,2 ~mg~ = {\color{red}  0,028 602 }~hg
\item   8 256,1 ~kg~ = {\color{red}  825 610 }~dag
\item   230,94 ~hL~ = {\color{red}  2 309 400 }~cL
\item   7 070,9 ~dag~ = {\color{red}  70,709 }~kg
\item   812,14 ~kL~ = {\color{red}  8 121,4 }~hL
\item   7 209,6 ~cm~ = {\color{red}  0,072 096 }~km
\item   774,17 ~dm~ = {\color{red}  7 741,7 }~cm
\item   8 839,4 ~hm~ = {\color{red}  88 394 000 }~cm
\end{itemize}
\end{multicols}
\end{document}
