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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 369}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{12}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{66}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,022  ~ \(\times\)  ~ 10
\item   0,088  ~ \(\times\)  ~ 10
\item   0,091  ~ \(\times\)  ~ 100
\item   846  ~ \(\times\)  ~ 100
\item   40,5  ~ \(\times\)  ~ 100
\item   9  ~ \(\times\)  ~ 100
\item   5,76  ~ \(\times\)  ~ 1 000
\item   0,051  ~ \(\times\)  ~ 10
\item   84,1  ~ \(\times\)  ~ 1 000
\item   2,46  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,625  ~ : ~ 100
\item   3,398  ~ : ~ 1 000
\item   43,6  ~ : ~ 10
\item   5,877  ~ : ~ 100
\item   7,003  ~ : ~ 100
\item   887,3  ~ : ~ 1 000
\item   9 340  ~ : ~ 10
\item   3 740  ~ : ~ 1 000
\item   42,86  ~ : ~ 10
\item   8 413  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,65  ~ \(\times\)  ~ ... ~ = ~ 16,5
\item   0,954  ~ \(\times\)  ~ ... ~ = ~ 9,54
\item   0,04  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   0,04  ~ \(\times\)  ~ ... ~ = ~ 40
\item   3,15  ~ \(\times\)  ~ ... ~ = ~ 31,5
\item   67,4  ~ \(\times\)  ~ ... ~ = ~ 6 740
\item   0,029  ~ \(\times\)  ~ ... ~ = ~ 29
\item   0,669  ~ \(\times\)  ~ ... ~ = ~ 669
\item   0,66  ~ \(\times\)  ~ ... ~ = ~ 660
\item   0,841  ~ \(\times\)  ~ ... ~ = ~ 84,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,488  ~ \(\times\)  ~ 0,1
\item   72,74  ~ \(\times\)  ~ 0,001
\item   191,1  ~ \(\times\)  ~ 0,01
\item   1 131  ~ \(\times\)  ~ 0,001
\item   367,5  ~ \(\times\)  ~ 0,001
\item   8,235  ~ \(\times\)  ~ 0,01
\item   588,6  ~ \(\times\)  ~ 0,001
\item   7 457  ~ \(\times\)  ~ 0,01
\item   33,5  ~ \(\times\)  ~ 0,1
\item   5,57  ~ \(\times\)  ~ 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   6,198  ~ \(\times\)  ~ ... ~ = ~  0,061 98
\item   90,72  ~ \(\times\)  ~ ... ~ = ~  0,907 2
\item   54,58  ~ \(\times\)  ~ ... ~ = ~  0,545 8
\item   752,5  ~ \(\times\)  ~ ... ~ = ~  0,752 5
\item   5 346  ~ \(\times\)  ~ ... ~ = ~  5,346
\item   898  ~ \(\times\)  ~ ... ~ = ~  8,98
\item   9,311  ~ \(\times\)  ~ ... ~ = ~  0,093 11
\item   9,077  ~ \(\times\)  ~ ... ~ = ~  0,009 077
\item   3,755  ~ \(\times\)  ~ ... ~ = ~  0,003 755
\item   3 193  ~ \(\times\)  ~ ... ~ = ~  319,3
\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 ~dm~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 707,3 ~mm~ = ...~dam
\item   4 621,8 ~daL~ = ...~L
\item   5 938,2 ~m~ = ...~km
\item   9 798,1 ~hL~ = ...~mL
\item   450,89 ~mm~ = ...~cm
\item   4 179,1 ~hm~ = ...~cm
\item   547,17 ~hg~ = ...~kg
\item   3 525,1 ~hm~ = ...~mm
\item   2 908,8 ~dag~ = ...~hg
\item   4 889 ~cm~ = ...~mm
\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   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{410}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{12}{10}\) = \(\dfrac{120}{100}\)
\item   \(\dfrac{66}{100}\) = \(\dfrac{660}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,022  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,22}
\item   0,088  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,88}
\item   0,091  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,1}
\item   846  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 84 600}
\item   40,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 050}
\item   9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 900}
\item   5,76  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 760}
\item   0,051  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,51}
\item   84,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84 100}
\item   2,46  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 246}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,625 ~ : ~ 100 ~ = ~{\color{red} 0,066 25}
\item   3,398 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 398}
\item   43,6 ~ : ~ 10 ~ = ~{\color{red} 4,36}
\item   5,877 ~ : ~ 100 ~ = ~{\color{red} 0,058 77}
\item   7,003 ~ : ~ 100 ~ = ~{\color{red} 0,070 03}
\item   887,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,887 3}
\item   9 340 ~ : ~ 10 ~ = ~{\color{red} 934}
\item   3 740 ~ : ~ 1 000 ~ = ~{\color{red} 3,74}
\item   42,86 ~ : ~ 10 ~ = ~{\color{red} 4,286}
\item   8 413 ~ : ~ 1 000 ~ = ~{\color{red} 8,413}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,65 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~16,5
\item   0,954 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,54
\item   0,04 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,4
\item   0,04 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~40
\item   3,15 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~31,5
\item   67,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 740
\item   0,029 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~29
\item   0,669 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~669
\item   0,66 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~660
\item   0,841 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~84,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,488 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,648 8
}\item   72,74 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,072 74
}\item   191,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,911
}\item   1 131 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,131
}\item   367,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,367 5
}\item   8,235 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,082 35
}\item   588,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,588 6
}\item   7 457 ~ \(\times\)  0,01 ~ = ~{\color{red} 74,57
}\item   33,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,35
}\item   5,57 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,557
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,198 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,061 98
\item   90,72 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,907 2
\item   54,58 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,545 8
\item   752,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,752 5
\item   5 346 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,346
\item   898 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,98
\item   9,311 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,093 11
\item   9,077 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 077
\item   3,755 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 755
\item   3 193 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 319,3
\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 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 707,3 ~mm~ = {\color{red}  0,370 73 }~dam
\item   4 621,8 ~daL~ = {\color{red}  46 218 }~L
\item   5 938,2 ~m~ = {\color{red}  5,938 2 }~km
\item   9 798,1 ~hL~ = {\color{red}  979 810 000 }~mL
\item   450,89 ~mm~ = {\color{red}  45,089 }~cm
\item   4 179,1 ~hm~ = {\color{red}  41 791 000 }~cm
\item   547,17 ~hg~ = {\color{red}  54,717 }~kg
\item   3 525,1 ~hm~ = {\color{red}  352 510 000 }~mm
\item   2 908,8 ~dag~ = {\color{red}  290,88 }~hg
\item   4 889 ~cm~ = {\color{red}  48 890 }~mm
\end{itemize}
\end{multicols}
\end{document}
