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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 219}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{47}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   3,56  ~ \(\times\)  ~ 100
\item   5  ~ \(\times\)  ~ 10
\item   0,661  ~ \(\times\)  ~ 100
\item   64,4  ~ \(\times\)  ~ 10
\item   143  ~ \(\times\)  ~ 100
\item   0,346  ~ \(\times\)  ~ 100
\item   0,083  ~ \(\times\)  ~ 10
\item   0,087  ~ \(\times\)  ~ 1 000
\item   0,11  ~ \(\times\)  ~ 100
\item   7,28  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 438  ~ : ~ 10
\item   320  ~ : ~ 100
\item   8,811  ~ : ~ 1 000
\item   315  ~ : ~ 10
\item   59,77  ~ : ~ 100
\item   1 545  ~ : ~ 10
\item   75,1  ~ : ~ 1 000
\item   585,3  ~ : ~ 100
\item   2,095  ~ : ~ 1 000
\item   6,246  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,3  ~ \(\times\)  ~ ... ~ = ~ 2 300
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 0,89
\item   307  ~ \(\times\)  ~ ... ~ = ~ 307 000
\item   48,4  ~ \(\times\)  ~ ... ~ = ~ 484
\item   76,7  ~ \(\times\)  ~ ... ~ = ~ 767
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 28
\item   0,678  ~ \(\times\)  ~ ... ~ = ~ 67,8
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 9,7
\item   57,5  ~ \(\times\)  ~ ... ~ = ~ 5 750
\item   80,8  ~ \(\times\)  ~ ... ~ = ~ 808
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   704,9  ~ \(\times\)  ~ 0,1
\item   2 277  ~ \(\times\)  ~ 0,01
\item   2 570  ~ \(\times\)  ~ 0,1
\item   0,702  ~ \(\times\)  ~ 0,1
\item   6 881  ~ \(\times\)  ~ 0,1
\item   1,317  ~ \(\times\)  ~ 0,001
\item   9,295  ~ \(\times\)  ~ 0,01
\item   3,497  ~ \(\times\)  ~ 0,001
\item   42,18  ~ \(\times\)  ~ 0,1
\item   95,8  ~ \(\times\)  ~ 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   1 581  ~ \(\times\)  ~ ... ~ = ~  158,1
\item   3,813  ~ \(\times\)  ~ ... ~ = ~  0,003 813
\item   34,9  ~ \(\times\)  ~ ... ~ = ~  0,034 9
\item   3,047  ~ \(\times\)  ~ ... ~ = ~  0,030 47
\item   51,4  ~ \(\times\)  ~ ... ~ = ~  0,051 4
\item   327,9  ~ \(\times\)  ~ ... ~ = ~  3,279
\item   35,46  ~ \(\times\)  ~ ... ~ = ~  0,035 46
\item   40,82  ~ \(\times\)  ~ ... ~ = ~  0,408 2
\item   364,4  ~ \(\times\)  ~ ... ~ = ~  36,44
\item   746  ~ \(\times\)  ~ ... ~ = ~  0,746
\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~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 785,6 ~dag~ = ...~hg
\item   7 580,5 ~cL~ = ...~L
\item   4 936,3 ~mg~ = ...~dg
\item   3 838,3 ~dg~ = ...~hg
\item   312,43 ~km~ = ...~hm
\item   986,2 ~mg~ = ...~hg
\item   6 356,1 ~dL~ = ...~kL
\item   5 517,5 ~hg~ = ...~cg
\item   1 142,2 ~daL~ = ...~hL
\item   301,84 ~mL~ = ...~dL
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{530}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{47}{10}\) = \(\dfrac{470}{100}\)
\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   3,56  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 356}
\item   5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 50}
\item   0,661  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66,1}
\item   64,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 644}
\item   143  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14 300}
\item   0,346  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 34,6}
\item   0,083  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,83}
\item   0,087  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 87}
\item   0,11  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 11}
\item   7,28  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 728}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 438 ~ : ~ 10 ~ = ~{\color{red} 543,8}
\item   320 ~ : ~ 100 ~ = ~{\color{red} 3,2}
\item   8,811 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 811}
\item   315 ~ : ~ 10 ~ = ~{\color{red} 31,5}
\item   59,77 ~ : ~ 100 ~ = ~{\color{red} 0,597 7}
\item   1 545 ~ : ~ 10 ~ = ~{\color{red} 154,5}
\item   75,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,075 1}
\item   585,3 ~ : ~ 100 ~ = ~{\color{red} 5,853}
\item   2,095 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 095}
\item   6,246 ~ : ~ 10 ~ = ~{\color{red} 0,624 6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 300
\item   0,089 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,89
\item   307 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~307 000
\item   48,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~484
\item   76,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~767
\item   0,028 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~28
\item   0,678 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~67,8
\item   0,097 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,7
\item   57,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 750
\item   80,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~808
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   704,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 70,49
}\item   2 277 ~ \(\times\)  0,01 ~ = ~{\color{red} 22,77
}\item   2 570 ~ \(\times\)  0,1 ~ = ~{\color{red} 257
}\item   0,702 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,070 2
}\item   6 881 ~ \(\times\)  0,1 ~ = ~{\color{red} 688,1
}\item   1,317 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 317
}\item   9,295 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,092 95
}\item   3,497 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 497
}\item   42,18 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,218
}\item   95,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,095 8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 581 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 158,1
\item   3,813 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 813
\item   34,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,034 9
\item   3,047 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,030 47
\item   51,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,051 4
\item   327,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,279
\item   35,46 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,035 46
\item   40,82 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,408 2
\item   364,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 36,44
\item   746 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,746
\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}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 785,6 ~dag~ = {\color{red}  378,56 }~hg
\item   7 580,5 ~cL~ = {\color{red}  75,805 }~L
\item   4 936,3 ~mg~ = {\color{red}  49,363 }~dg
\item   3 838,3 ~dg~ = {\color{red}  3,838 3 }~hg
\item   312,43 ~km~ = {\color{red}  3 124,3 }~hm
\item   986,2 ~mg~ = {\color{red}  0,009 862 }~hg
\item   6 356,1 ~dL~ = {\color{red}  0,635 61 }~kL
\item   5 517,5 ~hg~ = {\color{red}  55 175 000 }~cg
\item   1 142,2 ~daL~ = {\color{red}  114,22 }~hL
\item   301,84 ~mL~ = {\color{red}  3,018 4 }~dL
\end{itemize}
\end{multicols}
\end{document}
