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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 311}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{71}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{30}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03  ~ \(\times\)  ~ 10
\item   0,554  ~ \(\times\)  ~ 10
\item   7,4  ~ \(\times\)  ~ 100
\item   10,5  ~ \(\times\)  ~ 1 000
\item   2,73  ~ \(\times\)  ~ 10
\item   59,6  ~ \(\times\)  ~ 1 000
\item   2,76  ~ \(\times\)  ~ 100
\item   0,466  ~ \(\times\)  ~ 10
\item   274  ~ \(\times\)  ~ 1 000
\item   748  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 474  ~ : ~ 100
\item   358,3  ~ : ~ 10
\item   72,84  ~ : ~ 1 000
\item   45,3  ~ : ~ 10
\item   91,4  ~ : ~ 1 000
\item   8,518  ~ : ~ 1 000
\item   10,39  ~ : ~ 10
\item   5 228  ~ : ~ 1 000
\item   5,755  ~ : ~ 100
\item   248,8  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,013  ~ \(\times\)  ~ ... ~ = ~ 13
\item   85,4  ~ \(\times\)  ~ ... ~ = ~ 85 400
\item   42  ~ \(\times\)  ~ ... ~ = ~ 4 200
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 6,2
\item   0,081  ~ \(\times\)  ~ ... ~ = ~ 81
\item   22,1  ~ \(\times\)  ~ ... ~ = ~ 22 100
\item   7,35  ~ \(\times\)  ~ ... ~ = ~ 735
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 0,63
\item   36,3  ~ \(\times\)  ~ ... ~ = ~ 3 630
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 45
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 376  ~ \(\times\)  ~ 0,01
\item   732,6  ~ \(\times\)  ~ 0,001
\item   98,44  ~ \(\times\)  ~ 0,1
\item   792  ~ \(\times\)  ~ 0,001
\item   5,531  ~ \(\times\)  ~ 0,01
\item   702  ~ \(\times\)  ~ 0,01
\item   3 820  ~ \(\times\)  ~ 0,01
\item   8 793  ~ \(\times\)  ~ 0,01
\item   64,93  ~ \(\times\)  ~ 0,1
\item   30,52  ~ \(\times\)  ~ 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   6 851  ~ \(\times\)  ~ ... ~ = ~  685,1
\item   6 609  ~ \(\times\)  ~ ... ~ = ~  6,609
\item   8,44  ~ \(\times\)  ~ ... ~ = ~  0,844
\item   92,61  ~ \(\times\)  ~ ... ~ = ~  9,261
\item   61,88  ~ \(\times\)  ~ ... ~ = ~  6,188
\item   5 317  ~ \(\times\)  ~ ... ~ = ~  531,7
\item   119,5  ~ \(\times\)  ~ ... ~ = ~  1,195
\item   38,57  ~ \(\times\)  ~ ... ~ = ~  0,038 57
\item   157,5  ~ \(\times\)  ~ ... ~ = ~  1,575
\item   691,1  ~ \(\times\)  ~ ... ~ = ~  6,911
\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~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 176 ~dL~ = ...~kL
\item   781,13 ~dam~ = ...~km
\item   175,05 ~km~ = ...~m
\item   9 805,6 ~hL~ = ...~kL
\item   767,54 ~dam~ = ...~dm
\item   295,38 ~cg~ = ...~hg
\item   151,41 ~hg~ = ...~g
\item   6 705,2 ~g~ = ...~dg
\item   684,43 ~dam~ = ...~hm
\item   7 767,3 ~dag~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{2000}{100}\) = \(\dfrac{200}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{71}{10}\) = \(\dfrac{710}{100}\)
\item   \(\dfrac{30}{100}\) = \(\dfrac{300}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,3}
\item   0,554  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,54}
\item   7,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 740}
\item   10,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 10 500}
\item   2,73  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 27,3}
\item   59,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 59 600}
\item   2,76  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 276}
\item   0,466  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,66}
\item   274  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 274 000}
\item   748  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 748 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 474 ~ : ~ 100 ~ = ~{\color{red} 94,74}
\item   358,3 ~ : ~ 10 ~ = ~{\color{red} 35,83}
\item   72,84 ~ : ~ 1 000 ~ = ~{\color{red} 0,072 84}
\item   45,3 ~ : ~ 10 ~ = ~{\color{red} 4,53}
\item   91,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,091 4}
\item   8,518 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 518}
\item   10,39 ~ : ~ 10 ~ = ~{\color{red} 1,039}
\item   5 228 ~ : ~ 1 000 ~ = ~{\color{red} 5,228}
\item   5,755 ~ : ~ 100 ~ = ~{\color{red} 0,057 55}
\item   248,8 ~ : ~ 10 ~ = ~{\color{red} 24,88}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,013 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~13
\item   85,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~85 400
\item   42 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 200
\item   0,062 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,2
\item   0,081 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~81
\item   22,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~22 100
\item   7,35 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~735
\item   0,063 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,63
\item   36,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 630
\item   0,045 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~45
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 376 ~ \(\times\)  0,01 ~ = ~{\color{red} 63,76
}\item   732,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,732 6
}\item   98,44 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,844
}\item   792 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,792
}\item   5,531 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,055 31
}\item   702 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,02
}\item   3 820 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,2
}\item   8 793 ~ \(\times\)  0,01 ~ = ~{\color{red} 87,93
}\item   64,93 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,493
}\item   30,52 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 52
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 851 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 685,1
\item   6 609 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,609
\item   8,44 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,844
\item   92,61 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,261
\item   61,88 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,188
\item   5 317 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 531,7
\item   119,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,195
\item   38,57 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,038 57
\item   157,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,575
\item   691,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,911
\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~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 176 ~dL~ = {\color{red}  0,417 6 }~kL
\item   781,13 ~dam~ = {\color{red}  7,811 3 }~km
\item   175,05 ~km~ = {\color{red}  175 050 }~m
\item   9 805,6 ~hL~ = {\color{red}  980,56 }~kL
\item   767,54 ~dam~ = {\color{red}  76 754 }~dm
\item   295,38 ~cg~ = {\color{red}  0,029 538 }~hg
\item   151,41 ~hg~ = {\color{red}  15 141 }~g
\item   6 705,2 ~g~ = {\color{red}  67 052 }~dg
\item   684,43 ~dam~ = {\color{red}  68,443 }~hm
\item   7 767,3 ~dag~ = {\color{red}  776 730 }~dg
\end{itemize}
\end{multicols}
\end{document}
