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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 29}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,58  ~ \(\times\)  ~ 100
\item   434  ~ \(\times\)  ~ 10
\item   0,115  ~ \(\times\)  ~ 1 000
\item   2,39  ~ \(\times\)  ~ 10
\item   5,18  ~ \(\times\)  ~ 1 000
\item   0,564  ~ \(\times\)  ~ 1 000
\item   0,213  ~ \(\times\)  ~ 10
\item   0,233  ~ \(\times\)  ~ 100
\item   0,07  ~ \(\times\)  ~ 1 000
\item   0,021  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   70,22  ~ : ~ 100
\item   848,7  ~ : ~ 100
\item   784,2  ~ : ~ 100
\item   5,004  ~ : ~ 100
\item   17,26  ~ : ~ 10
\item   442,7  ~ : ~ 1 000
\item   5 682  ~ : ~ 1 000
\item   661,9  ~ : ~ 100
\item   7,08  ~ : ~ 100
\item   26,51  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,4  ~ \(\times\)  ~ ... ~ = ~ 90 400
\item   294  ~ \(\times\)  ~ ... ~ = ~ 2 940
\item   0,417  ~ \(\times\)  ~ ... ~ = ~ 417
\item   0,148  ~ \(\times\)  ~ ... ~ = ~ 1,48
\item   306  ~ \(\times\)  ~ ... ~ = ~ 3 060
\item   750  ~ \(\times\)  ~ ... ~ = ~ 750 000
\item   324  ~ \(\times\)  ~ ... ~ = ~ 3 240
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 0,97
\item   980  ~ \(\times\)  ~ ... ~ = ~ 980 000
\item   792  ~ \(\times\)  ~ ... ~ = ~ 7 920
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,957  ~ \(\times\)  ~ 0,01
\item   3 879  ~ \(\times\)  ~ 0,1
\item   32,58  ~ \(\times\)  ~ 0,01
\item   46,6  ~ \(\times\)  ~ 0,1
\item   194,8  ~ \(\times\)  ~ 0,1
\item   629,9  ~ \(\times\)  ~ 0,1
\item   343,2  ~ \(\times\)  ~ 0,01
\item   3 819  ~ \(\times\)  ~ 0,001
\item   19,89  ~ \(\times\)  ~ 0,01
\item   3,89  ~ \(\times\)  ~ 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   5,378  ~ \(\times\)  ~ ... ~ = ~  0,053 78
\item   953,2  ~ \(\times\)  ~ ... ~ = ~  9,532
\item   6 777  ~ \(\times\)  ~ ... ~ = ~  67,77
\item   0,963  ~ \(\times\)  ~ ... ~ = ~  0,009 63
\item   8 292  ~ \(\times\)  ~ ... ~ = ~  8,292
\item   5,424  ~ \(\times\)  ~ ... ~ = ~  0,542 4
\item   256,5  ~ \(\times\)  ~ ... ~ = ~  2,565
\item   7,815  ~ \(\times\)  ~ ... ~ = ~  0,007 815
\item   8 515  ~ \(\times\)  ~ ... ~ = ~  85,15
\item   3,351  ~ \(\times\)  ~ ... ~ = ~  0,335 1
\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 ~km~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 751,6 ~dg~ = ...~mg
\item   6 898,1 ~dg~ = ...~kg
\item   8 093,4 ~dg~ = ...~cg
\item   692,13 ~dL~ = ...~mL
\item   849,75 ~hL~ = ...~cL
\item   884,81 ~kL~ = ...~L
\item   553,95 ~dam~ = ...~m
\item   550,72 ~m~ = ...~hm
\item   140,2 ~cm~ = ...~hm
\item   1 626,7 ~mm~ = ...~dam
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{5500}{100}\) = \(\dfrac{550}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{220}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{760}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,58  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 958}
\item   434  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 340}
\item   0,115  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 115}
\item   2,39  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 23,9}
\item   5,18  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 180}
\item   0,564  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 564}
\item   0,213  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,13}
\item   0,233  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 23,3}
\item   0,07  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 70}
\item   0,021  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 21}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   70,22 ~ : ~ 100 ~ = ~{\color{red} 0,702 2}
\item   848,7 ~ : ~ 100 ~ = ~{\color{red} 8,487}
\item   784,2 ~ : ~ 100 ~ = ~{\color{red} 7,842}
\item   5,004 ~ : ~ 100 ~ = ~{\color{red} 0,050 04}
\item   17,26 ~ : ~ 10 ~ = ~{\color{red} 1,726}
\item   442,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,442 7}
\item   5 682 ~ : ~ 1 000 ~ = ~{\color{red} 5,682}
\item   661,9 ~ : ~ 100 ~ = ~{\color{red} 6,619}
\item   7,08 ~ : ~ 100 ~ = ~{\color{red} 0,070 8}
\item   26,51 ~ : ~ 1 000 ~ = ~{\color{red} 0,026 51}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~90 400
\item   294 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 940
\item   0,417 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~417
\item   0,148 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,48
\item   306 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 060
\item   750 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~750 000
\item   324 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 240
\item   0,097 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,97
\item   980 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~980 000
\item   792 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 920
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,957 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,029 57
}\item   3 879 ~ \(\times\)  0,1 ~ = ~{\color{red} 387,9
}\item   32,58 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,325 8
}\item   46,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,66
}\item   194,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 19,48
}\item   629,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 62,99
}\item   343,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,432
}\item   3 819 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,819
}\item   19,89 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,198 9
}\item   3,89 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,389
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,378 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,053 78
\item   953,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,532
\item   6 777 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 67,77
\item   0,963 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,009 63
\item   8 292 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,292
\item   5,424 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,542 4
\item   256,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,565
\item   7,815 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 815
\item   8 515 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 85,15
\item   3,351 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,335 1
\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 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 751,6 ~dg~ = {\color{red}  375 160 }~mg
\item   6 898,1 ~dg~ = {\color{red}  0,689 81 }~kg
\item   8 093,4 ~dg~ = {\color{red}  80 934 }~cg
\item   692,13 ~dL~ = {\color{red}  69 213 }~mL
\item   849,75 ~hL~ = {\color{red}  8 497 500 }~cL
\item   884,81 ~kL~ = {\color{red}  884 810 }~L
\item   553,95 ~dam~ = {\color{red}  5 539,5 }~m
\item   550,72 ~m~ = {\color{red}  5,507 2 }~hm
\item   140,2 ~cm~ = {\color{red}  0,014 02 }~hm
\item   1 626,7 ~mm~ = {\color{red}  0,162 67 }~dam
\end{itemize}
\end{multicols}
\end{document}
