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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 124}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{64}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{46}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,15  ~ \(\times\)  ~ 10
\item   33,3  ~ \(\times\)  ~ 100
\item   0,327  ~ \(\times\)  ~ 10
\item   0,565  ~ \(\times\)  ~ 1 000
\item   444  ~ \(\times\)  ~ 10
\item   232  ~ \(\times\)  ~ 100
\item   33,2  ~ \(\times\)  ~ 10
\item   40,6  ~ \(\times\)  ~ 1 000
\item   0,037  ~ \(\times\)  ~ 100
\item   0,781  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,838  ~ : ~ 1 000
\item   8 506  ~ : ~ 100
\item   9,414  ~ : ~ 10
\item   7 396  ~ : ~ 10
\item   8,836  ~ : ~ 10
\item   3,117  ~ : ~ 1 000
\item   8 498  ~ : ~ 1 000
\item   7,434  ~ : ~ 1 000
\item   5,861  ~ : ~ 10
\item   2 933  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   936  ~ \(\times\)  ~ ... ~ = ~ 9 360
\item   0,025  ~ \(\times\)  ~ ... ~ = ~ 25
\item   0,011  ~ \(\times\)  ~ ... ~ = ~ 1,1
\item   0,819  ~ \(\times\)  ~ ... ~ = ~ 819
\item   492  ~ \(\times\)  ~ ... ~ = ~ 492 000
\item   501  ~ \(\times\)  ~ ... ~ = ~ 50 100
\item   0,252  ~ \(\times\)  ~ ... ~ = ~ 252
\item   17,1  ~ \(\times\)  ~ ... ~ = ~ 171
\item   8,24  ~ \(\times\)  ~ ... ~ = ~ 8 240
\item   9,85  ~ \(\times\)  ~ ... ~ = ~ 985
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   726,8  ~ \(\times\)  ~ 0,01
\item   83,15  ~ \(\times\)  ~ 0,01
\item   1 298  ~ \(\times\)  ~ 0,01
\item   6 507  ~ \(\times\)  ~ 0,1
\item   650,6  ~ \(\times\)  ~ 0,001
\item   3,4  ~ \(\times\)  ~ 0,001
\item   3 780  ~ \(\times\)  ~ 0,1
\item   616  ~ \(\times\)  ~ 0,1
\item   189,6  ~ \(\times\)  ~ 0,1
\item   350,2  ~ \(\times\)  ~ 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   0,7  ~ \(\times\)  ~ ... ~ = ~  0,007
\item   7 827  ~ \(\times\)  ~ ... ~ = ~  7,827
\item   967  ~ \(\times\)  ~ ... ~ = ~  9,67
\item   5 935  ~ \(\times\)  ~ ... ~ = ~  593,5
\item   8,829  ~ \(\times\)  ~ ... ~ = ~  0,088 29
\item   30,14  ~ \(\times\)  ~ ... ~ = ~  3,014
\item   4,288  ~ \(\times\)  ~ ... ~ = ~  0,428 8
\item   7 290  ~ \(\times\)  ~ ... ~ = ~  72,9
\item   86,67  ~ \(\times\)  ~ ... ~ = ~  8,667
\item   5,709  ~ \(\times\)  ~ ... ~ = ~  0,005 709
\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~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 068,3 ~cg~ = ...~kg
\item   8 097,2 ~mL~ = ...~dL
\item   259,83 ~cm~ = ...~dm
\item   299,58 ~kL~ = ...~hL
\item   8 940,5 ~hg~ = ...~dg
\item   9 156,8 ~dam~ = ...~dm
\item   812,67 ~g~ = ...~mg
\item   2 783,3 ~kg~ = ...~dag
\item   879,51 ~hm~ = ...~km
\item   9 777,4 ~g~ = ...~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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{3300}{100}\) = \(\dfrac{330}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{64}{10}\) = \(\dfrac{640}{100}\)
\item   \(\dfrac{46}{100}\) = \(\dfrac{460}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,15  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 81,5}
\item   33,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 330}
\item   0,327  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,27}
\item   0,565  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 565}
\item   444  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 440}
\item   232  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 23 200}
\item   33,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 332}
\item   40,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 40 600}
\item   0,037  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,7}
\item   0,781  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,81}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,838 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 838}
\item   8 506 ~ : ~ 100 ~ = ~{\color{red} 85,06}
\item   9,414 ~ : ~ 10 ~ = ~{\color{red} 0,941 4}
\item   7 396 ~ : ~ 10 ~ = ~{\color{red} 739,6}
\item   8,836 ~ : ~ 10 ~ = ~{\color{red} 0,883 6}
\item   3,117 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 117}
\item   8 498 ~ : ~ 1 000 ~ = ~{\color{red} 8,498}
\item   7,434 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 434}
\item   5,861 ~ : ~ 10 ~ = ~{\color{red} 0,586 1}
\item   2 933 ~ : ~ 1 000 ~ = ~{\color{red} 2,933}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   936 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 360
\item   0,025 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~25
\item   0,011 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,1
\item   0,819 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~819
\item   492 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~492 000
\item   501 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~50 100
\item   0,252 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~252
\item   17,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~171
\item   8,24 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 240
\item   9,85 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~985
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   726,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,268
}\item   83,15 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,831 5
}\item   1 298 ~ \(\times\)  0,01 ~ = ~{\color{red} 12,98
}\item   6 507 ~ \(\times\)  0,1 ~ = ~{\color{red} 650,7
}\item   650,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,650 6
}\item   3,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 4
}\item   3 780 ~ \(\times\)  0,1 ~ = ~{\color{red} 378
}\item   616 ~ \(\times\)  0,1 ~ = ~{\color{red} 61,6
}\item   189,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 18,96
}\item   350,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 35,02
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,007
\item   7 827 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,827
\item   967 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,67
\item   5 935 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 593,5
\item   8,829 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,088 29
\item   30,14 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,014
\item   4,288 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,428 8
\item   7 290 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 72,9
\item   86,67 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,667
\item   5,709 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 709
\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~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 068,3 ~cg~ = {\color{red}  0,020 683 }~kg
\item   8 097,2 ~mL~ = {\color{red}  80,972 }~dL
\item   259,83 ~cm~ = {\color{red}  25,983 }~dm
\item   299,58 ~kL~ = {\color{red}  2 995,8 }~hL
\item   8 940,5 ~hg~ = {\color{red}  8 940 500 }~dg
\item   9 156,8 ~dam~ = {\color{red}  915 680 }~dm
\item   812,67 ~g~ = {\color{red}  812 670 }~mg
\item   2 783,3 ~kg~ = {\color{red}  278 330 }~dag
\item   879,51 ~hm~ = {\color{red}  87,951 }~km
\item   9 777,4 ~g~ = {\color{red}  97 774 }~dg
\end{itemize}
\end{multicols}
\end{document}
