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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 273}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{27}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   873  ~ \(\times\)  ~ 1 000
\item   0,02  ~ \(\times\)  ~ 10
\item   0,499  ~ \(\times\)  ~ 1 000
\item   8,77  ~ \(\times\)  ~ 10
\item   0,753  ~ \(\times\)  ~ 100
\item   0,025  ~ \(\times\)  ~ 1 000
\item   16,9  ~ \(\times\)  ~ 1 000
\item   0,055  ~ \(\times\)  ~ 100
\item   39,2  ~ \(\times\)  ~ 100
\item   0,082  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 874  ~ : ~ 100
\item   251,3  ~ : ~ 100
\item   1,127  ~ : ~ 100
\item   757,4  ~ : ~ 100
\item   0,791  ~ : ~ 1 000
\item   41,31  ~ : ~ 100
\item   720,8  ~ : ~ 1 000
\item   2 313  ~ : ~ 1 000
\item   44,54  ~ : ~ 1 000
\item   8,272  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,55  ~ \(\times\)  ~ ... ~ = ~ 5,5
\item   44,8  ~ \(\times\)  ~ ... ~ = ~ 448
\item   0,016  ~ \(\times\)  ~ ... ~ = ~ 0,16
\item   698  ~ \(\times\)  ~ ... ~ = ~ 698 000
\item   0,054  ~ \(\times\)  ~ ... ~ = ~ 0,54
\item   0,846  ~ \(\times\)  ~ ... ~ = ~ 84,6
\item   0,066  ~ \(\times\)  ~ ... ~ = ~ 66
\item   58  ~ \(\times\)  ~ ... ~ = ~ 5 800
\item   7,51  ~ \(\times\)  ~ ... ~ = ~ 75,1
\item   0,078  ~ \(\times\)  ~ ... ~ = ~ 78
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,566  ~ \(\times\)  ~ 0,01
\item   30,92  ~ \(\times\)  ~ 0,001
\item   4 836  ~ \(\times\)  ~ 0,1
\item   8,201  ~ \(\times\)  ~ 0,001
\item   1,05  ~ \(\times\)  ~ 0,1
\item   5,489  ~ \(\times\)  ~ 0,001
\item   595,6  ~ \(\times\)  ~ 0,01
\item   5 288  ~ \(\times\)  ~ 0,1
\item   813  ~ \(\times\)  ~ 0,001
\item   1 127  ~ \(\times\)  ~ 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   37,6  ~ \(\times\)  ~ ... ~ = ~  0,376
\item   1,385  ~ \(\times\)  ~ ... ~ = ~  0,013 85
\item   8,562  ~ \(\times\)  ~ ... ~ = ~  0,085 62
\item   5,972  ~ \(\times\)  ~ ... ~ = ~  0,597 2
\item   8 501  ~ \(\times\)  ~ ... ~ = ~  8,501
\item   509  ~ \(\times\)  ~ ... ~ = ~  50,9
\item   28,7  ~ \(\times\)  ~ ... ~ = ~  2,87
\item   9,062  ~ \(\times\)  ~ ... ~ = ~  0,090 62
\item   617  ~ \(\times\)  ~ ... ~ = ~  0,617
\item   1,467  ~ \(\times\)  ~ ... ~ = ~  0,001 467
\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~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   948,65 ~mL~ = ...~hL
\item   6 630,9 ~g~ = ...~hg
\item   6 375,9 ~hm~ = ...~m
\item   186,65 ~cm~ = ...~dm
\item   1 954,6 ~m~ = ...~hm
\item   855,27 ~mm~ = ...~hm
\item   7 696 ~g~ = ...~mg
\item   399,64 ~daL~ = ...~dL
\item   790,37 ~cg~ = ...~dg
\item   9 222,2 ~m~ = ...~km
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{5000}{100}\) = \(\dfrac{500}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{27}{10}\) = \(\dfrac{270}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{390}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   873  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 873 000}
\item   0,02  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,2}
\item   0,499  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 499}
\item   8,77  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 87,7}
\item   0,753  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 75,3}
\item   0,025  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 25}
\item   16,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 16 900}
\item   0,055  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,5}
\item   39,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 920}
\item   0,082  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 82}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 874 ~ : ~ 100 ~ = ~{\color{red} 48,74}
\item   251,3 ~ : ~ 100 ~ = ~{\color{red} 2,513}
\item   1,127 ~ : ~ 100 ~ = ~{\color{red} 0,011 27}
\item   757,4 ~ : ~ 100 ~ = ~{\color{red} 7,574}
\item   0,791 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 791}
\item   41,31 ~ : ~ 100 ~ = ~{\color{red} 0,413 1}
\item   720,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,720 8}
\item   2 313 ~ : ~ 1 000 ~ = ~{\color{red} 2,313}
\item   44,54 ~ : ~ 1 000 ~ = ~{\color{red} 0,044 54}
\item   8,272 ~ : ~ 100 ~ = ~{\color{red} 0,082 72}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,55 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,5
\item   44,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~448
\item   0,016 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,16
\item   698 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~698 000
\item   0,054 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,54
\item   0,846 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~84,6
\item   0,066 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~66
\item   58 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 800
\item   7,51 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~75,1
\item   0,078 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~78
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,566 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,005 66
}\item   30,92 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 92
}\item   4 836 ~ \(\times\)  0,1 ~ = ~{\color{red} 483,6
}\item   8,201 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 201
}\item   1,05 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,105
}\item   5,489 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 489
}\item   595,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,956
}\item   5 288 ~ \(\times\)  0,1 ~ = ~{\color{red} 528,8
}\item   813 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,813
}\item   1 127 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,127
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   37,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,376
\item   1,385 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,013 85
\item   8,562 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,085 62
\item   5,972 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,597 2
\item   8 501 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,501
\item   509 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 50,9
\item   28,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,87
\item   9,062 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,090 62
\item   617 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,617
\item   1,467 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 467
\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}  100 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   948,65 ~mL~ = {\color{red}  0,009 486 5 }~hL
\item   6 630,9 ~g~ = {\color{red}  66,309 }~hg
\item   6 375,9 ~hm~ = {\color{red}  637 590 }~m
\item   186,65 ~cm~ = {\color{red}  18,665 }~dm
\item   1 954,6 ~m~ = {\color{red}  19,546 }~hm
\item   855,27 ~mm~ = {\color{red}  0,008 552 7 }~hm
\item   7 696 ~g~ = {\color{red}  7 696 000 }~mg
\item   399,64 ~daL~ = {\color{red}  39 964 }~dL
\item   790,37 ~cg~ = {\color{red}  79,037 }~dg
\item   9 222,2 ~m~ = {\color{red}  9,222 2 }~km
\end{itemize}
\end{multicols}
\end{document}
