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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 177}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{62}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,045  ~ \(\times\)  ~ 1 000
\item   8,47  ~ \(\times\)  ~ 1 000
\item   8,47  ~ \(\times\)  ~ 10
\item   854  ~ \(\times\)  ~ 10
\item   0,084  ~ \(\times\)  ~ 1 000
\item   8,27  ~ \(\times\)  ~ 100
\item   9,43  ~ \(\times\)  ~ 1 000
\item   0,477  ~ \(\times\)  ~ 1 000
\item   86  ~ \(\times\)  ~ 1 000
\item   80,7  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   494,8  ~ : ~ 1 000
\item   7 169  ~ : ~ 10
\item   22,17  ~ : ~ 10
\item   68,56  ~ : ~ 1 000
\item   57,55  ~ : ~ 100
\item   164  ~ : ~ 10
\item   9,091  ~ : ~ 1 000
\item   937,6  ~ : ~ 1 000
\item   551,3  ~ : ~ 10
\item   685  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 6,2
\item   51,9  ~ \(\times\)  ~ ... ~ = ~ 51 900
\item   0,114  ~ \(\times\)  ~ ... ~ = ~ 11,4
\item   6,53  ~ \(\times\)  ~ ... ~ = ~ 6 530
\item   0,346  ~ \(\times\)  ~ ... ~ = ~ 346
\item   6,05  ~ \(\times\)  ~ ... ~ = ~ 605
\item   0,24  ~ \(\times\)  ~ ... ~ = ~ 24
\item   6,02  ~ \(\times\)  ~ ... ~ = ~ 6 020
\item   0,003  ~ \(\times\)  ~ ... ~ = ~ 0,03
\item   775  ~ \(\times\)  ~ ... ~ = ~ 775 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,67  ~ \(\times\)  ~ 0,01
\item   0,693  ~ \(\times\)  ~ 0,001
\item   45,35  ~ \(\times\)  ~ 0,1
\item   34  ~ \(\times\)  ~ 0,001
\item   54,69  ~ \(\times\)  ~ 0,01
\item   7 868  ~ \(\times\)  ~ 0,1
\item   67,83  ~ \(\times\)  ~ 0,01
\item   24,56  ~ \(\times\)  ~ 0,001
\item   8,767  ~ \(\times\)  ~ 0,1
\item   913,2  ~ \(\times\)  ~ 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   11,03  ~ \(\times\)  ~ ... ~ = ~  0,110 3
\item   85,63  ~ \(\times\)  ~ ... ~ = ~  8,563
\item   0,854  ~ \(\times\)  ~ ... ~ = ~  0,000 854
\item   93,33  ~ \(\times\)  ~ ... ~ = ~  0,093 33
\item   455,6  ~ \(\times\)  ~ ... ~ = ~  4,556
\item   8,99  ~ \(\times\)  ~ ... ~ = ~  0,899
\item   5 035  ~ \(\times\)  ~ ... ~ = ~  5,035
\item   985,4  ~ \(\times\)  ~ ... ~ = ~  9,854
\item   268,5  ~ \(\times\)  ~ ... ~ = ~  0,268 5
\item   7 305  ~ \(\times\)  ~ ... ~ = ~  730,5
\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 ~dm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 743,8 ~dam~ = ...~mm
\item   849,87 ~kg~ = ...~hg
\item   919,38 ~m~ = ...~dam
\item   226,64 ~dm~ = ...~cm
\item   2 835,8 ~dam~ = ...~hm
\item   449,96 ~dg~ = ...~cg
\item   878,35 ~kL~ = ...~L
\item   7 485,8 ~kg~ = ...~mg
\item   7 432,9 ~m~ = ...~hm
\item   2 802,1 ~daL~ = ...~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   4 = \(\dfrac{40}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{6400}{100}\) = \(\dfrac{640}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{62}{10}\) = \(\dfrac{620}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{160}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,045  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 45}
\item   8,47  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 470}
\item   8,47  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 84,7}
\item   854  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 540}
\item   0,084  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84}
\item   8,27  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 827}
\item   9,43  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 430}
\item   0,477  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 477}
\item   86  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 86 000}
\item   80,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 80 700}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   494,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,494 8}
\item   7 169 ~ : ~ 10 ~ = ~{\color{red} 716,9}
\item   22,17 ~ : ~ 10 ~ = ~{\color{red} 2,217}
\item   68,56 ~ : ~ 1 000 ~ = ~{\color{red} 0,068 56}
\item   57,55 ~ : ~ 100 ~ = ~{\color{red} 0,575 5}
\item   164 ~ : ~ 10 ~ = ~{\color{red} 16,4}
\item   9,091 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 091}
\item   937,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,937 6}
\item   551,3 ~ : ~ 10 ~ = ~{\color{red} 55,13}
\item   685 ~ : ~ 100 ~ = ~{\color{red} 6,85}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,062 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,2
\item   51,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~51 900
\item   0,114 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~11,4
\item   6,53 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 530
\item   0,346 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~346
\item   6,05 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~605
\item   0,24 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~24
\item   6,02 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 020
\item   0,003 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,03
\item   775 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~775 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,67 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,786 7
}\item   0,693 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 693
}\item   45,35 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,535
}\item   34 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,034
}\item   54,69 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,546 9
}\item   7 868 ~ \(\times\)  0,1 ~ = ~{\color{red} 786,8
}\item   67,83 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,678 3
}\item   24,56 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,024 56
}\item   8,767 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,876 7
}\item   913,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,913 2
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,03 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,110 3
\item   85,63 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,563
\item   0,854 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 854
\item   93,33 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,093 33
\item   455,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,556
\item   8,99 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,899
\item   5 035 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,035
\item   985,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,854
\item   268,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,268 5
\item   7 305 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 730,5
\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 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 743,8 ~dam~ = {\color{red}  37 438 000 }~mm
\item   849,87 ~kg~ = {\color{red}  8 498,7 }~hg
\item   919,38 ~m~ = {\color{red}  91,938 }~dam
\item   226,64 ~dm~ = {\color{red}  2 266,4 }~cm
\item   2 835,8 ~dam~ = {\color{red}  283,58 }~hm
\item   449,96 ~dg~ = {\color{red}  4 499,6 }~cg
\item   878,35 ~kL~ = {\color{red}  878 350 }~L
\item   7 485,8 ~kg~ = {\color{red}  7 485 800 000 }~mg
\item   7 432,9 ~m~ = {\color{red}  74,329 }~hm
\item   2 802,1 ~daL~ = {\color{red}  280 210 }~dL
\end{itemize}
\end{multicols}
\end{document}
