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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 184}

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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   \(\dfrac{4100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{53}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,084  ~ \(\times\)  ~ 1 000
\item   95,8  ~ \(\times\)  ~ 100
\item   608  ~ \(\times\)  ~ 10
\item   5,31  ~ \(\times\)  ~ 100
\item   1,85  ~ \(\times\)  ~ 10
\item   0,78  ~ \(\times\)  ~ 10
\item   671  ~ \(\times\)  ~ 1 000
\item   0,008  ~ \(\times\)  ~ 100
\item   0,22  ~ \(\times\)  ~ 100
\item   617  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 808  ~ : ~ 100
\item   5,818  ~ : ~ 1 000
\item   17,22  ~ : ~ 1 000
\item   335,5  ~ : ~ 10
\item   2 447  ~ : ~ 10
\item   4,679  ~ : ~ 100
\item   75,39  ~ : ~ 10
\item   2,128  ~ : ~ 10
\item   6,553  ~ : ~ 100
\item   9,844  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,092  ~ \(\times\)  ~ ... ~ = ~ 9,2
\item   0,338  ~ \(\times\)  ~ ... ~ = ~ 3,38
\item   0,078  ~ \(\times\)  ~ ... ~ = ~ 7,8
\item   1,78  ~ \(\times\)  ~ ... ~ = ~ 1 780
\item   593  ~ \(\times\)  ~ ... ~ = ~ 593 000
\item   9,43  ~ \(\times\)  ~ ... ~ = ~ 94,3
\item   2,6  ~ \(\times\)  ~ ... ~ = ~ 26
\item   0,049  ~ \(\times\)  ~ ... ~ = ~ 4,9
\item   137  ~ \(\times\)  ~ ... ~ = ~ 1 370
\item   0,486  ~ \(\times\)  ~ ... ~ = ~ 48,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 997  ~ \(\times\)  ~ 0,1
\item   4 842  ~ \(\times\)  ~ 0,1
\item   452,2  ~ \(\times\)  ~ 0,01
\item   312,4  ~ \(\times\)  ~ 0,01
\item   4,366  ~ \(\times\)  ~ 0,01
\item   6,86  ~ \(\times\)  ~ 0,001
\item   9 270  ~ \(\times\)  ~ 0,001
\item   0,361  ~ \(\times\)  ~ 0,1
\item   7,583  ~ \(\times\)  ~ 0,1
\item   46,46  ~ \(\times\)  ~ 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   65,88  ~ \(\times\)  ~ ... ~ = ~  0,658 8
\item   78,13  ~ \(\times\)  ~ ... ~ = ~  0,078 13
\item   3 847  ~ \(\times\)  ~ ... ~ = ~  384,7
\item   815,3  ~ \(\times\)  ~ ... ~ = ~  8,153
\item   5,79  ~ \(\times\)  ~ ... ~ = ~  0,005 79
\item   1 764  ~ \(\times\)  ~ ... ~ = ~  1,764
\item   4,846  ~ \(\times\)  ~ ... ~ = ~  0,484 6
\item   5 504  ~ \(\times\)  ~ ... ~ = ~  550,4
\item   198,9  ~ \(\times\)  ~ ... ~ = ~  19,89
\item   74,59  ~ \(\times\)  ~ ... ~ = ~  7,459
\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~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   682,19 ~g~ = ...~dag
\item   441,58 ~mm~ = ...~dm
\item   4 426,1 ~dam~ = ...~km
\item   511,27 ~dm~ = ...~m
\item   1 123,3 ~cm~ = ...~dam
\item   268,73 ~m~ = ...~hm
\item   515,01 ~mm~ = ...~cm
\item   787 ~mg~ = ...~g
\item   635,73 ~hg~ = ...~mg
\item   198,92 ~mm~ = ...~hm
\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   \(\dfrac{4100}{100}\) = \(\dfrac{410}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{53}{10}\) = \(\dfrac{530}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{540}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,084  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84}
\item   95,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 580}
\item   608  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 080}
\item   5,31  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 531}
\item   1,85  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 18,5}
\item   0,78  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,8}
\item   671  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 671 000}
\item   0,008  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,8}
\item   0,22  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 22}
\item   617  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 617 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 808 ~ : ~ 100 ~ = ~{\color{red} 48,08}
\item   5,818 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 818}
\item   17,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,017 22}
\item   335,5 ~ : ~ 10 ~ = ~{\color{red} 33,55}
\item   2 447 ~ : ~ 10 ~ = ~{\color{red} 244,7}
\item   4,679 ~ : ~ 100 ~ = ~{\color{red} 0,046 79}
\item   75,39 ~ : ~ 10 ~ = ~{\color{red} 7,539}
\item   2,128 ~ : ~ 10 ~ = ~{\color{red} 0,212 8}
\item   6,553 ~ : ~ 100 ~ = ~{\color{red} 0,065 53}
\item   9,844 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 844}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,092 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,2
\item   0,338 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,38
\item   0,078 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,8
\item   1,78 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 780
\item   593 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~593 000
\item   9,43 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~94,3
\item   2,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~26
\item   0,049 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4,9
\item   137 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 370
\item   0,486 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~48,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 997 ~ \(\times\)  0,1 ~ = ~{\color{red} 299,7
}\item   4 842 ~ \(\times\)  0,1 ~ = ~{\color{red} 484,2
}\item   452,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,522
}\item   312,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,124
}\item   4,366 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,043 66
}\item   6,86 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 86
}\item   9 270 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,27
}\item   0,361 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,036 1
}\item   7,583 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,758 3
}\item   46,46 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,646
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   65,88 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,658 8
\item   78,13 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,078 13
\item   3 847 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 384,7
\item   815,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,153
\item   5,79 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 79
\item   1 764 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,764
\item   4,846 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,484 6
\item   5 504 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 550,4
\item   198,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 19,89
\item   74,59 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,459
\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 ~ }hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   682,19 ~g~ = {\color{red}  68,219 }~dag
\item   441,58 ~mm~ = {\color{red}  4,415 8 }~dm
\item   4 426,1 ~dam~ = {\color{red}  44,261 }~km
\item   511,27 ~dm~ = {\color{red}  51,127 }~m
\item   1 123,3 ~cm~ = {\color{red}  1,123 3 }~dam
\item   268,73 ~m~ = {\color{red}  2,687 3 }~hm
\item   515,01 ~mm~ = {\color{red}  51,501 }~cm
\item   787 ~mg~ = {\color{red}  0,787 }~g
\item   635,73 ~hg~ = {\color{red}  63 573 000 }~mg
\item   198,92 ~mm~ = {\color{red}  0,001 989 2 }~hm
\end{itemize}
\end{multicols}
\end{document}
