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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 393}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\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   \(\dfrac{69}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,7  ~ \(\times\)  ~ 10
\item   23,7  ~ \(\times\)  ~ 10
\item   24  ~ \(\times\)  ~ 10
\item   0,048  ~ \(\times\)  ~ 1 000
\item   21,8  ~ \(\times\)  ~ 1 000
\item   0,061  ~ \(\times\)  ~ 100
\item   550  ~ \(\times\)  ~ 100
\item   15,3  ~ \(\times\)  ~ 1 000
\item   0,648  ~ \(\times\)  ~ 1 000
\item   35,4  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,432  ~ : ~ 100
\item   4,455  ~ : ~ 100
\item   1,89  ~ : ~ 10
\item   8,088  ~ : ~ 100
\item   9,232  ~ : ~ 10
\item   1,004  ~ : ~ 100
\item   3 034  ~ : ~ 1 000
\item   1 344  ~ : ~ 10
\item   883,1  ~ : ~ 10
\item   1,39  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   875  ~ \(\times\)  ~ ... ~ = ~ 875 000
\item   29  ~ \(\times\)  ~ ... ~ = ~ 2 900
\item   46,6  ~ \(\times\)  ~ ... ~ = ~ 466
\item   0,796  ~ \(\times\)  ~ ... ~ = ~ 796
\item   913  ~ \(\times\)  ~ ... ~ = ~ 91 300
\item   33,6  ~ \(\times\)  ~ ... ~ = ~ 33 600
\item   9,12  ~ \(\times\)  ~ ... ~ = ~ 91,2
\item   0,432  ~ \(\times\)  ~ ... ~ = ~ 4,32
\item   22  ~ \(\times\)  ~ ... ~ = ~ 2 200
\item   6,52  ~ \(\times\)  ~ ... ~ = ~ 652
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   740,7  ~ \(\times\)  ~ 0,01
\item   311,3  ~ \(\times\)  ~ 0,001
\item   8 994  ~ \(\times\)  ~ 0,01
\item   5 258  ~ \(\times\)  ~ 0,1
\item   97,64  ~ \(\times\)  ~ 0,001
\item   1,512  ~ \(\times\)  ~ 0,001
\item   3 390  ~ \(\times\)  ~ 0,001
\item   6,438  ~ \(\times\)  ~ 0,001
\item   862,8  ~ \(\times\)  ~ 0,1
\item   5 069  ~ \(\times\)  ~ 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   20,73  ~ \(\times\)  ~ ... ~ = ~  2,073
\item   9,057  ~ \(\times\)  ~ ... ~ = ~  0,009 057
\item   912,2  ~ \(\times\)  ~ ... ~ = ~  9,122
\item   440,1  ~ \(\times\)  ~ ... ~ = ~  44,01
\item   465,2  ~ \(\times\)  ~ ... ~ = ~  4,652
\item   233,2  ~ \(\times\)  ~ ... ~ = ~  0,233 2
\item   4,151  ~ \(\times\)  ~ ... ~ = ~  0,415 1
\item   617,9  ~ \(\times\)  ~ ... ~ = ~  61,79
\item   78,49  ~ \(\times\)  ~ ... ~ = ~  0,784 9
\item   44,97  ~ \(\times\)  ~ ... ~ = ~  0,449 7
\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 ~dam~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   593,19 ~cg~ = ...~hg
\item   9 281,2 ~mm~ = ...~dm
\item   4 561 ~cL~ = ...~hL
\item   6 863,1 ~dm~ = ...~km
\item   205,83 ~cg~ = ...~dag
\item   9 104 ~hL~ = ...~mL
\item   8 919 ~dL~ = ...~cL
\item   2 734,7 ~hL~ = ...~kL
\item   516,86 ~dam~ = ...~dm
\item   3 685,2 ~hL~ = ...~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   6 = \(\dfrac{60}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{320}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{64}{10}\) = \(\dfrac{640}{100}\)
\item   \(\dfrac{69}{100}\) = \(\dfrac{690}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 587}
\item   23,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 237}
\item   24  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 240}
\item   0,048  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 48}
\item   21,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 21 800}
\item   0,061  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,1}
\item   550  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 55 000}
\item   15,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 15 300}
\item   0,648  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 648}
\item   35,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 35 400}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,432 ~ : ~ 100 ~ = ~{\color{red} 0,084 32}
\item   4,455 ~ : ~ 100 ~ = ~{\color{red} 0,044 55}
\item   1,89 ~ : ~ 10 ~ = ~{\color{red} 0,189}
\item   8,088 ~ : ~ 100 ~ = ~{\color{red} 0,080 88}
\item   9,232 ~ : ~ 10 ~ = ~{\color{red} 0,923 2}
\item   1,004 ~ : ~ 100 ~ = ~{\color{red} 0,010 04}
\item   3 034 ~ : ~ 1 000 ~ = ~{\color{red} 3,034}
\item   1 344 ~ : ~ 10 ~ = ~{\color{red} 134,4}
\item   883,1 ~ : ~ 10 ~ = ~{\color{red} 88,31}
\item   1,39 ~ : ~ 100 ~ = ~{\color{red} 0,013 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   875 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~875 000
\item   29 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 900
\item   46,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~466
\item   0,796 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~796
\item   913 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~91 300
\item   33,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33 600
\item   9,12 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~91,2
\item   0,432 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,32
\item   22 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 200
\item   6,52 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~652
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   740,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,407
}\item   311,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,311 3
}\item   8 994 ~ \(\times\)  0,01 ~ = ~{\color{red} 89,94
}\item   5 258 ~ \(\times\)  0,1 ~ = ~{\color{red} 525,8
}\item   97,64 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,097 64
}\item   1,512 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 512
}\item   3 390 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,39
}\item   6,438 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 438
}\item   862,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 86,28
}\item   5 069 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,069
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,73 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,073
\item   9,057 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 057
\item   912,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,122
\item   440,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 44,01
\item   465,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,652
\item   233,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,233 2
\item   4,151 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,415 1
\item   617,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 61,79
\item   78,49 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,784 9
\item   44,97 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,449 7
\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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   593,19 ~cg~ = {\color{red}  0,059 319 }~hg
\item   9 281,2 ~mm~ = {\color{red}  92,812 }~dm
\item   4 561 ~cL~ = {\color{red}  0,456 1 }~hL
\item   6 863,1 ~dm~ = {\color{red}  0,686 31 }~km
\item   205,83 ~cg~ = {\color{red}  0,205 83 }~dag
\item   9 104 ~hL~ = {\color{red}  910 400 000 }~mL
\item   8 919 ~dL~ = {\color{red}  89 190 }~cL
\item   2 734,7 ~hL~ = {\color{red}  273,47 }~kL
\item   516,86 ~dam~ = {\color{red}  51 686 }~dm
\item   3 685,2 ~hL~ = {\color{red}  3 685 200 }~dL
\end{itemize}
\end{multicols}
\end{document}
