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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 313}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,63  ~ \(\times\)  ~ 100
\item   2,9  ~ \(\times\)  ~ 100
\item   0,421  ~ \(\times\)  ~ 1 000
\item   41,6  ~ \(\times\)  ~ 100
\item   236  ~ \(\times\)  ~ 1 000
\item   0,001  ~ \(\times\)  ~ 10
\item   0,084  ~ \(\times\)  ~ 100
\item   2,33  ~ \(\times\)  ~ 10
\item   0,52  ~ \(\times\)  ~ 100
\item   0,871  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   13,94  ~ : ~ 100
\item   385,1  ~ : ~ 1 000
\item   386,8  ~ : ~ 100
\item   8,09  ~ : ~ 100
\item   0,896  ~ : ~ 100
\item   71  ~ : ~ 1 000
\item   8 004  ~ : ~ 1 000
\item   1,223  ~ : ~ 1 000
\item   265,4  ~ : ~ 100
\item   8,18  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   523  ~ \(\times\)  ~ ... ~ = ~ 52 300
\item   39  ~ \(\times\)  ~ ... ~ = ~ 390
\item   420  ~ \(\times\)  ~ ... ~ = ~ 4 200
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 64
\item   646  ~ \(\times\)  ~ ... ~ = ~ 646 000
\item   0,202  ~ \(\times\)  ~ ... ~ = ~ 202
\item   0,647  ~ \(\times\)  ~ ... ~ = ~ 6,47
\item   0,059  ~ \(\times\)  ~ ... ~ = ~ 0,59
\item   0,059  ~ \(\times\)  ~ ... ~ = ~ 59
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 6,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,961  ~ \(\times\)  ~ 0,1
\item   388,4  ~ \(\times\)  ~ 0,1
\item   615,7  ~ \(\times\)  ~ 0,001
\item   7,855  ~ \(\times\)  ~ 0,01
\item   94,29  ~ \(\times\)  ~ 0,001
\item   6,867  ~ \(\times\)  ~ 0,1
\item   53,08  ~ \(\times\)  ~ 0,1
\item   5 841  ~ \(\times\)  ~ 0,01
\item   22,21  ~ \(\times\)  ~ 0,01
\item   8 983  ~ \(\times\)  ~ 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   5,028  ~ \(\times\)  ~ ... ~ = ~  0,050 28
\item   18,5  ~ \(\times\)  ~ ... ~ = ~  0,018 5
\item   23,32  ~ \(\times\)  ~ ... ~ = ~  2,332
\item   4 227  ~ \(\times\)  ~ ... ~ = ~  422,7
\item   7 884  ~ \(\times\)  ~ ... ~ = ~  78,84
\item   0,909  ~ \(\times\)  ~ ... ~ = ~  0,000 909
\item   770,2  ~ \(\times\)  ~ ... ~ = ~  77,02
\item   0,558  ~ \(\times\)  ~ ... ~ = ~  0,000 558
\item   5,517  ~ \(\times\)  ~ ... ~ = ~  0,551 7
\item   3 748  ~ \(\times\)  ~ ... ~ = ~  374,8
\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~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 854 ~mm~ = ...~km
\item   6 037,5 ~cL~ = ...~daL
\item   8 323,1 ~mL~ = ...~kL
\item   940,37 ~hL~ = ...~mL
\item   2 816,7 ~cm~ = ...~mm
\item   765,13 ~cm~ = ...~m
\item   459,65 ~kg~ = ...~cg
\item   367,25 ~kg~ = ...~mg
\item   444,98 ~dg~ = ...~g
\item   359,34 ~dam~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{720}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{280}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,63  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 63}
\item   2,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 290}
\item   0,421  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 421}
\item   41,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 160}
\item   236  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 236 000}
\item   0,001  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,01}
\item   0,084  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,4}
\item   2,33  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 23,3}
\item   0,52  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 52}
\item   0,871  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,71}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   13,94 ~ : ~ 100 ~ = ~{\color{red} 0,139 4}
\item   385,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,385 1}
\item   386,8 ~ : ~ 100 ~ = ~{\color{red} 3,868}
\item   8,09 ~ : ~ 100 ~ = ~{\color{red} 0,080 9}
\item   0,896 ~ : ~ 100 ~ = ~{\color{red} 0,008 96}
\item   71 ~ : ~ 1 000 ~ = ~{\color{red} 0,071}
\item   8 004 ~ : ~ 1 000 ~ = ~{\color{red} 8,004}
\item   1,223 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 223}
\item   265,4 ~ : ~ 100 ~ = ~{\color{red} 2,654}
\item   8,18 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 18}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   523 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~52 300
\item   39 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~390
\item   420 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 200
\item   0,064 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~64
\item   646 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~646 000
\item   0,202 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~202
\item   0,647 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,47
\item   0,059 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,59
\item   0,059 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~59
\item   0,063 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,961 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,596 1
}\item   388,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 38,84
}\item   615,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,615 7
}\item   7,855 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,078 55
}\item   94,29 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,094 29
}\item   6,867 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,686 7
}\item   53,08 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,308
}\item   5 841 ~ \(\times\)  0,01 ~ = ~{\color{red} 58,41
}\item   22,21 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,222 1
}\item   8 983 ~ \(\times\)  0,1 ~ = ~{\color{red} 898,3
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,028 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,050 28
\item   18,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,018 5
\item   23,32 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,332
\item   4 227 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 422,7
\item   7 884 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 78,84
\item   0,909 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 909
\item   770,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 77,02
\item   0,558 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 558
\item   5,517 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,551 7
\item   3 748 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 374,8
\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~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 854 ~mm~ = {\color{red}  0,008 854 }~km
\item   6 037,5 ~cL~ = {\color{red}  6,037 5 }~daL
\item   8 323,1 ~mL~ = {\color{red}  0,008 323 1 }~kL
\item   940,37 ~hL~ = {\color{red}  94 037 000 }~mL
\item   2 816,7 ~cm~ = {\color{red}  28 167 }~mm
\item   765,13 ~cm~ = {\color{red}  7,651 3 }~m
\item   459,65 ~kg~ = {\color{red}  45 965 000 }~cg
\item   367,25 ~kg~ = {\color{red}  367 250 000 }~mg
\item   444,98 ~dg~ = {\color{red}  44,498 }~g
\item   359,34 ~dam~ = {\color{red}  35 934 }~dm
\end{itemize}
\end{multicols}
\end{document}
