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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 240}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,76  ~ \(\times\)  ~ 10
\item   390  ~ \(\times\)  ~ 10
\item   0,1  ~ \(\times\)  ~ 100
\item   0,032  ~ \(\times\)  ~ 1 000
\item   64  ~ \(\times\)  ~ 1 000
\item   26,4  ~ \(\times\)  ~ 1 000
\item   836  ~ \(\times\)  ~ 100
\item   0,088  ~ \(\times\)  ~ 1 000
\item   0,603  ~ \(\times\)  ~ 1 000
\item   0,99  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 076  ~ : ~ 10
\item   82,41  ~ : ~ 1 000
\item   28,03  ~ : ~ 10
\item   633  ~ : ~ 1 000
\item   3 202  ~ : ~ 1 000
\item   544  ~ : ~ 100
\item   1 402  ~ : ~ 1 000
\item   807,8  ~ : ~ 100
\item   2,852  ~ : ~ 100
\item   1 838  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,69  ~ \(\times\)  ~ ... ~ = ~ 869
\item   0,563  ~ \(\times\)  ~ ... ~ = ~ 56,3
\item   0,015  ~ \(\times\)  ~ ... ~ = ~ 15
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 8,4
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 84
\item   9,69  ~ \(\times\)  ~ ... ~ = ~ 969
\item   0,054  ~ \(\times\)  ~ ... ~ = ~ 54
\item   93,4  ~ \(\times\)  ~ ... ~ = ~ 93 400
\item   921  ~ \(\times\)  ~ ... ~ = ~ 92 100
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 3,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,085  ~ \(\times\)  ~ 0,01
\item   15,48  ~ \(\times\)  ~ 0,001
\item   4 194  ~ \(\times\)  ~ 0,01
\item   1 734  ~ \(\times\)  ~ 0,01
\item   4 946  ~ \(\times\)  ~ 0,001
\item   941,6  ~ \(\times\)  ~ 0,1
\item   76,73  ~ \(\times\)  ~ 0,01
\item   67,84  ~ \(\times\)  ~ 0,001
\item   55,12  ~ \(\times\)  ~ 0,01
\item   6,094  ~ \(\times\)  ~ 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   57,94  ~ \(\times\)  ~ ... ~ = ~  5,794
\item   15,3  ~ \(\times\)  ~ ... ~ = ~  1,53
\item   8,62  ~ \(\times\)  ~ ... ~ = ~  0,086 2
\item   81,25  ~ \(\times\)  ~ ... ~ = ~  8,125
\item   8 541  ~ \(\times\)  ~ ... ~ = ~  8,541
\item   6 128  ~ \(\times\)  ~ ... ~ = ~  6,128
\item   3 006  ~ \(\times\)  ~ ... ~ = ~  300,6
\item   545,4  ~ \(\times\)  ~ ... ~ = ~  0,545 4
\item   4 675  ~ \(\times\)  ~ ... ~ = ~  4,675
\item   5 225  ~ \(\times\)  ~ ... ~ = ~  522,5
\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 ~m~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 503,3 ~cL~ = ...~kL
\item   494,33 ~kg~ = ...~dag
\item   952,95 ~mL~ = ...~dL
\item   381,59 ~daL~ = ...~dL
\item   593,78 ~mg~ = ...~dag
\item   9 912,5 ~dam~ = ...~km
\item   614,2 ~cm~ = ...~km
\item   7 562 ~m~ = ...~mm
\item   5 492,5 ~dL~ = ...~L
\item   5 738,7 ~L~ = ...~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   1 = \(\dfrac{10}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{510}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{900}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{780}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,76  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 97,6}
\item   390  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 900}
\item   0,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 10}
\item   0,032  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32}
\item   64  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 64 000}
\item   26,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 26 400}
\item   836  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 83 600}
\item   0,088  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 88}
\item   0,603  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 603}
\item   0,99  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 990}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 076 ~ : ~ 10 ~ = ~{\color{red} 507,6}
\item   82,41 ~ : ~ 1 000 ~ = ~{\color{red} 0,082 41}
\item   28,03 ~ : ~ 10 ~ = ~{\color{red} 2,803}
\item   633 ~ : ~ 1 000 ~ = ~{\color{red} 0,633}
\item   3 202 ~ : ~ 1 000 ~ = ~{\color{red} 3,202}
\item   544 ~ : ~ 100 ~ = ~{\color{red} 5,44}
\item   1 402 ~ : ~ 1 000 ~ = ~{\color{red} 1,402}
\item   807,8 ~ : ~ 100 ~ = ~{\color{red} 8,078}
\item   2,852 ~ : ~ 100 ~ = ~{\color{red} 0,028 52}
\item   1 838 ~ : ~ 10 ~ = ~{\color{red} 183,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,69 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~869
\item   0,563 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~56,3
\item   0,015 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~15
\item   0,084 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,4
\item   0,084 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~84
\item   9,69 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~969
\item   0,054 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~54
\item   93,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~93 400
\item   921 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~92 100
\item   0,032 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,085 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,030 85
}\item   15,48 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,015 48
}\item   4 194 ~ \(\times\)  0,01 ~ = ~{\color{red} 41,94
}\item   1 734 ~ \(\times\)  0,01 ~ = ~{\color{red} 17,34
}\item   4 946 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,946
}\item   941,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 94,16
}\item   76,73 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,767 3
}\item   67,84 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,067 84
}\item   55,12 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,551 2
}\item   6,094 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 094
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   57,94 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,794
\item   15,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,53
\item   8,62 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,086 2
\item   81,25 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,125
\item   8 541 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,541
\item   6 128 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,128
\item   3 006 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 300,6
\item   545,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,545 4
\item   4 675 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,675
\item   5 225 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 522,5
\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 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 503,3 ~cL~ = {\color{red}  0,095 033 }~kL
\item   494,33 ~kg~ = {\color{red}  49 433 }~dag
\item   952,95 ~mL~ = {\color{red}  9,529 5 }~dL
\item   381,59 ~daL~ = {\color{red}  38 159 }~dL
\item   593,78 ~mg~ = {\color{red}  0,059 378 }~dag
\item   9 912,5 ~dam~ = {\color{red}  99,125 }~km
\item   614,2 ~cm~ = {\color{red}  0,006 142 }~km
\item   7 562 ~m~ = {\color{red}  7 562 000 }~mm
\item   5 492,5 ~dL~ = {\color{red}  549,25 }~L
\item   5 738,7 ~L~ = {\color{red}  57 387 }~dL
\end{itemize}
\end{multicols}
\end{document}
