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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 43}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{96}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   724  ~ \(\times\)  ~ 100
\item   0,622  ~ \(\times\)  ~ 1 000
\item   0,003  ~ \(\times\)  ~ 100
\item   5,99  ~ \(\times\)  ~ 1 000
\item   0,088  ~ \(\times\)  ~ 100
\item   41,2  ~ \(\times\)  ~ 10
\item   880  ~ \(\times\)  ~ 10
\item   39,3  ~ \(\times\)  ~ 10
\item   0,017  ~ \(\times\)  ~ 100
\item   0,14  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   84,02  ~ : ~ 1 000
\item   3,08  ~ : ~ 10
\item   902  ~ : ~ 10
\item   110,7  ~ : ~ 100
\item   4 611  ~ : ~ 1 000
\item   1 789  ~ : ~ 10
\item   75,95  ~ : ~ 100
\item   8,766  ~ : ~ 10
\item   2 170  ~ : ~ 100
\item   9,21  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   75,4  ~ \(\times\)  ~ ... ~ = ~ 75 400
\item   627  ~ \(\times\)  ~ ... ~ = ~ 627 000
\item   687  ~ \(\times\)  ~ ... ~ = ~ 68 700
\item   5,15  ~ \(\times\)  ~ ... ~ = ~ 5 150
\item   453  ~ \(\times\)  ~ ... ~ = ~ 45 300
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 0,43
\item   37,5  ~ \(\times\)  ~ ... ~ = ~ 37 500
\item   9,7  ~ \(\times\)  ~ ... ~ = ~ 9 700
\item   8,35  ~ \(\times\)  ~ ... ~ = ~ 83,5
\item   0,072  ~ \(\times\)  ~ ... ~ = ~ 7,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 360  ~ \(\times\)  ~ 0,1
\item   142  ~ \(\times\)  ~ 0,1
\item   2 165  ~ \(\times\)  ~ 0,01
\item   2,043  ~ \(\times\)  ~ 0,01
\item   75,75  ~ \(\times\)  ~ 0,01
\item   1 528  ~ \(\times\)  ~ 0,1
\item   3,477  ~ \(\times\)  ~ 0,1
\item   9,532  ~ \(\times\)  ~ 0,01
\item   9,837  ~ \(\times\)  ~ 0,01
\item   66,2  ~ \(\times\)  ~ 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   314,5  ~ \(\times\)  ~ ... ~ = ~  31,45
\item   93,8  ~ \(\times\)  ~ ... ~ = ~  0,938
\item   37,37  ~ \(\times\)  ~ ... ~ = ~  3,737
\item   3,648  ~ \(\times\)  ~ ... ~ = ~  0,036 48
\item   3 785  ~ \(\times\)  ~ ... ~ = ~  37,85
\item   8 316  ~ \(\times\)  ~ ... ~ = ~  831,6
\item   546  ~ \(\times\)  ~ ... ~ = ~  0,546
\item   8 470  ~ \(\times\)  ~ ... ~ = ~  8,47
\item   57,62  ~ \(\times\)  ~ ... ~ = ~  5,762
\item   2,229  ~ \(\times\)  ~ ... ~ = ~  0,022 29
\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~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   254,44 ~cL~ = ...~hL
\item   355,18 ~dam~ = ...~km
\item   6 927,4 ~mm~ = ...~dm
\item   507,82 ~L~ = ...~mL
\item   531,03 ~mL~ = ...~hL
\item   7 395,6 ~hm~ = ...~mm
\item   742,53 ~kg~ = ...~g
\item   3 538,2 ~dam~ = ...~cm
\item   2 238,9 ~kL~ = ...~mL
\item   379,85 ~m~ = ...~km
\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   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{290}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{580}{100}\)
\item   \(\dfrac{96}{100}\) = \(\dfrac{960}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   724  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 72 400}
\item   0,622  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 622}
\item   0,003  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,3}
\item   5,99  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 990}
\item   0,088  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,8}
\item   41,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 412}
\item   880  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 800}
\item   39,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 393}
\item   0,017  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,7}
\item   0,14  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 140}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   84,02 ~ : ~ 1 000 ~ = ~{\color{red} 0,084 02}
\item   3,08 ~ : ~ 10 ~ = ~{\color{red} 0,308}
\item   902 ~ : ~ 10 ~ = ~{\color{red} 90,2}
\item   110,7 ~ : ~ 100 ~ = ~{\color{red} 1,107}
\item   4 611 ~ : ~ 1 000 ~ = ~{\color{red} 4,611}
\item   1 789 ~ : ~ 10 ~ = ~{\color{red} 178,9}
\item   75,95 ~ : ~ 100 ~ = ~{\color{red} 0,759 5}
\item   8,766 ~ : ~ 10 ~ = ~{\color{red} 0,876 6}
\item   2 170 ~ : ~ 100 ~ = ~{\color{red} 21,7}
\item   9,21 ~ : ~ 100 ~ = ~{\color{red} 0,092 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   75,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~75 400
\item   627 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~627 000
\item   687 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~68 700
\item   5,15 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 150
\item   453 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~45 300
\item   0,043 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,43
\item   37,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~37 500
\item   9,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 700
\item   8,35 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~83,5
\item   0,072 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 360 ~ \(\times\)  0,1 ~ = ~{\color{red} 736
}\item   142 ~ \(\times\)  0,1 ~ = ~{\color{red} 14,2
}\item   2 165 ~ \(\times\)  0,01 ~ = ~{\color{red} 21,65
}\item   2,043 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,020 43
}\item   75,75 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,757 5
}\item   1 528 ~ \(\times\)  0,1 ~ = ~{\color{red} 152,8
}\item   3,477 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,347 7
}\item   9,532 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,095 32
}\item   9,837 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,098 37
}\item   66,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,62
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   314,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 31,45
\item   93,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,938
\item   37,37 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,737
\item   3,648 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,036 48
\item   3 785 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 37,85
\item   8 316 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 831,6
\item   546 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,546
\item   8 470 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,47
\item   57,62 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,762
\item   2,229 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,022 29
\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~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   254,44 ~cL~ = {\color{red}  0,025 444 }~hL
\item   355,18 ~dam~ = {\color{red}  3,551 8 }~km
\item   6 927,4 ~mm~ = {\color{red}  69,274 }~dm
\item   507,82 ~L~ = {\color{red}  507 820 }~mL
\item   531,03 ~mL~ = {\color{red}  0,005 310 3 }~hL
\item   7 395,6 ~hm~ = {\color{red}  739 560 000 }~mm
\item   742,53 ~kg~ = {\color{red}  742 530 }~g
\item   3 538,2 ~dam~ = {\color{red}  3 538 200 }~cm
\item   2 238,9 ~kL~ = {\color{red}  2 238 900 000 }~mL
\item   379,85 ~m~ = {\color{red}  0,379 85 }~km
\end{itemize}
\end{multicols}
\end{document}
