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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 357}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,015  ~ \(\times\)  ~ 10
\item   0,823  ~ \(\times\)  ~ 100
\item   89,9  ~ \(\times\)  ~ 1 000
\item   0,53  ~ \(\times\)  ~ 100
\item   0,046  ~ \(\times\)  ~ 1 000
\item   1,28  ~ \(\times\)  ~ 100
\item   0,691  ~ \(\times\)  ~ 1 000
\item   1,03  ~ \(\times\)  ~ 10
\item   814  ~ \(\times\)  ~ 100
\item   7,4  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,63  ~ : ~ 100
\item   1,385  ~ : ~ 10
\item   5 057  ~ : ~ 10
\item   9 093  ~ : ~ 100
\item   0,103  ~ : ~ 10
\item   23,39  ~ : ~ 1 000
\item   98,7  ~ : ~ 10
\item   222,3  ~ : ~ 1 000
\item   975,7  ~ : ~ 10
\item   398,9  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   33,6  ~ \(\times\)  ~ ... ~ = ~ 33 600
\item   0,49  ~ \(\times\)  ~ ... ~ = ~ 49
\item   0,43  ~ \(\times\)  ~ ... ~ = ~ 430
\item   539  ~ \(\times\)  ~ ... ~ = ~ 539 000
\item   0,43  ~ \(\times\)  ~ ... ~ = ~ 4,3
\item   0,01  ~ \(\times\)  ~ ... ~ = ~ 0,1
\item   317  ~ \(\times\)  ~ ... ~ = ~ 31 700
\item   25,5  ~ \(\times\)  ~ ... ~ = ~ 255
\item   0,079  ~ \(\times\)  ~ ... ~ = ~ 0,79
\item   0,056  ~ \(\times\)  ~ ... ~ = ~ 56
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 851  ~ \(\times\)  ~ 0,1
\item   98,71  ~ \(\times\)  ~ 0,001
\item   237,3  ~ \(\times\)  ~ 0,1
\item   3,179  ~ \(\times\)  ~ 0,001
\item   7,394  ~ \(\times\)  ~ 0,01
\item   4,713  ~ \(\times\)  ~ 0,001
\item   6,672  ~ \(\times\)  ~ 0,001
\item   38,12  ~ \(\times\)  ~ 0,001
\item   60,79  ~ \(\times\)  ~ 0,1
\item   443,2  ~ \(\times\)  ~ 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   484,7  ~ \(\times\)  ~ ... ~ = ~  48,47
\item   4,394  ~ \(\times\)  ~ ... ~ = ~  0,004 394
\item   2 728  ~ \(\times\)  ~ ... ~ = ~  27,28
\item   629  ~ \(\times\)  ~ ... ~ = ~  62,9
\item   9 872  ~ \(\times\)  ~ ... ~ = ~  9,872
\item   52,07  ~ \(\times\)  ~ ... ~ = ~  0,052 07
\item   2,783  ~ \(\times\)  ~ ... ~ = ~  0,278 3
\item   4,617  ~ \(\times\)  ~ ... ~ = ~  0,046 17
\item   57,11  ~ \(\times\)  ~ ... ~ = ~  0,571 1
\item   19,14  ~ \(\times\)  ~ ... ~ = ~  0,191 4
\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~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   744,54 ~dam~ = ...~cm
\item   8 452,6 ~dam~ = ...~km
\item   965,77 ~dg~ = ...~hg
\item   412,41 ~kL~ = ...~hL
\item   6 000 ~dL~ = ...~hL
\item   930,2 ~m~ = ...~mm
\item   967,13 ~mg~ = ...~cg
\item   1 670,1 ~cm~ = ...~m
\item   9 280 ~L~ = ...~daL
\item   242,09 ~dam~ = ...~mm
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{1900}{100}\) = \(\dfrac{190}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{410}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{450}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,015  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,15}
\item   0,823  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 82,3}
\item   89,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 89 900}
\item   0,53  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 53}
\item   0,046  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 46}
\item   1,28  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 128}
\item   0,691  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 691}
\item   1,03  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 10,3}
\item   814  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 81 400}
\item   7,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 400}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,63 ~ : ~ 100 ~ = ~{\color{red} 0,076 3}
\item   1,385 ~ : ~ 10 ~ = ~{\color{red} 0,138 5}
\item   5 057 ~ : ~ 10 ~ = ~{\color{red} 505,7}
\item   9 093 ~ : ~ 100 ~ = ~{\color{red} 90,93}
\item   0,103 ~ : ~ 10 ~ = ~{\color{red} 0,010 3}
\item   23,39 ~ : ~ 1 000 ~ = ~{\color{red} 0,023 39}
\item   98,7 ~ : ~ 10 ~ = ~{\color{red} 9,87}
\item   222,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,222 3}
\item   975,7 ~ : ~ 10 ~ = ~{\color{red} 97,57}
\item   398,9 ~ : ~ 100 ~ = ~{\color{red} 3,989}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   33,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33 600
\item   0,49 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~49
\item   0,43 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~430
\item   539 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~539 000
\item   0,43 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,3
\item   0,01 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,1
\item   317 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~31 700
\item   25,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~255
\item   0,079 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,79
\item   0,056 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~56
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 851 ~ \(\times\)  0,1 ~ = ~{\color{red} 385,1
}\item   98,71 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,098 71
}\item   237,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 23,73
}\item   3,179 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 179
}\item   7,394 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,073 94
}\item   4,713 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 713
}\item   6,672 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 672
}\item   38,12 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,038 12
}\item   60,79 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,079
}\item   443,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 44,32
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   484,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 48,47
\item   4,394 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 394
\item   2 728 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 27,28
\item   629 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 62,9
\item   9 872 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,872
\item   52,07 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,052 07
\item   2,783 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,278 3
\item   4,617 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,046 17
\item   57,11 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,571 1
\item   19,14 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,191 4
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\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   744,54 ~dam~ = {\color{red}  744 540 }~cm
\item   8 452,6 ~dam~ = {\color{red}  84,526 }~km
\item   965,77 ~dg~ = {\color{red}  0,965 77 }~hg
\item   412,41 ~kL~ = {\color{red}  4 124,1 }~hL
\item   6 000 ~dL~ = {\color{red}  6 }~hL
\item   930,2 ~m~ = {\color{red}  930 200 }~mm
\item   967,13 ~mg~ = {\color{red}  96,713 }~cg
\item   1 670,1 ~cm~ = {\color{red}  16,701 }~m
\item   9 280 ~L~ = {\color{red}  928 }~daL
\item   242,09 ~dam~ = {\color{red}  2 420 900 }~mm
\end{itemize}
\end{multicols}
\end{document}
