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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 363}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,009  ~ \(\times\)  ~ 1 000
\item   430  ~ \(\times\)  ~ 100
\item   15,3  ~ \(\times\)  ~ 100
\item   97,1  ~ \(\times\)  ~ 10
\item   843  ~ \(\times\)  ~ 10
\item   0,534  ~ \(\times\)  ~ 10
\item   69,1  ~ \(\times\)  ~ 1 000
\item   0,086  ~ \(\times\)  ~ 100
\item   44,9  ~ \(\times\)  ~ 1 000
\item   0,037  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   562,2  ~ : ~ 100
\item   762,3  ~ : ~ 100
\item   3 129  ~ : ~ 100
\item   9 194  ~ : ~ 100
\item   1,44  ~ : ~ 100
\item   20,6  ~ : ~ 10
\item   23,02  ~ : ~ 10
\item   27,12  ~ : ~ 1 000
\item   71,07  ~ : ~ 1 000
\item   616,7  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 6,9
\item   0,749  ~ \(\times\)  ~ ... ~ = ~ 74,9
\item   0,034  ~ \(\times\)  ~ ... ~ = ~ 0,34
\item   0,082  ~ \(\times\)  ~ ... ~ = ~ 8,2
\item   641  ~ \(\times\)  ~ ... ~ = ~ 64 100
\item   640  ~ \(\times\)  ~ ... ~ = ~ 6 400
\item   2,25  ~ \(\times\)  ~ ... ~ = ~ 2 250
\item   0,051  ~ \(\times\)  ~ ... ~ = ~ 0,51
\item   0,25  ~ \(\times\)  ~ ... ~ = ~ 25
\item   7,22  ~ \(\times\)  ~ ... ~ = ~ 72,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   425,2  ~ \(\times\)  ~ 0,001
\item   772,9  ~ \(\times\)  ~ 0,1
\item   1 545  ~ \(\times\)  ~ 0,01
\item   4 930  ~ \(\times\)  ~ 0,001
\item   675  ~ \(\times\)  ~ 0,01
\item   8 561  ~ \(\times\)  ~ 0,001
\item   1,703  ~ \(\times\)  ~ 0,001
\item   2 313  ~ \(\times\)  ~ 0,01
\item   8 456  ~ \(\times\)  ~ 0,001
\item   9,9  ~ \(\times\)  ~ 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   1 509  ~ \(\times\)  ~ ... ~ = ~  150,9
\item   78,55  ~ \(\times\)  ~ ... ~ = ~  0,078 55
\item   88,61  ~ \(\times\)  ~ ... ~ = ~  0,886 1
\item   74,8  ~ \(\times\)  ~ ... ~ = ~  7,48
\item   485,4  ~ \(\times\)  ~ ... ~ = ~  4,854
\item   405,5  ~ \(\times\)  ~ ... ~ = ~  40,55
\item   2,38  ~ \(\times\)  ~ ... ~ = ~  0,002 38
\item   2,492  ~ \(\times\)  ~ ... ~ = ~  0,002 492
\item   1 901  ~ \(\times\)  ~ ... ~ = ~  19,01
\item   7 942  ~ \(\times\)  ~ ... ~ = ~  79,42
\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~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   334,84 ~km~ = ...~cm
\item   624,71 ~hL~ = ...~mL
\item   345,56 ~mL~ = ...~dL
\item   4 732,8 ~hg~ = ...~cg
\item   520,14 ~km~ = ...~mm
\item   207,52 ~mL~ = ...~cL
\item   3 626,9 ~cm~ = ...~mm
\item   1 893,8 ~dm~ = ...~cm
\item   8 952,9 ~cL~ = ...~hL
\item   529 ~cL~ = ...~daL
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{790}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{490}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{190}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,009  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9}
\item   430  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 43 000}
\item   15,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 530}
\item   97,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 971}
\item   843  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 430}
\item   0,534  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,34}
\item   69,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 69 100}
\item   0,086  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,6}
\item   44,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 44 900}
\item   0,037  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,37}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   562,2 ~ : ~ 100 ~ = ~{\color{red} 5,622}
\item   762,3 ~ : ~ 100 ~ = ~{\color{red} 7,623}
\item   3 129 ~ : ~ 100 ~ = ~{\color{red} 31,29}
\item   9 194 ~ : ~ 100 ~ = ~{\color{red} 91,94}
\item   1,44 ~ : ~ 100 ~ = ~{\color{red} 0,014 4}
\item   20,6 ~ : ~ 10 ~ = ~{\color{red} 2,06}
\item   23,02 ~ : ~ 10 ~ = ~{\color{red} 2,302}
\item   27,12 ~ : ~ 1 000 ~ = ~{\color{red} 0,027 12}
\item   71,07 ~ : ~ 1 000 ~ = ~{\color{red} 0,071 07}
\item   616,7 ~ : ~ 10 ~ = ~{\color{red} 61,67}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,069 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,9
\item   0,749 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74,9
\item   0,034 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,34
\item   0,082 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,2
\item   641 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~64 100
\item   640 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 400
\item   2,25 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 250
\item   0,051 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,51
\item   0,25 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~25
\item   7,22 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~72,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   425,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,425 2
}\item   772,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 77,29
}\item   1 545 ~ \(\times\)  0,01 ~ = ~{\color{red} 15,45
}\item   4 930 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,93
}\item   675 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,75
}\item   8 561 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,561
}\item   1,703 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 703
}\item   2 313 ~ \(\times\)  0,01 ~ = ~{\color{red} 23,13
}\item   8 456 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,456
}\item   9,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,99
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 509 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 150,9
\item   78,55 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,078 55
\item   88,61 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,886 1
\item   74,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,48
\item   485,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,854
\item   405,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 40,55
\item   2,38 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 38
\item   2,492 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 492
\item   1 901 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 19,01
\item   7 942 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 79,42
\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}  100 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   334,84 ~km~ = {\color{red}  33 484 000 }~cm
\item   624,71 ~hL~ = {\color{red}  62 471 000 }~mL
\item   345,56 ~mL~ = {\color{red}  3,455 6 }~dL
\item   4 732,8 ~hg~ = {\color{red}  47 328 000 }~cg
\item   520,14 ~km~ = {\color{red}  520 140 000 }~mm
\item   207,52 ~mL~ = {\color{red}  20,752 }~cL
\item   3 626,9 ~cm~ = {\color{red}  36 269 }~mm
\item   1 893,8 ~dm~ = {\color{red}  18 938 }~cm
\item   8 952,9 ~cL~ = {\color{red}  0,895 29 }~hL
\item   529 ~cL~ = {\color{red}  0,529 }~daL
\end{itemize}
\end{multicols}
\end{document}
