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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 229}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{66}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85,4  ~ \(\times\)  ~ 1 000
\item   0,018  ~ \(\times\)  ~ 100
\item   7,19  ~ \(\times\)  ~ 10
\item   528  ~ \(\times\)  ~ 10
\item   249  ~ \(\times\)  ~ 1 000
\item   3,32  ~ \(\times\)  ~ 10
\item   985  ~ \(\times\)  ~ 10
\item   0,767  ~ \(\times\)  ~ 1 000
\item   633  ~ \(\times\)  ~ 1 000
\item   2,83  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,825  ~ : ~ 100
\item   7 906  ~ : ~ 1 000
\item   9,297  ~ : ~ 100
\item   50,4  ~ : ~ 1 000
\item   6,204  ~ : ~ 10
\item   2,086  ~ : ~ 100
\item   8,864  ~ : ~ 1 000
\item   424,9  ~ : ~ 10
\item   5,002  ~ : ~ 10
\item   4,081  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 0,97
\item   93,9  ~ \(\times\)  ~ ... ~ = ~ 93 900
\item   6,22  ~ \(\times\)  ~ ... ~ = ~ 6 220
\item   2,88  ~ \(\times\)  ~ ... ~ = ~ 2 880
\item   585  ~ \(\times\)  ~ ... ~ = ~ 5 850
\item   0,111  ~ \(\times\)  ~ ... ~ = ~ 11,1
\item   2,62  ~ \(\times\)  ~ ... ~ = ~ 2 620
\item   0,029  ~ \(\times\)  ~ ... ~ = ~ 2,9
\item   9,7  ~ \(\times\)  ~ ... ~ = ~ 97
\item   13,6  ~ \(\times\)  ~ ... ~ = ~ 13 600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 238  ~ \(\times\)  ~ 0,1
\item   5,62  ~ \(\times\)  ~ 0,1
\item   3 067  ~ \(\times\)  ~ 0,1
\item   4 399  ~ \(\times\)  ~ 0,1
\item   68,16  ~ \(\times\)  ~ 0,1
\item   2 517  ~ \(\times\)  ~ 0,1
\item   4,621  ~ \(\times\)  ~ 0,1
\item   88,5  ~ \(\times\)  ~ 0,001
\item   3 274  ~ \(\times\)  ~ 0,01
\item   645,5  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   585  ~ \(\times\)  ~ ... ~ = ~  58,5
\item   2,516  ~ \(\times\)  ~ ... ~ = ~  0,002 516
\item   4,702  ~ \(\times\)  ~ ... ~ = ~  0,047 02
\item   1,444  ~ \(\times\)  ~ ... ~ = ~  0,014 44
\item   677  ~ \(\times\)  ~ ... ~ = ~  0,677
\item   142,1  ~ \(\times\)  ~ ... ~ = ~  14,21
\item   855,3  ~ \(\times\)  ~ ... ~ = ~  85,53
\item   0,983  ~ \(\times\)  ~ ... ~ = ~  0,098 3
\item   3,278  ~ \(\times\)  ~ ... ~ = ~  0,032 78
\item   8 997  ~ \(\times\)  ~ ... ~ = ~  8,997
\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 ~m~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~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   922,23 ~m~ = ...~dam
\item   9 543,5 ~hg~ = ...~dg
\item   217,28 ~cL~ = ...~kL
\item   1 276,2 ~dam~ = ...~cm
\item   817,82 ~kg~ = ...~g
\item   684,88 ~dg~ = ...~kg
\item   584,65 ~mL~ = ...~cL
\item   204,86 ~kL~ = ...~cL
\item   420,54 ~mL~ = ...~dL
\item   876,89 ~kg~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{3900}{100}\) = \(\dfrac{390}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{66}{10}\) = \(\dfrac{660}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{440}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 85 400}
\item   0,018  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,8}
\item   7,19  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 71,9}
\item   528  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 280}
\item   249  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 249 000}
\item   3,32  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 33,2}
\item   985  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9 850}
\item   0,767  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 767}
\item   633  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 633 000}
\item   2,83  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 830}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,825 ~ : ~ 100 ~ = ~{\color{red} 0,038 25}
\item   7 906 ~ : ~ 1 000 ~ = ~{\color{red} 7,906}
\item   9,297 ~ : ~ 100 ~ = ~{\color{red} 0,092 97}
\item   50,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,050 4}
\item   6,204 ~ : ~ 10 ~ = ~{\color{red} 0,620 4}
\item   2,086 ~ : ~ 100 ~ = ~{\color{red} 0,020 86}
\item   8,864 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 864}
\item   424,9 ~ : ~ 10 ~ = ~{\color{red} 42,49}
\item   5,002 ~ : ~ 10 ~ = ~{\color{red} 0,500 2}
\item   4,081 ~ : ~ 100 ~ = ~{\color{red} 0,040 81}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,097 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,97
\item   93,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~93 900
\item   6,22 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 220
\item   2,88 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 880
\item   585 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 850
\item   0,111 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~11,1
\item   2,62 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 620
\item   0,029 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,9
\item   9,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~97
\item   13,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~13 600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 238 ~ \(\times\)  0,1 ~ = ~{\color{red} 423,8
}\item   5,62 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,562
}\item   3 067 ~ \(\times\)  0,1 ~ = ~{\color{red} 306,7
}\item   4 399 ~ \(\times\)  0,1 ~ = ~{\color{red} 439,9
}\item   68,16 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,816
}\item   2 517 ~ \(\times\)  0,1 ~ = ~{\color{red} 251,7
}\item   4,621 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,462 1
}\item   88,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,088 5
}\item   3 274 ~ \(\times\)  0,01 ~ = ~{\color{red} 32,74
}\item   645,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,455
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   585 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 58,5
\item   2,516 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 516
\item   4,702 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,047 02
\item   1,444 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,014 44
\item   677 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,677
\item   142,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 14,21
\item   855,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 85,53
\item   0,983 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,098 3
\item   3,278 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,032 78
\item   8 997 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,997
\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 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }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   922,23 ~m~ = {\color{red}  92,223 }~dam
\item   9 543,5 ~hg~ = {\color{red}  9 543 500 }~dg
\item   217,28 ~cL~ = {\color{red}  0,002 172 8 }~kL
\item   1 276,2 ~dam~ = {\color{red}  1 276 200 }~cm
\item   817,82 ~kg~ = {\color{red}  817 820 }~g
\item   684,88 ~dg~ = {\color{red}  0,068 488 }~kg
\item   584,65 ~mL~ = {\color{red}  58,465 }~cL
\item   204,86 ~kL~ = {\color{red}  20 486 000 }~cL
\item   420,54 ~mL~ = {\color{red}  4,205 4 }~dL
\item   876,89 ~kg~ = {\color{red}  8 768 900 }~dg
\end{itemize}
\end{multicols}
\end{document}
