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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 9}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{34}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{97}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,15  ~ \(\times\)  ~ 1 000
\item   0,048  ~ \(\times\)  ~ 10
\item   0,035  ~ \(\times\)  ~ 1 000
\item   725  ~ \(\times\)  ~ 1 000
\item   39,7  ~ \(\times\)  ~ 1 000
\item   0,977  ~ \(\times\)  ~ 1 000
\item   44,1  ~ \(\times\)  ~ 10
\item   252  ~ \(\times\)  ~ 10
\item   0,014  ~ \(\times\)  ~ 1 000
\item   0,073  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,66  ~ : ~ 10
\item   3,775  ~ : ~ 10
\item   447,1  ~ : ~ 100
\item   47,07  ~ : ~ 10
\item   3 369  ~ : ~ 100
\item   0,998  ~ : ~ 100
\item   2 380  ~ : ~ 10
\item   7 059  ~ : ~ 1 000
\item   164  ~ : ~ 1 000
\item   333,9  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17  ~ \(\times\)  ~ ... ~ = ~ 170
\item   561  ~ \(\times\)  ~ ... ~ = ~ 561 000
\item   0,01  ~ \(\times\)  ~ ... ~ = ~ 1
\item   55,9  ~ \(\times\)  ~ ... ~ = ~ 5 590
\item   0,079  ~ \(\times\)  ~ ... ~ = ~ 0,79
\item   663  ~ \(\times\)  ~ ... ~ = ~ 663 000
\item   60,2  ~ \(\times\)  ~ ... ~ = ~ 602
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 97
\item   51  ~ \(\times\)  ~ ... ~ = ~ 5 100
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 0,58
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 497  ~ \(\times\)  ~ 0,1
\item   669,3  ~ \(\times\)  ~ 0,1
\item   8 373  ~ \(\times\)  ~ 0,001
\item   6 096  ~ \(\times\)  ~ 0,01
\item   19,02  ~ \(\times\)  ~ 0,01
\item   3,542  ~ \(\times\)  ~ 0,1
\item   9 512  ~ \(\times\)  ~ 0,01
\item   5 486  ~ \(\times\)  ~ 0,01
\item   193,1  ~ \(\times\)  ~ 0,1
\item   73,75  ~ \(\times\)  ~ 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   15,56  ~ \(\times\)  ~ ... ~ = ~  0,015 56
\item   4 768  ~ \(\times\)  ~ ... ~ = ~  4,768
\item   1 004  ~ \(\times\)  ~ ... ~ = ~  10,04
\item   9,283  ~ \(\times\)  ~ ... ~ = ~  0,092 83
\item   577,1  ~ \(\times\)  ~ ... ~ = ~  0,577 1
\item   1,186  ~ \(\times\)  ~ ... ~ = ~  0,001 186
\item   3 884  ~ \(\times\)  ~ ... ~ = ~  38,84
\item   84,54  ~ \(\times\)  ~ ... ~ = ~  0,084 54
\item   615,2  ~ \(\times\)  ~ ... ~ = ~  0,615 2
\item   485,7  ~ \(\times\)  ~ ... ~ = ~  0,485 7
\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 ~dam~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 129 ~dag~ = ...~dg
\item   1 558,1 ~cg~ = ...~dg
\item   7 122,6 ~dg~ = ...~g
\item   9 307,9 ~mm~ = ...~hm
\item   5 890 ~mm~ = ...~km
\item   435,01 ~mL~ = ...~cL
\item   2 047,2 ~kL~ = ...~dL
\item   7 536,4 ~dg~ = ...~kg
\item   6 215,2 ~hL~ = ...~dL
\item   1 242,3 ~cL~ = ...~L
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{4500}{100}\) = \(\dfrac{450}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{34}{10}\) = \(\dfrac{340}{100}\)
\item   \(\dfrac{97}{100}\) = \(\dfrac{970}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,15  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 150}
\item   0,048  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,48}
\item   0,035  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 35}
\item   725  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 725 000}
\item   39,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 39 700}
\item   0,977  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 977}
\item   44,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 441}
\item   252  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 520}
\item   0,014  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 14}
\item   0,073  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 73}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,66 ~ : ~ 10 ~ = ~{\color{red} 1,766}
\item   3,775 ~ : ~ 10 ~ = ~{\color{red} 0,377 5}
\item   447,1 ~ : ~ 100 ~ = ~{\color{red} 4,471}
\item   47,07 ~ : ~ 10 ~ = ~{\color{red} 4,707}
\item   3 369 ~ : ~ 100 ~ = ~{\color{red} 33,69}
\item   0,998 ~ : ~ 100 ~ = ~{\color{red} 0,009 98}
\item   2 380 ~ : ~ 10 ~ = ~{\color{red} 238}
\item   7 059 ~ : ~ 1 000 ~ = ~{\color{red} 7,059}
\item   164 ~ : ~ 1 000 ~ = ~{\color{red} 0,164}
\item   333,9 ~ : ~ 100 ~ = ~{\color{red} 3,339}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~170
\item   561 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~561 000
\item   0,01 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1
\item   55,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 590
\item   0,079 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,79
\item   663 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~663 000
\item   60,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~602
\item   0,097 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~97
\item   51 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 100
\item   0,058 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,58
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 497 ~ \(\times\)  0,1 ~ = ~{\color{red} 449,7
}\item   669,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 66,93
}\item   8 373 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,373
}\item   6 096 ~ \(\times\)  0,01 ~ = ~{\color{red} 60,96
}\item   19,02 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,190 2
}\item   3,542 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,354 2
}\item   9 512 ~ \(\times\)  0,01 ~ = ~{\color{red} 95,12
}\item   5 486 ~ \(\times\)  0,01 ~ = ~{\color{red} 54,86
}\item   193,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 19,31
}\item   73,75 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,737 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,56 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,015 56
\item   4 768 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,768
\item   1 004 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 10,04
\item   9,283 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,092 83
\item   577,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,577 1
\item   1,186 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 186
\item   3 884 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 38,84
\item   84,54 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,084 54
\item   615,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,615 2
\item   485,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,485 7
\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 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 129 ~dag~ = {\color{red}  812 900 }~dg
\item   1 558,1 ~cg~ = {\color{red}  155,81 }~dg
\item   7 122,6 ~dg~ = {\color{red}  712,26 }~g
\item   9 307,9 ~mm~ = {\color{red}  0,093 079 }~hm
\item   5 890 ~mm~ = {\color{red}  0,005 89 }~km
\item   435,01 ~mL~ = {\color{red}  43,501 }~cL
\item   2 047,2 ~kL~ = {\color{red}  20 472 000 }~dL
\item   7 536,4 ~dg~ = {\color{red}  0,753 64 }~kg
\item   6 215,2 ~hL~ = {\color{red}  6 215 200 }~dL
\item   1 242,3 ~cL~ = {\color{red}  12,423 }~L
\end{itemize}
\end{multicols}
\end{document}
