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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 27}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   0,027  ~ \(\times\)  ~ 100
\item   2,67  ~ \(\times\)  ~ 100
\item   19,6  ~ \(\times\)  ~ 10
\item   511  ~ \(\times\)  ~ 1 000
\item   0,095  ~ \(\times\)  ~ 1 000
\item   0,009  ~ \(\times\)  ~ 100
\item   0,802  ~ \(\times\)  ~ 1 000
\item   0,062  ~ \(\times\)  ~ 100
\item   0,021  ~ \(\times\)  ~ 100
\item   0,015  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   382,7  ~ : ~ 10
\item   65,22  ~ : ~ 1 000
\item   716  ~ : ~ 10
\item   763  ~ : ~ 100
\item   8 953  ~ : ~ 10
\item   0,347  ~ : ~ 10
\item   5,775  ~ : ~ 10
\item   5,145  ~ : ~ 100
\item   5 879  ~ : ~ 100
\item   26,72  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,03  ~ \(\times\)  ~ ... ~ = ~ 5 030
\item   0,007  ~ \(\times\)  ~ ... ~ = ~ 0,07
\item   18,3  ~ \(\times\)  ~ ... ~ = ~ 18 300
\item   0,051  ~ \(\times\)  ~ ... ~ = ~ 0,51
\item   3,51  ~ \(\times\)  ~ ... ~ = ~ 35,1
\item   4,11  ~ \(\times\)  ~ ... ~ = ~ 4 110
\item   1,26  ~ \(\times\)  ~ ... ~ = ~ 126
\item   0,082  ~ \(\times\)  ~ ... ~ = ~ 82
\item   715  ~ \(\times\)  ~ ... ~ = ~ 71 500
\item   0,476  ~ \(\times\)  ~ ... ~ = ~ 47,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 509  ~ \(\times\)  ~ 0,001
\item   4,69  ~ \(\times\)  ~ 0,1
\item   7 926  ~ \(\times\)  ~ 0,1
\item   9 809  ~ \(\times\)  ~ 0,01
\item   32,08  ~ \(\times\)  ~ 0,001
\item   1 691  ~ \(\times\)  ~ 0,001
\item   7,029  ~ \(\times\)  ~ 0,001
\item   7 647  ~ \(\times\)  ~ 0,1
\item   5 863  ~ \(\times\)  ~ 0,001
\item   321,7  ~ \(\times\)  ~ 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   32,43  ~ \(\times\)  ~ ... ~ = ~  0,324 3
\item   11,29  ~ \(\times\)  ~ ... ~ = ~  1,129
\item   3 106  ~ \(\times\)  ~ ... ~ = ~  310,6
\item   492,5  ~ \(\times\)  ~ ... ~ = ~  49,25
\item   7,676  ~ \(\times\)  ~ ... ~ = ~  0,767 6
\item   39,09  ~ \(\times\)  ~ ... ~ = ~  0,390 9
\item   0,598  ~ \(\times\)  ~ ... ~ = ~  0,059 8
\item   5,217  ~ \(\times\)  ~ ... ~ = ~  0,521 7
\item   72,63  ~ \(\times\)  ~ ... ~ = ~  0,072 63
\item   343,4  ~ \(\times\)  ~ ... ~ = ~  0,343 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 ~dam~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 035,2 ~dg~ = ...~kg
\item   8 813,5 ~daL~ = ...~mL
\item   427,29 ~cg~ = ...~dg
\item   460,31 ~dg~ = ...~cg
\item   505,64 ~g~ = ...~cg
\item   139 ~cm~ = ...~mm
\item   545,8 ~g~ = ...~hg
\item   8 741,2 ~dag~ = ...~hg
\item   5 991,5 ~dam~ = ...~hm
\item   3 391,2 ~mg~ = ...~g
\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   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{470}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{200}{100}\)
\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   0,027  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,7}
\item   2,67  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 267}
\item   19,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 196}
\item   511  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 511 000}
\item   0,095  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 95}
\item   0,009  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,9}
\item   0,802  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 802}
\item   0,062  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,2}
\item   0,021  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,1}
\item   0,015  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   382,7 ~ : ~ 10 ~ = ~{\color{red} 38,27}
\item   65,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,065 22}
\item   716 ~ : ~ 10 ~ = ~{\color{red} 71,6}
\item   763 ~ : ~ 100 ~ = ~{\color{red} 7,63}
\item   8 953 ~ : ~ 10 ~ = ~{\color{red} 895,3}
\item   0,347 ~ : ~ 10 ~ = ~{\color{red} 0,034 7}
\item   5,775 ~ : ~ 10 ~ = ~{\color{red} 0,577 5}
\item   5,145 ~ : ~ 100 ~ = ~{\color{red} 0,051 45}
\item   5 879 ~ : ~ 100 ~ = ~{\color{red} 58,79}
\item   26,72 ~ : ~ 10 ~ = ~{\color{red} 2,672}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 030
\item   0,007 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,07
\item   18,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~18 300
\item   0,051 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,51
\item   3,51 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~35,1
\item   4,11 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 110
\item   1,26 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~126
\item   0,082 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~82
\item   715 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~71 500
\item   0,476 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~47,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 509 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,509
}\item   4,69 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,469
}\item   7 926 ~ \(\times\)  0,1 ~ = ~{\color{red} 792,6
}\item   9 809 ~ \(\times\)  0,01 ~ = ~{\color{red} 98,09
}\item   32,08 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,032 08
}\item   1 691 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,691
}\item   7,029 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 029
}\item   7 647 ~ \(\times\)  0,1 ~ = ~{\color{red} 764,7
}\item   5 863 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,863
}\item   321,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,217
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   32,43 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,324 3
\item   11,29 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,129
\item   3 106 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 310,6
\item   492,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 49,25
\item   7,676 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,767 6
\item   39,09 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,390 9
\item   0,598 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,059 8
\item   5,217 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,521 7
\item   72,63 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,072 63
\item   343,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,343 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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 035,2 ~dg~ = {\color{red}  0,803 52 }~kg
\item   8 813,5 ~daL~ = {\color{red}  88 135 000 }~mL
\item   427,29 ~cg~ = {\color{red}  42,729 }~dg
\item   460,31 ~dg~ = {\color{red}  4 603,1 }~cg
\item   505,64 ~g~ = {\color{red}  50 564 }~cg
\item   139 ~cm~ = {\color{red}  1 390 }~mm
\item   545,8 ~g~ = {\color{red}  5,458 }~hg
\item   8 741,2 ~dag~ = {\color{red}  874,12 }~hg
\item   5 991,5 ~dam~ = {\color{red}  599,15 }~hm
\item   3 391,2 ~mg~ = {\color{red}  3,391 2 }~g
\end{itemize}
\end{multicols}
\end{document}
