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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 47}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{84}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,6  ~ \(\times\)  ~ 1 000
\item   0,404  ~ \(\times\)  ~ 1 000
\item   0,05  ~ \(\times\)  ~ 1 000
\item   33  ~ \(\times\)  ~ 10
\item   0,279  ~ \(\times\)  ~ 1 000
\item   568  ~ \(\times\)  ~ 100
\item   0,59  ~ \(\times\)  ~ 10
\item   0,025  ~ \(\times\)  ~ 1 000
\item   0,376  ~ \(\times\)  ~ 10
\item   0,004  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,91  ~ : ~ 1 000
\item   952,3  ~ : ~ 10
\item   67,9  ~ : ~ 100
\item   17,05  ~ : ~ 1 000
\item   63,85  ~ : ~ 10
\item   38,19  ~ : ~ 10
\item   7 818  ~ : ~ 100
\item   58,85  ~ : ~ 10
\item   91,98  ~ : ~ 100
\item   8 828  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 3,3
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 0,28
\item   629  ~ \(\times\)  ~ ... ~ = ~ 629 000
\item   87  ~ \(\times\)  ~ ... ~ = ~ 8 700
\item   5,06  ~ \(\times\)  ~ ... ~ = ~ 5 060
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 0,96
\item   463  ~ \(\times\)  ~ ... ~ = ~ 4 630
\item   569  ~ \(\times\)  ~ ... ~ = ~ 5 690
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 28
\item   0,568  ~ \(\times\)  ~ ... ~ = ~ 56,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 090  ~ \(\times\)  ~ 0,001
\item   4,442  ~ \(\times\)  ~ 0,001
\item   5 261  ~ \(\times\)  ~ 0,001
\item   408,2  ~ \(\times\)  ~ 0,01
\item   717,2  ~ \(\times\)  ~ 0,1
\item   779,8  ~ \(\times\)  ~ 0,1
\item   171,3  ~ \(\times\)  ~ 0,001
\item   94,33  ~ \(\times\)  ~ 0,001
\item   6 529  ~ \(\times\)  ~ 0,01
\item   7 374  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,106  ~ \(\times\)  ~ ... ~ = ~  0,210 6
\item   6 150  ~ \(\times\)  ~ ... ~ = ~  61,5
\item   78,4  ~ \(\times\)  ~ ... ~ = ~  7,84
\item   8,484  ~ \(\times\)  ~ ... ~ = ~  0,848 4
\item   8,206  ~ \(\times\)  ~ ... ~ = ~  0,008 206
\item   9 396  ~ \(\times\)  ~ ... ~ = ~  9,396
\item   131  ~ \(\times\)  ~ ... ~ = ~  13,1
\item   90,04  ~ \(\times\)  ~ ... ~ = ~  0,090 04
\item   86,5  ~ \(\times\)  ~ ... ~ = ~  0,086 5
\item   1,104  ~ \(\times\)  ~ ... ~ = ~  0,110 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~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   665,2 ~cg~ = ...~hg
\item   5 373,7 ~dL~ = ...~kL
\item   8 453,7 ~hg~ = ...~cg
\item   654,62 ~kL~ = ...~daL
\item   566,59 ~cL~ = ...~mL
\item   990,51 ~hg~ = ...~dag
\item   4 118,4 ~L~ = ...~dL
\item   271,65 ~hm~ = ...~cm
\item   442,06 ~m~ = ...~cm
\item   869,31 ~dag~ = ...~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   6 = \(\dfrac{60}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{690}{100}\)
\item   \(\dfrac{84}{100}\) = \(\dfrac{840}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 600}
\item   0,404  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 404}
\item   0,05  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 50}
\item   33  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 330}
\item   0,279  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 279}
\item   568  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 56 800}
\item   0,59  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,9}
\item   0,025  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 25}
\item   0,376  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,76}
\item   0,004  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,91 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 91}
\item   952,3 ~ : ~ 10 ~ = ~{\color{red} 95,23}
\item   67,9 ~ : ~ 100 ~ = ~{\color{red} 0,679}
\item   17,05 ~ : ~ 1 000 ~ = ~{\color{red} 0,017 05}
\item   63,85 ~ : ~ 10 ~ = ~{\color{red} 6,385}
\item   38,19 ~ : ~ 10 ~ = ~{\color{red} 3,819}
\item   7 818 ~ : ~ 100 ~ = ~{\color{red} 78,18}
\item   58,85 ~ : ~ 10 ~ = ~{\color{red} 5,885}
\item   91,98 ~ : ~ 100 ~ = ~{\color{red} 0,919 8}
\item   8 828 ~ : ~ 100 ~ = ~{\color{red} 88,28}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,033 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,3
\item   0,028 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,28
\item   629 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~629 000
\item   87 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 700
\item   5,06 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 060
\item   0,096 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,96
\item   463 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 630
\item   569 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 690
\item   0,028 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~28
\item   0,568 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~56,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 090 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,09
}\item   4,442 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 442
}\item   5 261 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,261
}\item   408,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,082
}\item   717,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 71,72
}\item   779,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 77,98
}\item   171,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,171 3
}\item   94,33 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,094 33
}\item   6 529 ~ \(\times\)  0,01 ~ = ~{\color{red} 65,29
}\item   7 374 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,374
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,106 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,210 6
\item   6 150 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 61,5
\item   78,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,84
\item   8,484 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,848 4
\item   8,206 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 206
\item   9 396 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,396
\item   131 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 13,1
\item   90,04 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,090 04
\item   86,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,086 5
\item   1,104 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,110 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}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   665,2 ~cg~ = {\color{red}  0,066 52 }~hg
\item   5 373,7 ~dL~ = {\color{red}  0,537 37 }~kL
\item   8 453,7 ~hg~ = {\color{red}  84 537 000 }~cg
\item   654,62 ~kL~ = {\color{red}  65 462 }~daL
\item   566,59 ~cL~ = {\color{red}  5 665,9 }~mL
\item   990,51 ~hg~ = {\color{red}  9 905,1 }~dag
\item   4 118,4 ~L~ = {\color{red}  41 184 }~dL
\item   271,65 ~hm~ = {\color{red}  2 716 500 }~cm
\item   442,06 ~m~ = {\color{red}  44 206 }~cm
\item   869,31 ~dag~ = {\color{red}  86 931 }~dg
\end{itemize}
\end{multicols}
\end{document}
