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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 136}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{65}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   72,1  ~ \(\times\)  ~ 10
\item   0,661  ~ \(\times\)  ~ 10
\item   176  ~ \(\times\)  ~ 1 000
\item   625  ~ \(\times\)  ~ 10
\item   0,021  ~ \(\times\)  ~ 100
\item   6,43  ~ \(\times\)  ~ 100
\item   506  ~ \(\times\)  ~ 10
\item   8,67  ~ \(\times\)  ~ 1 000
\item   791  ~ \(\times\)  ~ 1 000
\item   817  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,67  ~ : ~ 10
\item   42,29  ~ : ~ 100
\item   17,35  ~ : ~ 1 000
\item   6 521  ~ : ~ 1 000
\item   8 873  ~ : ~ 1 000
\item   390,9  ~ : ~ 1 000
\item   564,8  ~ : ~ 1 000
\item   0,262  ~ : ~ 100
\item   154,1  ~ : ~ 100
\item   3,766  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,435  ~ \(\times\)  ~ ... ~ = ~ 43,5
\item   71,8  ~ \(\times\)  ~ ... ~ = ~ 7 180
\item   0,845  ~ \(\times\)  ~ ... ~ = ~ 84,5
\item   20,5  ~ \(\times\)  ~ ... ~ = ~ 2 050
\item   0,421  ~ \(\times\)  ~ ... ~ = ~ 42,1
\item   15,8  ~ \(\times\)  ~ ... ~ = ~ 1 580
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 6,9
\item   7,38  ~ \(\times\)  ~ ... ~ = ~ 738
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 77
\item   0,78  ~ \(\times\)  ~ ... ~ = ~ 78
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,02  ~ \(\times\)  ~ 0,01
\item   33,73  ~ \(\times\)  ~ 0,001
\item   1 392  ~ \(\times\)  ~ 0,01
\item   0,903  ~ \(\times\)  ~ 0,1
\item   6 831  ~ \(\times\)  ~ 0,001
\item   6,965  ~ \(\times\)  ~ 0,001
\item   4 658  ~ \(\times\)  ~ 0,1
\item   7 142  ~ \(\times\)  ~ 0,001
\item   6,034  ~ \(\times\)  ~ 0,1
\item   8 879  ~ \(\times\)  ~ 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   8,828  ~ \(\times\)  ~ ... ~ = ~  0,882 8
\item   409  ~ \(\times\)  ~ ... ~ = ~  40,9
\item   6 121  ~ \(\times\)  ~ ... ~ = ~  6,121
\item   8,005  ~ \(\times\)  ~ ... ~ = ~  0,080 05
\item   967,1  ~ \(\times\)  ~ ... ~ = ~  0,967 1
\item   629,5  ~ \(\times\)  ~ ... ~ = ~  62,95
\item   8,293  ~ \(\times\)  ~ ... ~ = ~  0,829 3
\item   77,36  ~ \(\times\)  ~ ... ~ = ~  0,077 36
\item   693,1  ~ \(\times\)  ~ ... ~ = ~  0,693 1
\item   59,56  ~ \(\times\)  ~ ... ~ = ~  0,059 56
\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 ~cm~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 636,6 ~daL~ = ...~L
\item   9 151,9 ~cm~ = ...~dm
\item   480,47 ~mL~ = ...~kL
\item   7 848,1 ~dam~ = ...~km
\item   2 345,9 ~dag~ = ...~kg
\item   617,85 ~hg~ = ...~mg
\item   5 898 ~kL~ = ...~dL
\item   717,52 ~cL~ = ...~kL
\item   1 664,2 ~daL~ = ...~mL
\item   161,95 ~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   7 = \(\dfrac{70}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{360}{100}\)
\item   \(\dfrac{65}{100}\) = \(\dfrac{650}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   72,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 721}
\item   0,661  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,61}
\item   176  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 176 000}
\item   625  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 250}
\item   0,021  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,1}
\item   6,43  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 643}
\item   506  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 060}
\item   8,67  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 670}
\item   791  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 791 000}
\item   817  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 170}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,67 ~ : ~ 10 ~ = ~{\color{red} 5,467}
\item   42,29 ~ : ~ 100 ~ = ~{\color{red} 0,422 9}
\item   17,35 ~ : ~ 1 000 ~ = ~{\color{red} 0,017 35}
\item   6 521 ~ : ~ 1 000 ~ = ~{\color{red} 6,521}
\item   8 873 ~ : ~ 1 000 ~ = ~{\color{red} 8,873}
\item   390,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,390 9}
\item   564,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,564 8}
\item   0,262 ~ : ~ 100 ~ = ~{\color{red} 0,002 62}
\item   154,1 ~ : ~ 100 ~ = ~{\color{red} 1,541}
\item   3,766 ~ : ~ 10 ~ = ~{\color{red} 0,376 6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,435 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~43,5
\item   71,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 180
\item   0,845 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~84,5
\item   20,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 050
\item   0,421 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~42,1
\item   15,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 580
\item   0,069 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,9
\item   7,38 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~738
\item   0,077 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~77
\item   0,78 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~78
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,02 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,040 2
}\item   33,73 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,033 73
}\item   1 392 ~ \(\times\)  0,01 ~ = ~{\color{red} 13,92
}\item   0,903 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,090 3
}\item   6 831 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,831
}\item   6,965 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 965
}\item   4 658 ~ \(\times\)  0,1 ~ = ~{\color{red} 465,8
}\item   7 142 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,142
}\item   6,034 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,603 4
}\item   8 879 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,879
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,828 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,882 8
\item   409 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 40,9
\item   6 121 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,121
\item   8,005 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,080 05
\item   967,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,967 1
\item   629,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 62,95
\item   8,293 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,829 3
\item   77,36 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,077 36
\item   693,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,693 1
\item   59,56 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,059 56
\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 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 636,6 ~daL~ = {\color{red}  66 366 }~L
\item   9 151,9 ~cm~ = {\color{red}  915,19 }~dm
\item   480,47 ~mL~ = {\color{red}  0,000 480 47 }~kL
\item   7 848,1 ~dam~ = {\color{red}  78,481 }~km
\item   2 345,9 ~dag~ = {\color{red}  23,459 }~kg
\item   617,85 ~hg~ = {\color{red}  61 785 000 }~mg
\item   5 898 ~kL~ = {\color{red}  58 980 000 }~dL
\item   717,52 ~cL~ = {\color{red}  0,007 175 2 }~kL
\item   1 664,2 ~daL~ = {\color{red}  16 642 000 }~mL
\item   161,95 ~kg~ = {\color{red}  1 619 500 }~dg
\end{itemize}
\end{multicols}
\end{document}
