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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 262}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   86,4  ~ \(\times\)  ~ 10
\item   0,072  ~ \(\times\)  ~ 1 000
\item   97  ~ \(\times\)  ~ 100
\item   18,2  ~ \(\times\)  ~ 100
\item   56,8  ~ \(\times\)  ~ 1 000
\item   9,87  ~ \(\times\)  ~ 1 000
\item   145  ~ \(\times\)  ~ 1 000
\item   453  ~ \(\times\)  ~ 10
\item   9,22  ~ \(\times\)  ~ 100
\item   0,895  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   98,56  ~ : ~ 100
\item   909,1  ~ : ~ 10
\item   47,1  ~ : ~ 100
\item   806,9  ~ : ~ 1 000
\item   5 084  ~ : ~ 10
\item   802,2  ~ : ~ 100
\item   64,46  ~ : ~ 10
\item   1,063  ~ : ~ 10
\item   1 611  ~ : ~ 10
\item   644,7  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 4,5
\item   0,758  ~ \(\times\)  ~ ... ~ = ~ 758
\item   0,582  ~ \(\times\)  ~ ... ~ = ~ 5,82
\item   0,02  ~ \(\times\)  ~ ... ~ = ~ 2
\item   0,819  ~ \(\times\)  ~ ... ~ = ~ 8,19
\item   44,7  ~ \(\times\)  ~ ... ~ = ~ 4 470
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 7
\item   0,035  ~ \(\times\)  ~ ... ~ = ~ 35
\item   512  ~ \(\times\)  ~ ... ~ = ~ 512 000
\item   386  ~ \(\times\)  ~ ... ~ = ~ 3 860
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   629,1  ~ \(\times\)  ~ 0,001
\item   4,304  ~ \(\times\)  ~ 0,01
\item   860,2  ~ \(\times\)  ~ 0,001
\item   5 562  ~ \(\times\)  ~ 0,1
\item   9,98  ~ \(\times\)  ~ 0,01
\item   162,4  ~ \(\times\)  ~ 0,1
\item   417,3  ~ \(\times\)  ~ 0,1
\item   2 696  ~ \(\times\)  ~ 0,01
\item   1 005  ~ \(\times\)  ~ 0,01
\item   3,433  ~ \(\times\)  ~ 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   4,226  ~ \(\times\)  ~ ... ~ = ~  0,042 26
\item   5,45  ~ \(\times\)  ~ ... ~ = ~  0,054 5
\item   2,264  ~ \(\times\)  ~ ... ~ = ~  0,022 64
\item   2,711  ~ \(\times\)  ~ ... ~ = ~  0,027 11
\item   181,7  ~ \(\times\)  ~ ... ~ = ~  18,17
\item   579,2  ~ \(\times\)  ~ ... ~ = ~  57,92
\item   957,8  ~ \(\times\)  ~ ... ~ = ~  9,578
\item   3,09  ~ \(\times\)  ~ ... ~ = ~  0,030 9
\item   2 556  ~ \(\times\)  ~ ... ~ = ~  2,556
\item   637,6  ~ \(\times\)  ~ ... ~ = ~  0,637 6
\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 ~dm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~km~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 032 ~kL~ = ...~dL
\item   7 905,3 ~dag~ = ...~dg
\item   164,2 ~m~ = ...~dam
\item   469,32 ~mm~ = ...~hm
\item   4 909,9 ~dg~ = ...~dag
\item   9 136,5 ~mL~ = ...~kL
\item   2 968,5 ~cL~ = ...~daL
\item   144,02 ~m~ = ...~dm
\item   349,33 ~mm~ = ...~cm
\item   4 420,6 ~cg~ = ...~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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{7000}{100}\) = \(\dfrac{700}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{570}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{530}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   86,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 864}
\item   0,072  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 72}
\item   97  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 700}
\item   18,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 820}
\item   56,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 56 800}
\item   9,87  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 870}
\item   145  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 145 000}
\item   453  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 530}
\item   9,22  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 922}
\item   0,895  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 89,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   98,56 ~ : ~ 100 ~ = ~{\color{red} 0,985 6}
\item   909,1 ~ : ~ 10 ~ = ~{\color{red} 90,91}
\item   47,1 ~ : ~ 100 ~ = ~{\color{red} 0,471}
\item   806,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,806 9}
\item   5 084 ~ : ~ 10 ~ = ~{\color{red} 508,4}
\item   802,2 ~ : ~ 100 ~ = ~{\color{red} 8,022}
\item   64,46 ~ : ~ 10 ~ = ~{\color{red} 6,446}
\item   1,063 ~ : ~ 10 ~ = ~{\color{red} 0,106 3}
\item   1 611 ~ : ~ 10 ~ = ~{\color{red} 161,1}
\item   644,7 ~ : ~ 10 ~ = ~{\color{red} 64,47}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,045 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4,5
\item   0,758 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~758
\item   0,582 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,82
\item   0,02 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2
\item   0,819 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,19
\item   44,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 470
\item   0,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7
\item   0,035 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~35
\item   512 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~512 000
\item   386 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 860
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   629,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,629 1
}\item   4,304 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,043 04
}\item   860,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,860 2
}\item   5 562 ~ \(\times\)  0,1 ~ = ~{\color{red} 556,2
}\item   9,98 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,099 8
}\item   162,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 16,24
}\item   417,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 41,73
}\item   2 696 ~ \(\times\)  0,01 ~ = ~{\color{red} 26,96
}\item   1 005 ~ \(\times\)  0,01 ~ = ~{\color{red} 10,05
}\item   3,433 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,034 33
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,226 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,042 26
\item   5,45 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,054 5
\item   2,264 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,022 64
\item   2,711 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,027 11
\item   181,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 18,17
\item   579,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 57,92
\item   957,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,578
\item   3,09 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,030 9
\item   2 556 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,556
\item   637,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,637 6
\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 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }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   3 032 ~kL~ = {\color{red}  30 320 000 }~dL
\item   7 905,3 ~dag~ = {\color{red}  790 530 }~dg
\item   164,2 ~m~ = {\color{red}  16,42 }~dam
\item   469,32 ~mm~ = {\color{red}  0,004 693 2 }~hm
\item   4 909,9 ~dg~ = {\color{red}  49,099 }~dag
\item   9 136,5 ~mL~ = {\color{red}  0,009 136 5 }~kL
\item   2 968,5 ~cL~ = {\color{red}  2,968 5 }~daL
\item   144,02 ~m~ = {\color{red}  1 440,2 }~dm
\item   349,33 ~mm~ = {\color{red}  34,933 }~cm
\item   4 420,6 ~cg~ = {\color{red}  442,06 }~dg
\end{itemize}
\end{multicols}
\end{document}
