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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 99}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{40}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   145  ~ \(\times\)  ~ 100
\item   0,755  ~ \(\times\)  ~ 1 000
\item   0,071  ~ \(\times\)  ~ 10
\item   0,097  ~ \(\times\)  ~ 100
\item   0,213  ~ \(\times\)  ~ 1 000
\item   0,064  ~ \(\times\)  ~ 10
\item   8,2  ~ \(\times\)  ~ 100
\item   89,1  ~ \(\times\)  ~ 10
\item   48,1  ~ \(\times\)  ~ 1 000
\item   355  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 763  ~ : ~ 100
\item   5,284  ~ : ~ 10
\item   4 514  ~ : ~ 100
\item   34,39  ~ : ~ 1 000
\item   1,425  ~ : ~ 1 000
\item   3,346  ~ : ~ 10
\item   595,8  ~ : ~ 10
\item   2,735  ~ : ~ 1 000
\item   301,1  ~ : ~ 10
\item   1 899  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,494  ~ \(\times\)  ~ ... ~ = ~ 4,94
\item   0,968  ~ \(\times\)  ~ ... ~ = ~ 968
\item   9,7  ~ \(\times\)  ~ ... ~ = ~ 970
\item   641  ~ \(\times\)  ~ ... ~ = ~ 64 100
\item   34,6  ~ \(\times\)  ~ ... ~ = ~ 34 600
\item   42,4  ~ \(\times\)  ~ ... ~ = ~ 424
\item   66,4  ~ \(\times\)  ~ ... ~ = ~ 6 640
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 2,7
\item   85,3  ~ \(\times\)  ~ ... ~ = ~ 8 530
\item   0,972  ~ \(\times\)  ~ ... ~ = ~ 9,72
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   224,6  ~ \(\times\)  ~ 0,001
\item   6 790  ~ \(\times\)  ~ 0,1
\item   204,6  ~ \(\times\)  ~ 0,01
\item   295,4  ~ \(\times\)  ~ 0,01
\item   248,5  ~ \(\times\)  ~ 0,001
\item   5,329  ~ \(\times\)  ~ 0,1
\item   4 321  ~ \(\times\)  ~ 0,01
\item   3 147  ~ \(\times\)  ~ 0,001
\item   4 814  ~ \(\times\)  ~ 0,001
\item   8,82  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,277  ~ \(\times\)  ~ ... ~ = ~  0,062 77
\item   6,644  ~ \(\times\)  ~ ... ~ = ~  0,066 44
\item   6 179  ~ \(\times\)  ~ ... ~ = ~  617,9
\item   7,16  ~ \(\times\)  ~ ... ~ = ~  0,007 16
\item   6,631  ~ \(\times\)  ~ ... ~ = ~  0,663 1
\item   520,3  ~ \(\times\)  ~ ... ~ = ~  0,520 3
\item   5 190  ~ \(\times\)  ~ ... ~ = ~  5,19
\item   524,4  ~ \(\times\)  ~ ... ~ = ~  0,524 4
\item   4,192  ~ \(\times\)  ~ ... ~ = ~  0,041 92
\item   7 279  ~ \(\times\)  ~ ... ~ = ~  72,79
\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~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 007,6 ~m~ = ...~dam
\item   4 146,1 ~hm~ = ...~mm
\item   6 830,2 ~daL~ = ...~L
\item   4 187,8 ~L~ = ...~hL
\item   841,48 ~dag~ = ...~cg
\item   853,95 ~m~ = ...~hm
\item   581,44 ~mL~ = ...~cL
\item   414 ~dam~ = ...~mm
\item   3 759,2 ~kL~ = ...~daL
\item   845,6 ~hg~ = ...~mg
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{360}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{40}{10}\) = \(\dfrac{400}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{420}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   145  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14 500}
\item   0,755  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 755}
\item   0,071  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,71}
\item   0,097  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,7}
\item   0,213  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 213}
\item   0,064  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,64}
\item   8,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 820}
\item   89,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 891}
\item   48,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 48 100}
\item   355  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 355 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 763 ~ : ~ 100 ~ = ~{\color{red} 87,63}
\item   5,284 ~ : ~ 10 ~ = ~{\color{red} 0,528 4}
\item   4 514 ~ : ~ 100 ~ = ~{\color{red} 45,14}
\item   34,39 ~ : ~ 1 000 ~ = ~{\color{red} 0,034 39}
\item   1,425 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 425}
\item   3,346 ~ : ~ 10 ~ = ~{\color{red} 0,334 6}
\item   595,8 ~ : ~ 10 ~ = ~{\color{red} 59,58}
\item   2,735 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 735}
\item   301,1 ~ : ~ 10 ~ = ~{\color{red} 30,11}
\item   1 899 ~ : ~ 10 ~ = ~{\color{red} 189,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,494 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,94
\item   0,968 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~968
\item   9,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~970
\item   641 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~64 100
\item   34,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~34 600
\item   42,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~424
\item   66,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 640
\item   0,027 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,7
\item   85,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 530
\item   0,972 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,72
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   224,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,224 6
}\item   6 790 ~ \(\times\)  0,1 ~ = ~{\color{red} 679
}\item   204,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,046
}\item   295,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,954
}\item   248,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,248 5
}\item   5,329 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,532 9
}\item   4 321 ~ \(\times\)  0,01 ~ = ~{\color{red} 43,21
}\item   3 147 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,147
}\item   4 814 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,814
}\item   8,82 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,882
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,277 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,062 77
\item   6,644 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,066 44
\item   6 179 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 617,9
\item   7,16 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 16
\item   6,631 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,663 1
\item   520,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,520 3
\item   5 190 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,19
\item   524,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,524 4
\item   4,192 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,041 92
\item   7 279 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 72,79
\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~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 007,6 ~m~ = {\color{red}  900,76 }~dam
\item   4 146,1 ~hm~ = {\color{red}  414 610 000 }~mm
\item   6 830,2 ~daL~ = {\color{red}  68 302 }~L
\item   4 187,8 ~L~ = {\color{red}  41,878 }~hL
\item   841,48 ~dag~ = {\color{red}  841 480 }~cg
\item   853,95 ~m~ = {\color{red}  8,539 5 }~hm
\item   581,44 ~mL~ = {\color{red}  58,144 }~cL
\item   414 ~dam~ = {\color{red}  4 140 000 }~mm
\item   3 759,2 ~kL~ = {\color{red}  375 920 }~daL
\item   845,6 ~hg~ = {\color{red}  84 560 000 }~mg
\end{itemize}
\end{multicols}
\end{document}
