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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 38}

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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   \(\dfrac{2400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   392  ~ \(\times\)  ~ 1 000
\item   68,9  ~ \(\times\)  ~ 1 000
\item   3,61  ~ \(\times\)  ~ 100
\item   7,36  ~ \(\times\)  ~ 1 000
\item   7,53  ~ \(\times\)  ~ 100
\item   0,079  ~ \(\times\)  ~ 100
\item   0,024  ~ \(\times\)  ~ 10
\item   0,549  ~ \(\times\)  ~ 10
\item   0,046  ~ \(\times\)  ~ 10
\item   0,02  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 889  ~ : ~ 10
\item   7 892  ~ : ~ 100
\item   197,6  ~ : ~ 100
\item   1 522  ~ : ~ 100
\item   490,5  ~ : ~ 100
\item   7,531  ~ : ~ 100
\item   48,11  ~ : ~ 10
\item   72,03  ~ : ~ 1 000
\item   27,86  ~ : ~ 10
\item   402  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   766  ~ \(\times\)  ~ ... ~ = ~ 7 660
\item   0,885  ~ \(\times\)  ~ ... ~ = ~ 8,85
\item   8,24  ~ \(\times\)  ~ ... ~ = ~ 82,4
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 4
\item   5,89  ~ \(\times\)  ~ ... ~ = ~ 5 890
\item   4,6  ~ \(\times\)  ~ ... ~ = ~ 460
\item   0,158  ~ \(\times\)  ~ ... ~ = ~ 158
\item   7,5  ~ \(\times\)  ~ ... ~ = ~ 7 500
\item   608  ~ \(\times\)  ~ ... ~ = ~ 608 000
\item   462  ~ \(\times\)  ~ ... ~ = ~ 4 620
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   625,5  ~ \(\times\)  ~ 0,001
\item   97,17  ~ \(\times\)  ~ 0,1
\item   6,38  ~ \(\times\)  ~ 0,001
\item   4 233  ~ \(\times\)  ~ 0,1
\item   767  ~ \(\times\)  ~ 0,01
\item   438,4  ~ \(\times\)  ~ 0,01
\item   3 133  ~ \(\times\)  ~ 0,001
\item   501,7  ~ \(\times\)  ~ 0,01
\item   788  ~ \(\times\)  ~ 0,001
\item   9 134  ~ \(\times\)  ~ 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   7,358  ~ \(\times\)  ~ ... ~ = ~  0,073 58
\item   0,212  ~ \(\times\)  ~ ... ~ = ~  0,002 12
\item   6,806  ~ \(\times\)  ~ ... ~ = ~  0,068 06
\item   528,7  ~ \(\times\)  ~ ... ~ = ~  52,87
\item   6 707  ~ \(\times\)  ~ ... ~ = ~  6,707
\item   54,09  ~ \(\times\)  ~ ... ~ = ~  5,409
\item   45,9  ~ \(\times\)  ~ ... ~ = ~  4,59
\item   5 180  ~ \(\times\)  ~ ... ~ = ~  518
\item   9 814  ~ \(\times\)  ~ ... ~ = ~  98,14
\item   0,879  ~ \(\times\)  ~ ... ~ = ~  0,008 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 ~m~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 350,5 ~dm~ = ...~dam
\item   168,35 ~cL~ = ...~dL
\item   731,05 ~mm~ = ...~dm
\item   5 145,5 ~km~ = ...~mm
\item   501,17 ~kL~ = ...~dL
\item   8 422,1 ~dam~ = ...~mm
\item   983,99 ~cm~ = ...~dm
\item   321,45 ~km~ = ...~dm
\item   1 661,6 ~dm~ = ...~m
\item   680,59 ~m~ = ...~mm
\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   \(\dfrac{2400}{100}\) = \(\dfrac{240}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{570}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{700}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   392  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 392 000}
\item   68,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 68 900}
\item   3,61  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 361}
\item   7,36  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 360}
\item   7,53  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 753}
\item   0,079  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,9}
\item   0,024  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,24}
\item   0,549  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,49}
\item   0,046  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,46}
\item   0,02  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 889 ~ : ~ 10 ~ = ~{\color{red} 888,9}
\item   7 892 ~ : ~ 100 ~ = ~{\color{red} 78,92}
\item   197,6 ~ : ~ 100 ~ = ~{\color{red} 1,976}
\item   1 522 ~ : ~ 100 ~ = ~{\color{red} 15,22}
\item   490,5 ~ : ~ 100 ~ = ~{\color{red} 4,905}
\item   7,531 ~ : ~ 100 ~ = ~{\color{red} 0,075 31}
\item   48,11 ~ : ~ 10 ~ = ~{\color{red} 4,811}
\item   72,03 ~ : ~ 1 000 ~ = ~{\color{red} 0,072 03}
\item   27,86 ~ : ~ 10 ~ = ~{\color{red} 2,786}
\item   402 ~ : ~ 100 ~ = ~{\color{red} 4,02}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   766 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 660
\item   0,885 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,85
\item   8,24 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~82,4
\item   0,004 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4
\item   5,89 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 890
\item   4,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~460
\item   0,158 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~158
\item   7,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 500
\item   608 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~608 000
\item   462 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 620
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   625,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,625 5
}\item   97,17 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,717
}\item   6,38 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 38
}\item   4 233 ~ \(\times\)  0,1 ~ = ~{\color{red} 423,3
}\item   767 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,67
}\item   438,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,384
}\item   3 133 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,133
}\item   501,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,017
}\item   788 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,788
}\item   9 134 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,134
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,358 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,073 58
\item   0,212 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,002 12
\item   6,806 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,068 06
\item   528,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 52,87
\item   6 707 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,707
\item   54,09 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,409
\item   45,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,59
\item   5 180 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 518
\item   9 814 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 98,14
\item   0,879 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,008 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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 350,5 ~dm~ = {\color{red}  13,505 }~dam
\item   168,35 ~cL~ = {\color{red}  16,835 }~dL
\item   731,05 ~mm~ = {\color{red}  7,310 5 }~dm
\item   5 145,5 ~km~ = {\color{red}  5 145 500 000 }~mm
\item   501,17 ~kL~ = {\color{red}  5 011 700 }~dL
\item   8 422,1 ~dam~ = {\color{red}  84 221 000 }~mm
\item   983,99 ~cm~ = {\color{red}  98,399 }~dm
\item   321,45 ~km~ = {\color{red}  3 214 500 }~dm
\item   1 661,6 ~dm~ = {\color{red}  166,16 }~m
\item   680,59 ~m~ = {\color{red}  680 590 }~mm
\end{itemize}
\end{multicols}
\end{document}
