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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 205}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   85,7  ~ \(\times\)  ~ 1 000
\item   194  ~ \(\times\)  ~ 10
\item   76,4  ~ \(\times\)  ~ 10
\item   65,1  ~ \(\times\)  ~ 1 000
\item   7,55  ~ \(\times\)  ~ 1 000
\item   985  ~ \(\times\)  ~ 1 000
\item   3,14  ~ \(\times\)  ~ 1 000
\item   7,87  ~ \(\times\)  ~ 100
\item   97  ~ \(\times\)  ~ 10
\item   6,29  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 095  ~ : ~ 1 000
\item   882,6  ~ : ~ 100
\item   89,12  ~ : ~ 10
\item   79,28  ~ : ~ 1 000
\item   5 068  ~ : ~ 10
\item   3 464  ~ : ~ 1 000
\item   24,99  ~ : ~ 100
\item   5,983  ~ : ~ 10
\item   8 588  ~ : ~ 100
\item   40,2  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,237  ~ \(\times\)  ~ ... ~ = ~ 237
\item   8  ~ \(\times\)  ~ ... ~ = ~ 8 000
\item   0,055  ~ \(\times\)  ~ ... ~ = ~ 0,55
\item   0,506  ~ \(\times\)  ~ ... ~ = ~ 5,06
\item   485  ~ \(\times\)  ~ ... ~ = ~ 48 500
\item   4,8  ~ \(\times\)  ~ ... ~ = ~ 480
\item   0,392  ~ \(\times\)  ~ ... ~ = ~ 392
\item   2,88  ~ \(\times\)  ~ ... ~ = ~ 288
\item   0,031  ~ \(\times\)  ~ ... ~ = ~ 0,31
\item   73,2  ~ \(\times\)  ~ ... ~ = ~ 7 320
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 825  ~ \(\times\)  ~ 0,1
\item   138,9  ~ \(\times\)  ~ 0,1
\item   90  ~ \(\times\)  ~ 0,001
\item   33,45  ~ \(\times\)  ~ 0,01
\item   54,08  ~ \(\times\)  ~ 0,01
\item   0,696  ~ \(\times\)  ~ 0,01
\item   8 723  ~ \(\times\)  ~ 0,1
\item   302,1  ~ \(\times\)  ~ 0,1
\item   825,7  ~ \(\times\)  ~ 0,001
\item   90,85  ~ \(\times\)  ~ 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   7,698  ~ \(\times\)  ~ ... ~ = ~  0,076 98
\item   3,977  ~ \(\times\)  ~ ... ~ = ~  0,003 977
\item   6 269  ~ \(\times\)  ~ ... ~ = ~  626,9
\item   847,3  ~ \(\times\)  ~ ... ~ = ~  84,73
\item   91,1  ~ \(\times\)  ~ ... ~ = ~  0,911
\item   2 414  ~ \(\times\)  ~ ... ~ = ~  2,414
\item   3,608  ~ \(\times\)  ~ ... ~ = ~  0,003 608
\item   54,79  ~ \(\times\)  ~ ... ~ = ~  0,054 79
\item   4 816  ~ \(\times\)  ~ ... ~ = ~  4,816
\item   872,4  ~ \(\times\)  ~ ... ~ = ~  8,724
\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 ~km~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 610,5 ~daL~ = ...~mL
\item   2 446 ~m~ = ...~km
\item   9 445 ~mg~ = ...~g
\item   7 423,8 ~km~ = ...~hm
\item   1 911,7 ~mm~ = ...~dam
\item   571,27 ~kg~ = ...~dg
\item   159,35 ~cg~ = ...~hg
\item   591,03 ~mg~ = ...~cg
\item   148,19 ~m~ = ...~dm
\item   1 280,4 ~hL~ = ...~mL
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{230}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{740}{100}\)
\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   85,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 85 700}
\item   194  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 940}
\item   76,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 764}
\item   65,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 65 100}
\item   7,55  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 550}
\item   985  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 985 000}
\item   3,14  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 140}
\item   7,87  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 787}
\item   97  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 970}
\item   6,29  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 62,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 095 ~ : ~ 1 000 ~ = ~{\color{red} 5,095}
\item   882,6 ~ : ~ 100 ~ = ~{\color{red} 8,826}
\item   89,12 ~ : ~ 10 ~ = ~{\color{red} 8,912}
\item   79,28 ~ : ~ 1 000 ~ = ~{\color{red} 0,079 28}
\item   5 068 ~ : ~ 10 ~ = ~{\color{red} 506,8}
\item   3 464 ~ : ~ 1 000 ~ = ~{\color{red} 3,464}
\item   24,99 ~ : ~ 100 ~ = ~{\color{red} 0,249 9}
\item   5,983 ~ : ~ 10 ~ = ~{\color{red} 0,598 3}
\item   8 588 ~ : ~ 100 ~ = ~{\color{red} 85,88}
\item   40,2 ~ : ~ 10 ~ = ~{\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   0,237 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~237
\item   8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 000
\item   0,055 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,55
\item   0,506 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,06
\item   485 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~48 500
\item   4,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~480
\item   0,392 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~392
\item   2,88 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~288
\item   0,031 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,31
\item   73,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 320
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 825 ~ \(\times\)  0,1 ~ = ~{\color{red} 382,5
}\item   138,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 13,89
}\item   90 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,09
}\item   33,45 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,334 5
}\item   54,08 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,540 8
}\item   0,696 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,006 96
}\item   8 723 ~ \(\times\)  0,1 ~ = ~{\color{red} 872,3
}\item   302,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 30,21
}\item   825,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,825 7
}\item   90,85 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,908 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,698 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,076 98
\item   3,977 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 977
\item   6 269 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 626,9
\item   847,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 84,73
\item   91,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,911
\item   2 414 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,414
\item   3,608 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 608
\item   54,79 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,054 79
\item   4 816 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,816
\item   872,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,724
\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 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 610,5 ~daL~ = {\color{red}  86 105 000 }~mL
\item   2 446 ~m~ = {\color{red}  2,446 }~km
\item   9 445 ~mg~ = {\color{red}  9,445 }~g
\item   7 423,8 ~km~ = {\color{red}  74 238 }~hm
\item   1 911,7 ~mm~ = {\color{red}  0,191 17 }~dam
\item   571,27 ~kg~ = {\color{red}  5 712 700 }~dg
\item   159,35 ~cg~ = {\color{red}  0,015 935 }~hg
\item   591,03 ~mg~ = {\color{red}  59,103 }~cg
\item   148,19 ~m~ = {\color{red}  1 481,9 }~dm
\item   1 280,4 ~hL~ = {\color{red}  128 040 000 }~mL
\end{itemize}
\end{multicols}
\end{document}
