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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 168}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,3  ~ \(\times\)  ~ 1 000
\item   0,533  ~ \(\times\)  ~ 1 000
\item   0,023  ~ \(\times\)  ~ 1 000
\item   401  ~ \(\times\)  ~ 10
\item   0,044  ~ \(\times\)  ~ 100
\item   3,63  ~ \(\times\)  ~ 1 000
\item   97,6  ~ \(\times\)  ~ 100
\item   0,09  ~ \(\times\)  ~ 100
\item   474  ~ \(\times\)  ~ 10
\item   2,24  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   321,7  ~ : ~ 100
\item   7 424  ~ : ~ 100
\item   52,87  ~ : ~ 100
\item   2,57  ~ : ~ 1 000
\item   6 872  ~ : ~ 1 000
\item   50,4  ~ : ~ 1 000
\item   670  ~ : ~ 10
\item   7,377  ~ : ~ 100
\item   146,7  ~ : ~ 100
\item   5 987  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   14,7  ~ \(\times\)  ~ ... ~ = ~ 14 700
\item   0,072  ~ \(\times\)  ~ ... ~ = ~ 0,72
\item   90,9  ~ \(\times\)  ~ ... ~ = ~ 90 900
\item   1  ~ \(\times\)  ~ ... ~ = ~ 10
\item   0,226  ~ \(\times\)  ~ ... ~ = ~ 226
\item   255  ~ \(\times\)  ~ ... ~ = ~ 2 550
\item   0,006  ~ \(\times\)  ~ ... ~ = ~ 6
\item   3,03  ~ \(\times\)  ~ ... ~ = ~ 3 030
\item   16,6  ~ \(\times\)  ~ ... ~ = ~ 1 660
\item   5  ~ \(\times\)  ~ ... ~ = ~ 500
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 928  ~ \(\times\)  ~ 0,01
\item   5 028  ~ \(\times\)  ~ 0,01
\item   7,98  ~ \(\times\)  ~ 0,1
\item   6 502  ~ \(\times\)  ~ 0,001
\item   5 466  ~ \(\times\)  ~ 0,01
\item   7,905  ~ \(\times\)  ~ 0,01
\item   58,39  ~ \(\times\)  ~ 0,1
\item   4 257  ~ \(\times\)  ~ 0,1
\item   21,85  ~ \(\times\)  ~ 0,01
\item   166,4  ~ \(\times\)  ~ 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   772,7  ~ \(\times\)  ~ ... ~ = ~  77,27
\item   248,1  ~ \(\times\)  ~ ... ~ = ~  24,81
\item   7 286  ~ \(\times\)  ~ ... ~ = ~  72,86
\item   2 489  ~ \(\times\)  ~ ... ~ = ~  24,89
\item   7,764  ~ \(\times\)  ~ ... ~ = ~  0,007 764
\item   90,76  ~ \(\times\)  ~ ... ~ = ~  0,907 6
\item   1 252  ~ \(\times\)  ~ ... ~ = ~  1,252
\item   5 412  ~ \(\times\)  ~ ... ~ = ~  54,12
\item   967  ~ \(\times\)  ~ ... ~ = ~  0,967
\item   547,7  ~ \(\times\)  ~ ... ~ = ~  54,77
\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~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   291,1 ~cg~ = ...~g
\item   9 088,9 ~g~ = ...~dag
\item   2 767,8 ~g~ = ...~hg
\item   420,59 ~g~ = ...~cg
\item   514,66 ~mL~ = ...~cL
\item   8 962,1 ~daL~ = ...~kL
\item   351,82 ~cL~ = ...~daL
\item   892,86 ~mL~ = ...~dL
\item   7 463,2 ~dam~ = ...~cm
\item   3 659,8 ~kg~ = ...~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   2 = \(\dfrac{20}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{5900}{100}\) = \(\dfrac{590}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{390}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{790}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 20 300}
\item   0,533  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 533}
\item   0,023  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 23}
\item   401  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 010}
\item   0,044  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,4}
\item   3,63  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 630}
\item   97,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 760}
\item   0,09  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9}
\item   474  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 740}
\item   2,24  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 240}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   321,7 ~ : ~ 100 ~ = ~{\color{red} 3,217}
\item   7 424 ~ : ~ 100 ~ = ~{\color{red} 74,24}
\item   52,87 ~ : ~ 100 ~ = ~{\color{red} 0,528 7}
\item   2,57 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 57}
\item   6 872 ~ : ~ 1 000 ~ = ~{\color{red} 6,872}
\item   50,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,050 4}
\item   670 ~ : ~ 10 ~ = ~{\color{red} 67}
\item   7,377 ~ : ~ 100 ~ = ~{\color{red} 0,073 77}
\item   146,7 ~ : ~ 100 ~ = ~{\color{red} 1,467}
\item   5 987 ~ : ~ 10 ~ = ~{\color{red} 598,7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   14,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14 700
\item   0,072 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,72
\item   90,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~90 900
\item   1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~10
\item   0,226 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~226
\item   255 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 550
\item   0,006 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6
\item   3,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 030
\item   16,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 660
\item   5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~500
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 928 ~ \(\times\)  0,01 ~ = ~{\color{red} 89,28
}\item   5 028 ~ \(\times\)  0,01 ~ = ~{\color{red} 50,28
}\item   7,98 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,798
}\item   6 502 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,502
}\item   5 466 ~ \(\times\)  0,01 ~ = ~{\color{red} 54,66
}\item   7,905 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,079 05
}\item   58,39 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,839
}\item   4 257 ~ \(\times\)  0,1 ~ = ~{\color{red} 425,7
}\item   21,85 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,218 5
}\item   166,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,664
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   772,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 77,27
\item   248,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 24,81
\item   7 286 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 72,86
\item   2 489 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 24,89
\item   7,764 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 764
\item   90,76 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,907 6
\item   1 252 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,252
\item   5 412 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 54,12
\item   967 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,967
\item   547,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 54,77
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   291,1 ~cg~ = {\color{red}  2,911 }~g
\item   9 088,9 ~g~ = {\color{red}  908,89 }~dag
\item   2 767,8 ~g~ = {\color{red}  27,678 }~hg
\item   420,59 ~g~ = {\color{red}  42 059 }~cg
\item   514,66 ~mL~ = {\color{red}  51,466 }~cL
\item   8 962,1 ~daL~ = {\color{red}  89,621 }~kL
\item   351,82 ~cL~ = {\color{red}  0,351 82 }~daL
\item   892,86 ~mL~ = {\color{red}  8,928 6 }~dL
\item   7 463,2 ~dam~ = {\color{red}  7 463 200 }~cm
\item   3 659,8 ~kg~ = {\color{red}  3 659 800 000 }~mg
\end{itemize}
\end{multicols}
\end{document}
