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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 135}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{26}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{68}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   298  ~ \(\times\)  ~ 1 000
\item   86  ~ \(\times\)  ~ 100
\item   6,6  ~ \(\times\)  ~ 100
\item   3,62  ~ \(\times\)  ~ 100
\item   6,13  ~ \(\times\)  ~ 100
\item   292  ~ \(\times\)  ~ 10
\item   298  ~ \(\times\)  ~ 100
\item   544  ~ \(\times\)  ~ 100
\item   2,78  ~ \(\times\)  ~ 1 000
\item   359  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   144,9  ~ : ~ 1 000
\item   3,073  ~ : ~ 1 000
\item   2 030  ~ : ~ 1 000
\item   7,85  ~ : ~ 1 000
\item   511  ~ : ~ 10
\item   40,26  ~ : ~ 10
\item   4,051  ~ : ~ 1 000
\item   25,61  ~ : ~ 100
\item   143,6  ~ : ~ 100
\item   141,7  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   65,1  ~ \(\times\)  ~ ... ~ = ~ 6 510
\item   0,042  ~ \(\times\)  ~ ... ~ = ~ 0,42
\item   923  ~ \(\times\)  ~ ... ~ = ~ 923 000
\item   1,96  ~ \(\times\)  ~ ... ~ = ~ 1 960
\item   247  ~ \(\times\)  ~ ... ~ = ~ 24 700
\item   4,7  ~ \(\times\)  ~ ... ~ = ~ 4 700
\item   0,017  ~ \(\times\)  ~ ... ~ = ~ 0,17
\item   0,496  ~ \(\times\)  ~ ... ~ = ~ 496
\item   37,8  ~ \(\times\)  ~ ... ~ = ~ 3 780
\item   62,8  ~ \(\times\)  ~ ... ~ = ~ 62 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,327  ~ \(\times\)  ~ 0,1
\item   2 440  ~ \(\times\)  ~ 0,001
\item   79,09  ~ \(\times\)  ~ 0,01
\item   1,556  ~ \(\times\)  ~ 0,1
\item   4 199  ~ \(\times\)  ~ 0,1
\item   3 644  ~ \(\times\)  ~ 0,01
\item   5,515  ~ \(\times\)  ~ 0,01
\item   609,7  ~ \(\times\)  ~ 0,001
\item   3,656  ~ \(\times\)  ~ 0,001
\item   28,48  ~ \(\times\)  ~ 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   8,901  ~ \(\times\)  ~ ... ~ = ~  0,890 1
\item   7,15  ~ \(\times\)  ~ ... ~ = ~  0,071 5
\item   7,062  ~ \(\times\)  ~ ... ~ = ~  0,070 62
\item   113,5  ~ \(\times\)  ~ ... ~ = ~  1,135
\item   92,51  ~ \(\times\)  ~ ... ~ = ~  0,925 1
\item   3 665  ~ \(\times\)  ~ ... ~ = ~  36,65
\item   5,363  ~ \(\times\)  ~ ... ~ = ~  0,005 363
\item   6,626  ~ \(\times\)  ~ ... ~ = ~  0,066 26
\item   49,64  ~ \(\times\)  ~ ... ~ = ~  0,049 64
\item   8,638  ~ \(\times\)  ~ ... ~ = ~  0,086 38
\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 ~hm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   294,72 ~km~ = ...~m
\item   379,13 ~dm~ = ...~mm
\item   3 930,5 ~cL~ = ...~daL
\item   942,03 ~cg~ = ...~dag
\item   3 392,5 ~dg~ = ...~mg
\item   1 877,6 ~hL~ = ...~L
\item   3 488,5 ~dam~ = ...~mm
\item   285,3 ~dam~ = ...~dm
\item   498,88 ~g~ = ...~mg
\item   4 527,2 ~g~ = ...~kg
\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   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{7300}{100}\) = \(\dfrac{730}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{26}{10}\) = \(\dfrac{260}{100}\)
\item   \(\dfrac{68}{100}\) = \(\dfrac{680}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   298  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 298 000}
\item   86  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 600}
\item   6,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 660}
\item   3,62  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 362}
\item   6,13  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 613}
\item   292  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 920}
\item   298  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 29 800}
\item   544  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 54 400}
\item   2,78  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 780}
\item   359  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 590}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   144,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,144 9}
\item   3,073 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 073}
\item   2 030 ~ : ~ 1 000 ~ = ~{\color{red} 2,03}
\item   7,85 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 85}
\item   511 ~ : ~ 10 ~ = ~{\color{red} 51,1}
\item   40,26 ~ : ~ 10 ~ = ~{\color{red} 4,026}
\item   4,051 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 051}
\item   25,61 ~ : ~ 100 ~ = ~{\color{red} 0,256 1}
\item   143,6 ~ : ~ 100 ~ = ~{\color{red} 1,436}
\item   141,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,141 7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   65,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 510
\item   0,042 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,42
\item   923 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~923 000
\item   1,96 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 960
\item   247 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~24 700
\item   4,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 700
\item   0,017 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,17
\item   0,496 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~496
\item   37,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 780
\item   62,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~62 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,327 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,232 7
}\item   2 440 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,44
}\item   79,09 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,790 9
}\item   1,556 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,155 6
}\item   4 199 ~ \(\times\)  0,1 ~ = ~{\color{red} 419,9
}\item   3 644 ~ \(\times\)  0,01 ~ = ~{\color{red} 36,44
}\item   5,515 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,055 15
}\item   609,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,609 7
}\item   3,656 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 656
}\item   28,48 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,028 48
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,901 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,890 1
\item   7,15 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,071 5
\item   7,062 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,070 62
\item   113,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,135
\item   92,51 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,925 1
\item   3 665 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 36,65
\item   5,363 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 363
\item   6,626 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,066 26
\item   49,64 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,049 64
\item   8,638 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,086 38
\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 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   294,72 ~km~ = {\color{red}  294 720 }~m
\item   379,13 ~dm~ = {\color{red}  37 913 }~mm
\item   3 930,5 ~cL~ = {\color{red}  3,930 5 }~daL
\item   942,03 ~cg~ = {\color{red}  0,942 03 }~dag
\item   3 392,5 ~dg~ = {\color{red}  339 250 }~mg
\item   1 877,6 ~hL~ = {\color{red}  187 760 }~L
\item   3 488,5 ~dam~ = {\color{red}  34 885 000 }~mm
\item   285,3 ~dam~ = {\color{red}  28 530 }~dm
\item   498,88 ~g~ = {\color{red}  498 880 }~mg
\item   4 527,2 ~g~ = {\color{red}  4,527 2 }~kg
\end{itemize}
\end{multicols}
\end{document}
