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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 83}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{59}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{15}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,9  ~ \(\times\)  ~ 10
\item   1,87  ~ \(\times\)  ~ 10
\item   847  ~ \(\times\)  ~ 100
\item   1,66  ~ \(\times\)  ~ 100
\item   58,3  ~ \(\times\)  ~ 100
\item   81,3  ~ \(\times\)  ~ 100
\item   179  ~ \(\times\)  ~ 10
\item   0,029  ~ \(\times\)  ~ 100
\item   0,04  ~ \(\times\)  ~ 1 000
\item   0,02  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,92  ~ : ~ 1 000
\item   5,367  ~ : ~ 10
\item   2,329  ~ : ~ 1 000
\item   846,3  ~ : ~ 1 000
\item   2 190  ~ : ~ 100
\item   734,7  ~ : ~ 1 000
\item   7 424  ~ : ~ 1 000
\item   2,115  ~ : ~ 1 000
\item   9,264  ~ : ~ 10
\item   35,6  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,09  ~ \(\times\)  ~ ... ~ = ~ 10,9
\item   171  ~ \(\times\)  ~ ... ~ = ~ 171 000
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 43
\item   7,9  ~ \(\times\)  ~ ... ~ = ~ 790
\item   0,833  ~ \(\times\)  ~ ... ~ = ~ 83,3
\item   0,336  ~ \(\times\)  ~ ... ~ = ~ 33,6
\item   0,017  ~ \(\times\)  ~ ... ~ = ~ 1,7
\item   0,066  ~ \(\times\)  ~ ... ~ = ~ 0,66
\item   0,057  ~ \(\times\)  ~ ... ~ = ~ 57
\item   0,031  ~ \(\times\)  ~ ... ~ = ~ 0,31
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,365  ~ \(\times\)  ~ 0,01
\item   6 572  ~ \(\times\)  ~ 0,1
\item   7 543  ~ \(\times\)  ~ 0,001
\item   768,8  ~ \(\times\)  ~ 0,1
\item   79,59  ~ \(\times\)  ~ 0,01
\item   1,35  ~ \(\times\)  ~ 0,001
\item   0,948  ~ \(\times\)  ~ 0,001
\item   2,432  ~ \(\times\)  ~ 0,01
\item   11,56  ~ \(\times\)  ~ 0,01
\item   5,278  ~ \(\times\)  ~ 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   3 801  ~ \(\times\)  ~ ... ~ = ~  380,1
\item   1 879  ~ \(\times\)  ~ ... ~ = ~  18,79
\item   0,883  ~ \(\times\)  ~ ... ~ = ~  0,008 83
\item   1 998  ~ \(\times\)  ~ ... ~ = ~  1,998
\item   931,5  ~ \(\times\)  ~ ... ~ = ~  0,931 5
\item   6,995  ~ \(\times\)  ~ ... ~ = ~  0,006 995
\item   1 739  ~ \(\times\)  ~ ... ~ = ~  1,739
\item   47,22  ~ \(\times\)  ~ ... ~ = ~  0,472 2
\item   361,5  ~ \(\times\)  ~ ... ~ = ~  36,15
\item   7,307  ~ \(\times\)  ~ ... ~ = ~  0,007 307
\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 ~m~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   865,18 ~km~ = ...~cm
\item   222,06 ~hm~ = ...~cm
\item   961,7 ~mL~ = ...~kL
\item   509,64 ~daL~ = ...~cL
\item   406,2 ~hm~ = ...~dm
\item   3 225,5 ~hg~ = ...~kg
\item   7 765,7 ~cL~ = ...~dL
\item   3 993,8 ~cL~ = ...~daL
\item   8 829,6 ~L~ = ...~dL
\item   842,92 ~g~ = ...~dag
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{2200}{100}\) = \(\dfrac{220}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{59}{10}\) = \(\dfrac{590}{100}\)
\item   \(\dfrac{15}{100}\) = \(\dfrac{150}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 59}
\item   1,87  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 18,7}
\item   847  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 84 700}
\item   1,66  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 166}
\item   58,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 830}
\item   81,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 130}
\item   179  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 790}
\item   0,029  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,9}
\item   0,04  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 40}
\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   7,92 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 92}
\item   5,367 ~ : ~ 10 ~ = ~{\color{red} 0,536 7}
\item   2,329 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 329}
\item   846,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,846 3}
\item   2 190 ~ : ~ 100 ~ = ~{\color{red} 21,9}
\item   734,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,734 7}
\item   7 424 ~ : ~ 1 000 ~ = ~{\color{red} 7,424}
\item   2,115 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 115}
\item   9,264 ~ : ~ 10 ~ = ~{\color{red} 0,926 4}
\item   35,6 ~ : ~ 100 ~ = ~{\color{red} 0,356}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,09 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~10,9
\item   171 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~171 000
\item   0,043 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43
\item   7,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~790
\item   0,833 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~83,3
\item   0,336 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~33,6
\item   0,017 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,7
\item   0,066 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,66
\item   0,057 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~57
\item   0,031 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,31
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,365 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,083 65
}\item   6 572 ~ \(\times\)  0,1 ~ = ~{\color{red} 657,2
}\item   7 543 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,543
}\item   768,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 76,88
}\item   79,59 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,795 9
}\item   1,35 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 35
}\item   0,948 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 948
}\item   2,432 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,024 32
}\item   11,56 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,115 6
}\item   5,278 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,527 8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 801 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 380,1
\item   1 879 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 18,79
\item   0,883 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,008 83
\item   1 998 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,998
\item   931,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,931 5
\item   6,995 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 995
\item   1 739 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,739
\item   47,22 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,472 2
\item   361,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 36,15
\item   7,307 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 307
\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 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   865,18 ~km~ = {\color{red}  86 518 000 }~cm
\item   222,06 ~hm~ = {\color{red}  2 220 600 }~cm
\item   961,7 ~mL~ = {\color{red}  0,000 961 7 }~kL
\item   509,64 ~daL~ = {\color{red}  509 640 }~cL
\item   406,2 ~hm~ = {\color{red}  406 200 }~dm
\item   3 225,5 ~hg~ = {\color{red}  322,55 }~kg
\item   7 765,7 ~cL~ = {\color{red}  776,57 }~dL
\item   3 993,8 ~cL~ = {\color{red}  3,993 8 }~daL
\item   8 829,6 ~L~ = {\color{red}  88 296 }~dL
\item   842,92 ~g~ = {\color{red}  84,292 }~dag
\end{itemize}
\end{multicols}
\end{document}
