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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 98}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{18}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03  ~ \(\times\)  ~ 10
\item   0,816  ~ \(\times\)  ~ 10
\item   416  ~ \(\times\)  ~ 1 000
\item   8,35  ~ \(\times\)  ~ 10
\item   803  ~ \(\times\)  ~ 100
\item   8  ~ \(\times\)  ~ 100
\item   0,056  ~ \(\times\)  ~ 10
\item   0,086  ~ \(\times\)  ~ 10
\item   42,1  ~ \(\times\)  ~ 1 000
\item   52,1  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   850,9  ~ : ~ 10
\item   896,1  ~ : ~ 1 000
\item   6 823  ~ : ~ 1 000
\item   2,697  ~ : ~ 10
\item   5,237  ~ : ~ 10
\item   4 941  ~ : ~ 10
\item   0,866  ~ : ~ 1 000
\item   81,63  ~ : ~ 1 000
\item   9 276  ~ : ~ 1 000
\item   109,7  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   31,9  ~ \(\times\)  ~ ... ~ = ~ 31 900
\item   268  ~ \(\times\)  ~ ... ~ = ~ 2 680
\item   630  ~ \(\times\)  ~ ... ~ = ~ 63 000
\item   0,447  ~ \(\times\)  ~ ... ~ = ~ 44,7
\item   440  ~ \(\times\)  ~ ... ~ = ~ 44 000
\item   7,61  ~ \(\times\)  ~ ... ~ = ~ 761
\item   27,9  ~ \(\times\)  ~ ... ~ = ~ 27 900
\item   887  ~ \(\times\)  ~ ... ~ = ~ 88 700
\item   596  ~ \(\times\)  ~ ... ~ = ~ 59 600
\item   690  ~ \(\times\)  ~ ... ~ = ~ 69 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,587  ~ \(\times\)  ~ 0,1
\item   9 024  ~ \(\times\)  ~ 0,001
\item   1,98  ~ \(\times\)  ~ 0,01
\item   3,734  ~ \(\times\)  ~ 0,001
\item   3,708  ~ \(\times\)  ~ 0,001
\item   73,71  ~ \(\times\)  ~ 0,01
\item   8,055  ~ \(\times\)  ~ 0,01
\item   7,063  ~ \(\times\)  ~ 0,1
\item   7 453  ~ \(\times\)  ~ 0,1
\item   88,5  ~ \(\times\)  ~ 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   4,313  ~ \(\times\)  ~ ... ~ = ~  0,004 313
\item   89,71  ~ \(\times\)  ~ ... ~ = ~  0,089 71
\item   312,5  ~ \(\times\)  ~ ... ~ = ~  3,125
\item   78,73  ~ \(\times\)  ~ ... ~ = ~  0,078 73
\item   20,92  ~ \(\times\)  ~ ... ~ = ~  2,092
\item   52,52  ~ \(\times\)  ~ ... ~ = ~  0,052 52
\item   956,6  ~ \(\times\)  ~ ... ~ = ~  95,66
\item   2  ~ \(\times\)  ~ ... ~ = ~  0,02
\item   6 809  ~ \(\times\)  ~ ... ~ = ~  6,809
\item   89,39  ~ \(\times\)  ~ ... ~ = ~  0,089 39
\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~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 249,3 ~kL~ = ...~cL
\item   365,55 ~dm~ = ...~km
\item   935,84 ~cL~ = ...~hL
\item   8 800 ~dam~ = ...~cm
\item   624,37 ~hm~ = ...~dam
\item   8 498,6 ~mg~ = ...~g
\item   7 203,5 ~kL~ = ...~daL
\item   345,2 ~dag~ = ...~kg
\item   5 393,4 ~dm~ = ...~cm
\item   6 595,5 ~dL~ = ...~daL
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{560}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{18}{10}\) = \(\dfrac{180}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,03  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,3}
\item   0,816  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,16}
\item   416  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 416 000}
\item   8,35  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 83,5}
\item   803  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80 300}
\item   8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 800}
\item   0,056  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,56}
\item   0,086  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,86}
\item   42,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 42 100}
\item   52,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 210}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   850,9 ~ : ~ 10 ~ = ~{\color{red} 85,09}
\item   896,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,896 1}
\item   6 823 ~ : ~ 1 000 ~ = ~{\color{red} 6,823}
\item   2,697 ~ : ~ 10 ~ = ~{\color{red} 0,269 7}
\item   5,237 ~ : ~ 10 ~ = ~{\color{red} 0,523 7}
\item   4 941 ~ : ~ 10 ~ = ~{\color{red} 494,1}
\item   0,866 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 866}
\item   81,63 ~ : ~ 1 000 ~ = ~{\color{red} 0,081 63}
\item   9 276 ~ : ~ 1 000 ~ = ~{\color{red} 9,276}
\item   109,7 ~ : ~ 100 ~ = ~{\color{red} 1,097}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   31,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~31 900
\item   268 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 680
\item   630 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~63 000
\item   0,447 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~44,7
\item   440 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~44 000
\item   7,61 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~761
\item   27,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27 900
\item   887 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88 700
\item   596 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~59 600
\item   690 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~69 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,587 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,358 7
}\item   9 024 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,024
}\item   1,98 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,019 8
}\item   3,734 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 734
}\item   3,708 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 708
}\item   73,71 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,737 1
}\item   8,055 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,080 55
}\item   7,063 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,706 3
}\item   7 453 ~ \(\times\)  0,1 ~ = ~{\color{red} 745,3
}\item   88,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,088 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   4,313 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 313
\item   89,71 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,089 71
\item   312,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,125
\item   78,73 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,078 73
\item   20,92 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,092
\item   52,52 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,052 52
\item   956,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 95,66
\item   2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,02
\item   6 809 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,809
\item   89,39 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,089 39
\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}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 249,3 ~kL~ = {\color{red}  524 930 000 }~cL
\item   365,55 ~dm~ = {\color{red}  0,036 555 }~km
\item   935,84 ~cL~ = {\color{red}  0,093 584 }~hL
\item   8 800 ~dam~ = {\color{red}  8 800 000 }~cm
\item   624,37 ~hm~ = {\color{red}  6 243,7 }~dam
\item   8 498,6 ~mg~ = {\color{red}  8,498 6 }~g
\item   7 203,5 ~kL~ = {\color{red}  720 350 }~daL
\item   345,2 ~dag~ = {\color{red}  3,452 }~kg
\item   5 393,4 ~dm~ = {\color{red}  53 934 }~cm
\item   6 595,5 ~dL~ = {\color{red}  65,955 }~daL
\end{itemize}
\end{multicols}
\end{document}
