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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 235}

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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   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26,6  ~ \(\times\)  ~ 10
\item   129  ~ \(\times\)  ~ 100
\item   17,8  ~ \(\times\)  ~ 100
\item   0,804  ~ \(\times\)  ~ 100
\item   46  ~ \(\times\)  ~ 1 000
\item   0,075  ~ \(\times\)  ~ 10
\item   1,16  ~ \(\times\)  ~ 100
\item   0,053  ~ \(\times\)  ~ 100
\item   812  ~ \(\times\)  ~ 100
\item   281  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   161,5  ~ : ~ 1 000
\item   687,1  ~ : ~ 100
\item   56,12  ~ : ~ 10
\item   4 177  ~ : ~ 100
\item   0,826  ~ : ~ 1 000
\item   1,947  ~ : ~ 1 000
\item   6 544  ~ : ~ 100
\item   4,804  ~ : ~ 1 000
\item   631,4  ~ : ~ 100
\item   51,09  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,02  ~ \(\times\)  ~ ... ~ = ~ 0,2
\item   579  ~ \(\times\)  ~ ... ~ = ~ 5 790
\item   0,584  ~ \(\times\)  ~ ... ~ = ~ 58,4
\item   0,085  ~ \(\times\)  ~ ... ~ = ~ 0,85
\item   4,41  ~ \(\times\)  ~ ... ~ = ~ 441
\item   557  ~ \(\times\)  ~ ... ~ = ~ 5 570
\item   701  ~ \(\times\)  ~ ... ~ = ~ 7 010
\item   0,592  ~ \(\times\)  ~ ... ~ = ~ 5,92
\item   0,044  ~ \(\times\)  ~ ... ~ = ~ 44
\item   0,727  ~ \(\times\)  ~ ... ~ = ~ 727
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 413  ~ \(\times\)  ~ 0,01
\item   782,7  ~ \(\times\)  ~ 0,1
\item   22,69  ~ \(\times\)  ~ 0,001
\item   3,758  ~ \(\times\)  ~ 0,1
\item   4,777  ~ \(\times\)  ~ 0,01
\item   1,933  ~ \(\times\)  ~ 0,1
\item   209,7  ~ \(\times\)  ~ 0,001
\item   1,044  ~ \(\times\)  ~ 0,01
\item   27,17  ~ \(\times\)  ~ 0,1
\item   5,528  ~ \(\times\)  ~ 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   91,87  ~ \(\times\)  ~ ... ~ = ~  0,918 7
\item   8,567  ~ \(\times\)  ~ ... ~ = ~  0,008 567
\item   17,03  ~ \(\times\)  ~ ... ~ = ~  0,017 03
\item   6 788  ~ \(\times\)  ~ ... ~ = ~  678,8
\item   9,11  ~ \(\times\)  ~ ... ~ = ~  0,009 11
\item   7,611  ~ \(\times\)  ~ ... ~ = ~  0,076 11
\item   31,81  ~ \(\times\)  ~ ... ~ = ~  3,181
\item   978,8  ~ \(\times\)  ~ ... ~ = ~  9,788
\item   3,361  ~ \(\times\)  ~ ... ~ = ~  0,033 61
\item   521,5  ~ \(\times\)  ~ ... ~ = ~  52,15
\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 ~cm~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   541,81 ~km~ = ...~hm
\item   618,86 ~L~ = ...~cL
\item   4 110 ~mm~ = ...~m
\item   1 213,3 ~cL~ = ...~kL
\item   8 423,9 ~mg~ = ...~g
\item   253,46 ~cL~ = ...~dL
\item   7 598,3 ~L~ = ...~mL
\item   8 866,8 ~g~ = ...~dg
\item   419,57 ~dL~ = ...~daL
\item   2 363,6 ~mm~ = ...~hm
\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   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{220}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{130}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 266}
\item   129  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 12 900}
\item   17,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 780}
\item   0,804  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80,4}
\item   46  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 46 000}
\item   0,075  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,75}
\item   1,16  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 116}
\item   0,053  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,3}
\item   812  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 81 200}
\item   281  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 28 100}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   161,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,161 5}
\item   687,1 ~ : ~ 100 ~ = ~{\color{red} 6,871}
\item   56,12 ~ : ~ 10 ~ = ~{\color{red} 5,612}
\item   4 177 ~ : ~ 100 ~ = ~{\color{red} 41,77}
\item   0,826 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 826}
\item   1,947 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 947}
\item   6 544 ~ : ~ 100 ~ = ~{\color{red} 65,44}
\item   4,804 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 804}
\item   631,4 ~ : ~ 100 ~ = ~{\color{red} 6,314}
\item   51,09 ~ : ~ 100 ~ = ~{\color{red} 0,510 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,02 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,2
\item   579 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 790
\item   0,584 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~58,4
\item   0,085 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,85
\item   4,41 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~441
\item   557 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 570
\item   701 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 010
\item   0,592 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,92
\item   0,044 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~44
\item   0,727 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~727
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 413 ~ \(\times\)  0,01 ~ = ~{\color{red} 54,13
}\item   782,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 78,27
}\item   22,69 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,022 69
}\item   3,758 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,375 8
}\item   4,777 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,047 77
}\item   1,933 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,193 3
}\item   209,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,209 7
}\item   1,044 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,010 44
}\item   27,17 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,717
}\item   5,528 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,055 28
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   91,87 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,918 7
\item   8,567 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 567
\item   17,03 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,017 03
\item   6 788 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 678,8
\item   9,11 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 11
\item   7,611 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,076 11
\item   31,81 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,181
\item   978,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,788
\item   3,361 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,033 61
\item   521,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 52,15
\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 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\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   541,81 ~km~ = {\color{red}  5 418,1 }~hm
\item   618,86 ~L~ = {\color{red}  61 886 }~cL
\item   4 110 ~mm~ = {\color{red}  4,11 }~m
\item   1 213,3 ~cL~ = {\color{red}  0,012 133 }~kL
\item   8 423,9 ~mg~ = {\color{red}  8,423 9 }~g
\item   253,46 ~cL~ = {\color{red}  25,346 }~dL
\item   7 598,3 ~L~ = {\color{red}  7 598 300 }~mL
\item   8 866,8 ~g~ = {\color{red}  88 668 }~dg
\item   419,57 ~dL~ = {\color{red}  4,195 7 }~daL
\item   2 363,6 ~mm~ = {\color{red}  0,023 636 }~hm
\end{itemize}
\end{multicols}
\end{document}
