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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 189}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{25}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{62}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   761  ~ \(\times\)  ~ 1 000
\item   18  ~ \(\times\)  ~ 1 000
\item   15,5  ~ \(\times\)  ~ 100
\item   305  ~ \(\times\)  ~ 100
\item   724  ~ \(\times\)  ~ 1 000
\item   0,126  ~ \(\times\)  ~ 1 000
\item   220  ~ \(\times\)  ~ 100
\item   17,6  ~ \(\times\)  ~ 10
\item   65,3  ~ \(\times\)  ~ 100
\item   0,728  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85,3  ~ : ~ 100
\item   1 803  ~ : ~ 10
\item   77,61  ~ : ~ 10
\item   5 552  ~ : ~ 1 000
\item   581,9  ~ : ~ 1 000
\item   16,99  ~ : ~ 10
\item   628,7  ~ : ~ 100
\item   8 454  ~ : ~ 10
\item   70,19  ~ : ~ 1 000
\item   7,52  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,21  ~ \(\times\)  ~ ... ~ = ~ 8 210
\item   0,014  ~ \(\times\)  ~ ... ~ = ~ 1,4
\item   6,04  ~ \(\times\)  ~ ... ~ = ~ 604
\item   0,036  ~ \(\times\)  ~ ... ~ = ~ 36
\item   0,075  ~ \(\times\)  ~ ... ~ = ~ 7,5
\item   887  ~ \(\times\)  ~ ... ~ = ~ 887 000
\item   1,09  ~ \(\times\)  ~ ... ~ = ~ 10,9
\item   0,809  ~ \(\times\)  ~ ... ~ = ~ 8,09
\item   0,031  ~ \(\times\)  ~ ... ~ = ~ 31
\item   0,769  ~ \(\times\)  ~ ... ~ = ~ 76,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,29  ~ \(\times\)  ~ 0,01
\item   2 184  ~ \(\times\)  ~ 0,001
\item   38,39  ~ \(\times\)  ~ 0,01
\item   939,1  ~ \(\times\)  ~ 0,001
\item   127,5  ~ \(\times\)  ~ 0,01
\item   132,7  ~ \(\times\)  ~ 0,1
\item   2 914  ~ \(\times\)  ~ 0,01
\item   576,7  ~ \(\times\)  ~ 0,001
\item   3 584  ~ \(\times\)  ~ 0,01
\item   44,99  ~ \(\times\)  ~ 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   240,6  ~ \(\times\)  ~ ... ~ = ~  24,06
\item   7 493  ~ \(\times\)  ~ ... ~ = ~  749,3
\item   439,4  ~ \(\times\)  ~ ... ~ = ~  0,439 4
\item   9 004  ~ \(\times\)  ~ ... ~ = ~  900,4
\item   50,49  ~ \(\times\)  ~ ... ~ = ~  0,050 49
\item   294,9  ~ \(\times\)  ~ ... ~ = ~  2,949
\item   1,118  ~ \(\times\)  ~ ... ~ = ~  0,001 118
\item   81,16  ~ \(\times\)  ~ ... ~ = ~  8,116
\item   0,277  ~ \(\times\)  ~ ... ~ = ~  0,002 77
\item   8 981  ~ \(\times\)  ~ ... ~ = ~  898,1
\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~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 270,8 ~dg~ = ...~cg
\item   2 223,9 ~hg~ = ...~g
\item   145,13 ~dm~ = ...~mm
\item   874,54 ~hg~ = ...~dag
\item   5 573,5 ~dg~ = ...~hg
\item   3 946,2 ~dam~ = ...~mm
\item   653,97 ~dm~ = ...~m
\item   265,42 ~dL~ = ...~hL
\item   9 946,2 ~cL~ = ...~L
\item   5 612,7 ~cm~ = ...~dam
\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   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{290}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{25}{10}\) = \(\dfrac{250}{100}\)
\item   \(\dfrac{62}{100}\) = \(\dfrac{620}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   761  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 761 000}
\item   18  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 18 000}
\item   15,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 550}
\item   305  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 30 500}
\item   724  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 724 000}
\item   0,126  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 126}
\item   220  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 22 000}
\item   17,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 176}
\item   65,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 530}
\item   0,728  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,28}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85,3 ~ : ~ 100 ~ = ~{\color{red} 0,853}
\item   1 803 ~ : ~ 10 ~ = ~{\color{red} 180,3}
\item   77,61 ~ : ~ 10 ~ = ~{\color{red} 7,761}
\item   5 552 ~ : ~ 1 000 ~ = ~{\color{red} 5,552}
\item   581,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,581 9}
\item   16,99 ~ : ~ 10 ~ = ~{\color{red} 1,699}
\item   628,7 ~ : ~ 100 ~ = ~{\color{red} 6,287}
\item   8 454 ~ : ~ 10 ~ = ~{\color{red} 845,4}
\item   70,19 ~ : ~ 1 000 ~ = ~{\color{red} 0,070 19}
\item   7,52 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 52}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,21 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 210
\item   0,014 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,4
\item   6,04 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~604
\item   0,036 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~36
\item   0,075 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,5
\item   887 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~887 000
\item   1,09 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~10,9
\item   0,809 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,09
\item   0,031 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~31
\item   0,769 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~76,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,29 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,072 9
}\item   2 184 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,184
}\item   38,39 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,383 9
}\item   939,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,939 1
}\item   127,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,275
}\item   132,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 13,27
}\item   2 914 ~ \(\times\)  0,01 ~ = ~{\color{red} 29,14
}\item   576,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,576 7
}\item   3 584 ~ \(\times\)  0,01 ~ = ~{\color{red} 35,84
}\item   44,99 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,044 99
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   240,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 24,06
\item   7 493 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 749,3
\item   439,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,439 4
\item   9 004 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 900,4
\item   50,49 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,050 49
\item   294,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,949
\item   1,118 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 118
\item   81,16 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,116
\item   0,277 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,002 77
\item   8 981 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 898,1
\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~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 270,8 ~dg~ = {\color{red}  12 708 }~cg
\item   2 223,9 ~hg~ = {\color{red}  222 390 }~g
\item   145,13 ~dm~ = {\color{red}  14 513 }~mm
\item   874,54 ~hg~ = {\color{red}  8 745,4 }~dag
\item   5 573,5 ~dg~ = {\color{red}  5,573 5 }~hg
\item   3 946,2 ~dam~ = {\color{red}  39 462 000 }~mm
\item   653,97 ~dm~ = {\color{red}  65,397 }~m
\item   265,42 ~dL~ = {\color{red}  0,265 42 }~hL
\item   9 946,2 ~cL~ = {\color{red}  99,462 }~L
\item   5 612,7 ~cm~ = {\color{red}  5,612 7 }~dam
\end{itemize}
\end{multicols}
\end{document}
