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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 115}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\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   \(\dfrac{53}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,078  ~ \(\times\)  ~ 100
\item   7,03  ~ \(\times\)  ~ 1 000
\item   0,356  ~ \(\times\)  ~ 10
\item   0,057  ~ \(\times\)  ~ 10
\item   166  ~ \(\times\)  ~ 100
\item   89,8  ~ \(\times\)  ~ 100
\item   0,077  ~ \(\times\)  ~ 10
\item   17,8  ~ \(\times\)  ~ 10
\item   55  ~ \(\times\)  ~ 10
\item   0,813  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   34,12  ~ : ~ 1 000
\item   41,5  ~ : ~ 1 000
\item   39,18  ~ : ~ 100
\item   615,8  ~ : ~ 100
\item   571,1  ~ : ~ 1 000
\item   6,696  ~ : ~ 100
\item   318,5  ~ : ~ 1 000
\item   55,47  ~ : ~ 1 000
\item   893,9  ~ : ~ 10
\item   1,421  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   281  ~ \(\times\)  ~ ... ~ = ~ 2 810
\item   147  ~ \(\times\)  ~ ... ~ = ~ 147 000
\item   0,306  ~ \(\times\)  ~ ... ~ = ~ 306
\item   3,93  ~ \(\times\)  ~ ... ~ = ~ 393
\item   0,392  ~ \(\times\)  ~ ... ~ = ~ 3,92
\item   712  ~ \(\times\)  ~ ... ~ = ~ 712 000
\item   207  ~ \(\times\)  ~ ... ~ = ~ 207 000
\item   0,79  ~ \(\times\)  ~ ... ~ = ~ 790
\item   925  ~ \(\times\)  ~ ... ~ = ~ 92 500
\item   0,086  ~ \(\times\)  ~ ... ~ = ~ 86
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   569,2  ~ \(\times\)  ~ 0,01
\item   7,238  ~ \(\times\)  ~ 0,001
\item   30,22  ~ \(\times\)  ~ 0,001
\item   83,22  ~ \(\times\)  ~ 0,01
\item   8 470  ~ \(\times\)  ~ 0,1
\item   107,7  ~ \(\times\)  ~ 0,1
\item   868,8  ~ \(\times\)  ~ 0,01
\item   8 879  ~ \(\times\)  ~ 0,1
\item   1,604  ~ \(\times\)  ~ 0,01
\item   418,3  ~ \(\times\)  ~ 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   7 224  ~ \(\times\)  ~ ... ~ = ~  7,224
\item   7 469  ~ \(\times\)  ~ ... ~ = ~  7,469
\item   862,4  ~ \(\times\)  ~ ... ~ = ~  86,24
\item   517,5  ~ \(\times\)  ~ ... ~ = ~  0,517 5
\item   9 508  ~ \(\times\)  ~ ... ~ = ~  950,8
\item   95,6  ~ \(\times\)  ~ ... ~ = ~  9,56
\item   6 438  ~ \(\times\)  ~ ... ~ = ~  643,8
\item   201,9  ~ \(\times\)  ~ ... ~ = ~  2,019
\item   568,3  ~ \(\times\)  ~ ... ~ = ~  5,683
\item   3 086  ~ \(\times\)  ~ ... ~ = ~  30,86
\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 ~km~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 411,2 ~daL~ = ...~L
\item   821,81 ~dag~ = ...~g
\item   871,64 ~hL~ = ...~dL
\item   151,73 ~cg~ = ...~mg
\item   897,24 ~dag~ = ...~kg
\item   706,78 ~g~ = ...~kg
\item   1 232,3 ~m~ = ...~hm
\item   9 684,1 ~cm~ = ...~dm
\item   1 855,8 ~dm~ = ...~cm
\item   273,2 ~hg~ = ...~cg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{250}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{25}{10}\) = \(\dfrac{250}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{530}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,078  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,8}
\item   7,03  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 030}
\item   0,356  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,56}
\item   0,057  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,57}
\item   166  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 16 600}
\item   89,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 980}
\item   0,077  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,77}
\item   17,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 178}
\item   55  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 550}
\item   0,813  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,13}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   34,12 ~ : ~ 1 000 ~ = ~{\color{red} 0,034 12}
\item   41,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,041 5}
\item   39,18 ~ : ~ 100 ~ = ~{\color{red} 0,391 8}
\item   615,8 ~ : ~ 100 ~ = ~{\color{red} 6,158}
\item   571,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,571 1}
\item   6,696 ~ : ~ 100 ~ = ~{\color{red} 0,066 96}
\item   318,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,318 5}
\item   55,47 ~ : ~ 1 000 ~ = ~{\color{red} 0,055 47}
\item   893,9 ~ : ~ 10 ~ = ~{\color{red} 89,39}
\item   1,421 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 421}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   281 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 810
\item   147 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~147 000
\item   0,306 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~306
\item   3,93 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~393
\item   0,392 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,92
\item   712 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~712 000
\item   207 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~207 000
\item   0,79 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~790
\item   925 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~92 500
\item   0,086 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~86
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   569,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,692
}\item   7,238 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 238
}\item   30,22 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 22
}\item   83,22 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,832 2
}\item   8 470 ~ \(\times\)  0,1 ~ = ~{\color{red} 847
}\item   107,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 10,77
}\item   868,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,688
}\item   8 879 ~ \(\times\)  0,1 ~ = ~{\color{red} 887,9
}\item   1,604 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,016 04
}\item   418,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 41,83
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 224 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,224
\item   7 469 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,469
\item   862,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 86,24
\item   517,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,517 5
\item   9 508 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 950,8
\item   95,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,56
\item   6 438 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 643,8
\item   201,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,019
\item   568,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,683
\item   3 086 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 30,86
\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 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\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   3 411,2 ~daL~ = {\color{red}  34 112 }~L
\item   821,81 ~dag~ = {\color{red}  8 218,1 }~g
\item   871,64 ~hL~ = {\color{red}  871 640 }~dL
\item   151,73 ~cg~ = {\color{red}  1 517,3 }~mg
\item   897,24 ~dag~ = {\color{red}  8,972 4 }~kg
\item   706,78 ~g~ = {\color{red}  0,706 78 }~kg
\item   1 232,3 ~m~ = {\color{red}  12,323 }~hm
\item   9 684,1 ~cm~ = {\color{red}  968,41 }~dm
\item   1 855,8 ~dm~ = {\color{red}  18 558 }~cm
\item   273,2 ~hg~ = {\color{red}  2 732 000 }~cg
\end{itemize}
\end{multicols}
\end{document}
