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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 81}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{60}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   499  ~ \(\times\)  ~ 10
\item   0,161  ~ \(\times\)  ~ 1 000
\item   0,079  ~ \(\times\)  ~ 10
\item   9,36  ~ \(\times\)  ~ 100
\item   7,46  ~ \(\times\)  ~ 10
\item   32,1  ~ \(\times\)  ~ 1 000
\item   8,6  ~ \(\times\)  ~ 1 000
\item   7,77  ~ \(\times\)  ~ 1 000
\item   58,1  ~ \(\times\)  ~ 1 000
\item   34,7  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,933  ~ : ~ 10
\item   7 438  ~ : ~ 1 000
\item   71,96  ~ : ~ 100
\item   58,23  ~ : ~ 1 000
\item   5 800  ~ : ~ 10
\item   1,116  ~ : ~ 1 000
\item   51,32  ~ : ~ 10
\item   3,775  ~ : ~ 10
\item   381,1  ~ : ~ 10
\item   31,18  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   880  ~ \(\times\)  ~ ... ~ = ~ 8 800
\item   0,041  ~ \(\times\)  ~ ... ~ = ~ 0,41
\item   145  ~ \(\times\)  ~ ... ~ = ~ 14 500
\item   40,7  ~ \(\times\)  ~ ... ~ = ~ 407
\item   6,05  ~ \(\times\)  ~ ... ~ = ~ 60,5
\item   71,4  ~ \(\times\)  ~ ... ~ = ~ 7 140
\item   0,933  ~ \(\times\)  ~ ... ~ = ~ 93,3
\item   322  ~ \(\times\)  ~ ... ~ = ~ 32 200
\item   962  ~ \(\times\)  ~ ... ~ = ~ 96 200
\item   84,6  ~ \(\times\)  ~ ... ~ = ~ 846
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,537  ~ \(\times\)  ~ 0,001
\item   32,15  ~ \(\times\)  ~ 0,01
\item   9 519  ~ \(\times\)  ~ 0,01
\item   8,542  ~ \(\times\)  ~ 0,001
\item   557,9  ~ \(\times\)  ~ 0,01
\item   67,23  ~ \(\times\)  ~ 0,01
\item   899,1  ~ \(\times\)  ~ 0,001
\item   777  ~ \(\times\)  ~ 0,1
\item   133,4  ~ \(\times\)  ~ 0,01
\item   10,04  ~ \(\times\)  ~ 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   361,6  ~ \(\times\)  ~ ... ~ = ~  0,361 6
\item   740,7  ~ \(\times\)  ~ ... ~ = ~  0,740 7
\item   125,4  ~ \(\times\)  ~ ... ~ = ~  0,125 4
\item   66,38  ~ \(\times\)  ~ ... ~ = ~  0,663 8
\item   355,9  ~ \(\times\)  ~ ... ~ = ~  35,59
\item   55,53  ~ \(\times\)  ~ ... ~ = ~  0,055 53
\item   18,79  ~ \(\times\)  ~ ... ~ = ~  0,187 9
\item   5,13  ~ \(\times\)  ~ ... ~ = ~  0,513
\item   7 182  ~ \(\times\)  ~ ... ~ = ~  718,2
\item   26,41  ~ \(\times\)  ~ ... ~ = ~  2,641
\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 ~dam~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 490 ~dam~ = ...~km
\item   184,95 ~cg~ = ...~hg
\item   557,91 ~g~ = ...~dag
\item   198,81 ~hg~ = ...~kg
\item   863 ~cL~ = ...~L
\item   5 115,7 ~km~ = ...~cm
\item   221,87 ~mg~ = ...~dag
\item   517,2 ~kg~ = ...~g
\item   2 749,9 ~hL~ = ...~mL
\item   7 626,1 ~dag~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{5400}{100}\) = \(\dfrac{540}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{79}{10}\) = \(\dfrac{790}{100}\)
\item   \(\dfrac{60}{100}\) = \(\dfrac{600}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   499  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 990}
\item   0,161  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 161}
\item   0,079  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,79}
\item   9,36  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 936}
\item   7,46  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 74,6}
\item   32,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32 100}
\item   8,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 600}
\item   7,77  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 770}
\item   58,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 58 100}
\item   34,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 470}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,933 ~ : ~ 10 ~ = ~{\color{red} 0,393 3}
\item   7 438 ~ : ~ 1 000 ~ = ~{\color{red} 7,438}
\item   71,96 ~ : ~ 100 ~ = ~{\color{red} 0,719 6}
\item   58,23 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 23}
\item   5 800 ~ : ~ 10 ~ = ~{\color{red} 580}
\item   1,116 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 116}
\item   51,32 ~ : ~ 10 ~ = ~{\color{red} 5,132}
\item   3,775 ~ : ~ 10 ~ = ~{\color{red} 0,377 5}
\item   381,1 ~ : ~ 10 ~ = ~{\color{red} 38,11}
\item   31,18 ~ : ~ 100 ~ = ~{\color{red} 0,311 8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   880 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 800
\item   0,041 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,41
\item   145 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~14 500
\item   40,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~407
\item   6,05 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~60,5
\item   71,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 140
\item   0,933 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~93,3
\item   322 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~32 200
\item   962 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96 200
\item   84,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~846
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,537 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 537
}\item   32,15 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,321 5
}\item   9 519 ~ \(\times\)  0,01 ~ = ~{\color{red} 95,19
}\item   8,542 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 542
}\item   557,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,579
}\item   67,23 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,672 3
}\item   899,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,899 1
}\item   777 ~ \(\times\)  0,1 ~ = ~{\color{red} 77,7
}\item   133,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,334
}\item   10,04 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,010 04
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   361,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,361 6
\item   740,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,740 7
\item   125,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,125 4
\item   66,38 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,663 8
\item   355,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 35,59
\item   55,53 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,055 53
\item   18,79 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,187 9
\item   5,13 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,513
\item   7 182 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 718,2
\item   26,41 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,641
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 490 ~dam~ = {\color{red}  64,9 }~km
\item   184,95 ~cg~ = {\color{red}  0,018 495 }~hg
\item   557,91 ~g~ = {\color{red}  55,791 }~dag
\item   198,81 ~hg~ = {\color{red}  19,881 }~kg
\item   863 ~cL~ = {\color{red}  8,63 }~L
\item   5 115,7 ~km~ = {\color{red}  511 570 000 }~cm
\item   221,87 ~mg~ = {\color{red}  0,022 187 }~dag
\item   517,2 ~kg~ = {\color{red}  517 200 }~g
\item   2 749,9 ~hL~ = {\color{red}  274 990 000 }~mL
\item   7 626,1 ~dag~ = {\color{red}  76 261 000 }~mg
\end{itemize}
\end{multicols}
\end{document}
