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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 141}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{33}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{84}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,723  ~ \(\times\)  ~ 10
\item   9,56  ~ \(\times\)  ~ 1 000
\item   583  ~ \(\times\)  ~ 1 000
\item   9,3  ~ \(\times\)  ~ 100
\item   2,53  ~ \(\times\)  ~ 1 000
\item   0,037  ~ \(\times\)  ~ 1 000
\item   0,05  ~ \(\times\)  ~ 10
\item   1,7  ~ \(\times\)  ~ 100
\item   59,2  ~ \(\times\)  ~ 1 000
\item   0,077  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,875  ~ : ~ 100
\item   79,47  ~ : ~ 100
\item   280,1  ~ : ~ 100
\item   0,758  ~ : ~ 1 000
\item   9,459  ~ : ~ 10
\item   1 742  ~ : ~ 100
\item   5,28  ~ : ~ 1 000
\item   9,216  ~ : ~ 100
\item   67,11  ~ : ~ 10
\item   9,544  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,04  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   281  ~ \(\times\)  ~ ... ~ = ~ 28 100
\item   0,54  ~ \(\times\)  ~ ... ~ = ~ 54
\item   84  ~ \(\times\)  ~ ... ~ = ~ 8 400
\item   0,071  ~ \(\times\)  ~ ... ~ = ~ 71
\item   677  ~ \(\times\)  ~ ... ~ = ~ 67 700
\item   2,8  ~ \(\times\)  ~ ... ~ = ~ 28
\item   631  ~ \(\times\)  ~ ... ~ = ~ 631 000
\item   22  ~ \(\times\)  ~ ... ~ = ~ 22 000
\item   729  ~ \(\times\)  ~ ... ~ = ~ 72 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,016  ~ \(\times\)  ~ 0,001
\item   871,8  ~ \(\times\)  ~ 0,01
\item   926,8  ~ \(\times\)  ~ 0,01
\item   2,672  ~ \(\times\)  ~ 0,1
\item   977,6  ~ \(\times\)  ~ 0,01
\item   50,36  ~ \(\times\)  ~ 0,1
\item   451,7  ~ \(\times\)  ~ 0,001
\item   521,9  ~ \(\times\)  ~ 0,001
\item   978,9  ~ \(\times\)  ~ 0,1
\item   51,41  ~ \(\times\)  ~ 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   745,7  ~ \(\times\)  ~ ... ~ = ~  74,57
\item   3,647  ~ \(\times\)  ~ ... ~ = ~  0,036 47
\item   5 604  ~ \(\times\)  ~ ... ~ = ~  5,604
\item   0,583  ~ \(\times\)  ~ ... ~ = ~  0,005 83
\item   8 869  ~ \(\times\)  ~ ... ~ = ~  88,69
\item   5 042  ~ \(\times\)  ~ ... ~ = ~  504,2
\item   69,38  ~ \(\times\)  ~ ... ~ = ~  0,693 8
\item   740,8  ~ \(\times\)  ~ ... ~ = ~  7,408
\item   0,683  ~ \(\times\)  ~ ... ~ = ~  0,006 83
\item   825,7  ~ \(\times\)  ~ ... ~ = ~  8,257
\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 ~dm~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 945 ~g~ = ...~cg
\item   241,86 ~dm~ = ...~m
\item   8 022,7 ~cL~ = ...~kL
\item   5 287,1 ~cg~ = ...~hg
\item   234,18 ~dm~ = ...~dam
\item   369,83 ~hg~ = ...~g
\item   732,14 ~dag~ = ...~g
\item   901,16 ~dg~ = ...~cg
\item   7 797,1 ~dg~ = ...~hg
\item   5 647,2 ~km~ = ...~cm
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{8500}{100}\) = \(\dfrac{850}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{33}{10}\) = \(\dfrac{330}{100}\)
\item   \(\dfrac{84}{100}\) = \(\dfrac{840}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,723  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,23}
\item   9,56  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 560}
\item   583  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 583 000}
\item   9,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 930}
\item   2,53  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 530}
\item   0,037  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 37}
\item   0,05  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,5}
\item   1,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 170}
\item   59,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 59 200}
\item   0,077  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,875 ~ : ~ 100 ~ = ~{\color{red} 0,078 75}
\item   79,47 ~ : ~ 100 ~ = ~{\color{red} 0,794 7}
\item   280,1 ~ : ~ 100 ~ = ~{\color{red} 2,801}
\item   0,758 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 758}
\item   9,459 ~ : ~ 10 ~ = ~{\color{red} 0,945 9}
\item   1 742 ~ : ~ 100 ~ = ~{\color{red} 17,42}
\item   5,28 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 28}
\item   9,216 ~ : ~ 100 ~ = ~{\color{red} 0,092 16}
\item   67,11 ~ : ~ 10 ~ = ~{\color{red} 6,711}
\item   9,544 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 544}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,04 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,4
\item   281 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~28 100
\item   0,54 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~54
\item   84 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 400
\item   0,071 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~71
\item   677 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~67 700
\item   2,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~28
\item   631 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~631 000
\item   22 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~22 000
\item   729 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~72 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,016 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 016
}\item   871,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,718
}\item   926,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,268
}\item   2,672 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,267 2
}\item   977,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,776
}\item   50,36 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,036
}\item   451,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,451 7
}\item   521,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,521 9
}\item   978,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 97,89
}\item   51,41 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,141
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   745,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 74,57
\item   3,647 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,036 47
\item   5 604 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,604
\item   0,583 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,005 83
\item   8 869 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 88,69
\item   5 042 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 504,2
\item   69,38 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,693 8
\item   740,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,408
\item   0,683 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,006 83
\item   825,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,257
\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 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 945 ~g~ = {\color{red}  394 500 }~cg
\item   241,86 ~dm~ = {\color{red}  24,186 }~m
\item   8 022,7 ~cL~ = {\color{red}  0,080 227 }~kL
\item   5 287,1 ~cg~ = {\color{red}  0,528 71 }~hg
\item   234,18 ~dm~ = {\color{red}  2,341 8 }~dam
\item   369,83 ~hg~ = {\color{red}  36 983 }~g
\item   732,14 ~dag~ = {\color{red}  7 321,4 }~g
\item   901,16 ~dg~ = {\color{red}  9 011,6 }~cg
\item   7 797,1 ~dg~ = {\color{red}  7,797 1 }~hg
\item   5 647,2 ~km~ = {\color{red}  564 720 000 }~cm
\end{itemize}
\end{multicols}
\end{document}
