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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 175}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{43}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   618  ~ \(\times\)  ~ 100
\item   0,533  ~ \(\times\)  ~ 100
\item   802  ~ \(\times\)  ~ 100
\item   0,078  ~ \(\times\)  ~ 10
\item   0,09  ~ \(\times\)  ~ 100
\item   0,199  ~ \(\times\)  ~ 1 000
\item   0,487  ~ \(\times\)  ~ 100
\item   62,6  ~ \(\times\)  ~ 100
\item   0,036  ~ \(\times\)  ~ 100
\item   492  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 422  ~ : ~ 10
\item   577,5  ~ : ~ 10
\item   32,71  ~ : ~ 1 000
\item   8,604  ~ : ~ 100
\item   44,74  ~ : ~ 1 000
\item   7 682  ~ : ~ 100
\item   1,46  ~ : ~ 100
\item   47,1  ~ : ~ 10
\item   547  ~ : ~ 1 000
\item   8,313  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   52  ~ \(\times\)  ~ ... ~ = ~ 520
\item   0,065  ~ \(\times\)  ~ ... ~ = ~ 6,5
\item   1,96  ~ \(\times\)  ~ ... ~ = ~ 19,6
\item   0,036  ~ \(\times\)  ~ ... ~ = ~ 36
\item   42  ~ \(\times\)  ~ ... ~ = ~ 420
\item   0,048  ~ \(\times\)  ~ ... ~ = ~ 0,48
\item   91,8  ~ \(\times\)  ~ ... ~ = ~ 91 800
\item   27,6  ~ \(\times\)  ~ ... ~ = ~ 27 600
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 63
\item   0,736  ~ \(\times\)  ~ ... ~ = ~ 73,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   435,8  ~ \(\times\)  ~ 0,1
\item   938,1  ~ \(\times\)  ~ 0,01
\item   6 179  ~ \(\times\)  ~ 0,001
\item   43,04  ~ \(\times\)  ~ 0,1
\item   50,95  ~ \(\times\)  ~ 0,01
\item   511,1  ~ \(\times\)  ~ 0,001
\item   4 786  ~ \(\times\)  ~ 0,01
\item   6,48  ~ \(\times\)  ~ 0,01
\item   856  ~ \(\times\)  ~ 0,001
\item   793,5  ~ \(\times\)  ~ 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   469,7  ~ \(\times\)  ~ ... ~ = ~  0,469 7
\item   376,8  ~ \(\times\)  ~ ... ~ = ~  3,768
\item   4,08  ~ \(\times\)  ~ ... ~ = ~  0,004 08
\item   5,182  ~ \(\times\)  ~ ... ~ = ~  0,005 182
\item   74,47  ~ \(\times\)  ~ ... ~ = ~  0,744 7
\item   8,184  ~ \(\times\)  ~ ... ~ = ~  0,818 4
\item   739  ~ \(\times\)  ~ ... ~ = ~  7,39
\item   88,36  ~ \(\times\)  ~ ... ~ = ~  0,883 6
\item   54,96  ~ \(\times\)  ~ ... ~ = ~  0,549 6
\item   529,6  ~ \(\times\)  ~ ... ~ = ~  0,529 6
\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 ~km~ = ...~m
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   220,8 ~mg~ = ...~g
\item   134,85 ~cm~ = ...~hm
\item   8 246 ~hg~ = ...~dag
\item   1 373,3 ~m~ = ...~cm
\item   327,95 ~mg~ = ...~dg
\item   4 911,9 ~dag~ = ...~dg
\item   798,17 ~kg~ = ...~g
\item   7 069,6 ~kg~ = ...~cg
\item   1 805 ~cm~ = ...~mm
\item   2 085,9 ~g~ = ...~dg
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{1700}{100}\) = \(\dfrac{170}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{43}{100}\) = \(\dfrac{430}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   618  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 61 800}
\item   0,533  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 53,3}
\item   802  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80 200}
\item   0,078  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,78}
\item   0,09  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9}
\item   0,199  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 199}
\item   0,487  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 48,7}
\item   62,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 260}
\item   0,036  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,6}
\item   492  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 492 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 422 ~ : ~ 10 ~ = ~{\color{red} 942,2}
\item   577,5 ~ : ~ 10 ~ = ~{\color{red} 57,75}
\item   32,71 ~ : ~ 1 000 ~ = ~{\color{red} 0,032 71}
\item   8,604 ~ : ~ 100 ~ = ~{\color{red} 0,086 04}
\item   44,74 ~ : ~ 1 000 ~ = ~{\color{red} 0,044 74}
\item   7 682 ~ : ~ 100 ~ = ~{\color{red} 76,82}
\item   1,46 ~ : ~ 100 ~ = ~{\color{red} 0,014 6}
\item   47,1 ~ : ~ 10 ~ = ~{\color{red} 4,71}
\item   547 ~ : ~ 1 000 ~ = ~{\color{red} 0,547}
\item   8,313 ~ : ~ 10 ~ = ~{\color{red} 0,831 3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   52 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~520
\item   0,065 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,5
\item   1,96 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~19,6
\item   0,036 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~36
\item   42 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~420
\item   0,048 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,48
\item   91,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~91 800
\item   27,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27 600
\item   0,063 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~63
\item   0,736 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~73,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   435,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 43,58
}\item   938,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,381
}\item   6 179 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,179
}\item   43,04 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,304
}\item   50,95 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,509 5
}\item   511,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,511 1
}\item   4 786 ~ \(\times\)  0,01 ~ = ~{\color{red} 47,86
}\item   6,48 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,064 8
}\item   856 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,856
}\item   793,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,935
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   469,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,469 7
\item   376,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,768
\item   4,08 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 08
\item   5,182 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 182
\item   74,47 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,744 7
\item   8,184 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,818 4
\item   739 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,39
\item   88,36 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,883 6
\item   54,96 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,549 6
\item   529,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,529 6
\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 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   220,8 ~mg~ = {\color{red}  0,220 8 }~g
\item   134,85 ~cm~ = {\color{red}  0,013 485 }~hm
\item   8 246 ~hg~ = {\color{red}  82 460 }~dag
\item   1 373,3 ~m~ = {\color{red}  137 330 }~cm
\item   327,95 ~mg~ = {\color{red}  3,279 5 }~dg
\item   4 911,9 ~dag~ = {\color{red}  491 190 }~dg
\item   798,17 ~kg~ = {\color{red}  798 170 }~g
\item   7 069,6 ~kg~ = {\color{red}  706 960 000 }~cg
\item   1 805 ~cm~ = {\color{red}  18 050 }~mm
\item   2 085,9 ~g~ = {\color{red}  20 859 }~dg
\end{itemize}
\end{multicols}
\end{document}
