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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 193}

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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   \(\dfrac{3300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{82}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,7  ~ \(\times\)  ~ 10
\item   32,8  ~ \(\times\)  ~ 100
\item   0,057  ~ \(\times\)  ~ 10
\item   96,8  ~ \(\times\)  ~ 100
\item   0,052  ~ \(\times\)  ~ 100
\item   6,82  ~ \(\times\)  ~ 1 000
\item   0,036  ~ \(\times\)  ~ 10
\item   75,4  ~ \(\times\)  ~ 100
\item   73,7  ~ \(\times\)  ~ 100
\item   0,974  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 938  ~ : ~ 1 000
\item   5 575  ~ : ~ 1 000
\item   90,59  ~ : ~ 100
\item   518,6  ~ : ~ 1 000
\item   356,7  ~ : ~ 1 000
\item   18,23  ~ : ~ 10
\item   609,4  ~ : ~ 1 000
\item   6,209  ~ : ~ 100
\item   791,3  ~ : ~ 10
\item   7 280  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,6  ~ \(\times\)  ~ ... ~ = ~ 860
\item   1,72  ~ \(\times\)  ~ ... ~ = ~ 1 720
\item   0,582  ~ \(\times\)  ~ ... ~ = ~ 582
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 0,89
\item   0,445  ~ \(\times\)  ~ ... ~ = ~ 44,5
\item   93,8  ~ \(\times\)  ~ ... ~ = ~ 93 800
\item   630  ~ \(\times\)  ~ ... ~ = ~ 630 000
\item   0,8  ~ \(\times\)  ~ ... ~ = ~ 800
\item   19,5  ~ \(\times\)  ~ ... ~ = ~ 19 500
\item   0,545  ~ \(\times\)  ~ ... ~ = ~ 5,45
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 086  ~ \(\times\)  ~ 0,1
\item   3,758  ~ \(\times\)  ~ 0,001
\item   1 968  ~ \(\times\)  ~ 0,1
\item   7,104  ~ \(\times\)  ~ 0,001
\item   967,4  ~ \(\times\)  ~ 0,1
\item   33,89  ~ \(\times\)  ~ 0,001
\item   573,9  ~ \(\times\)  ~ 0,01
\item   745  ~ \(\times\)  ~ 0,001
\item   7 553  ~ \(\times\)  ~ 0,1
\item   86,8  ~ \(\times\)  ~ 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   6 879  ~ \(\times\)  ~ ... ~ = ~  6,879
\item   742,3  ~ \(\times\)  ~ ... ~ = ~  7,423
\item   0,195  ~ \(\times\)  ~ ... ~ = ~  0,001 95
\item   4 344  ~ \(\times\)  ~ ... ~ = ~  43,44
\item   9 308  ~ \(\times\)  ~ ... ~ = ~  930,8
\item   63,44  ~ \(\times\)  ~ ... ~ = ~  6,344
\item   86,27  ~ \(\times\)  ~ ... ~ = ~  0,862 7
\item   4 802  ~ \(\times\)  ~ ... ~ = ~  48,02
\item   6,81  ~ \(\times\)  ~ ... ~ = ~  0,006 81
\item   7 591  ~ \(\times\)  ~ ... ~ = ~  7,591
\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~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   439,43 ~mg~ = ...~g
\item   647,2 ~mg~ = ...~hg
\item   5 492,8 ~dm~ = ...~m
\item   944,07 ~dag~ = ...~g
\item   672,82 ~dL~ = ...~hL
\item   9 534,9 ~daL~ = ...~cL
\item   812,7 ~dam~ = ...~hm
\item   586,85 ~dm~ = ...~cm
\item   3 912,9 ~hL~ = ...~daL
\item   1 703,6 ~dL~ = ...~L
\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   \(\dfrac{3300}{100}\) = \(\dfrac{330}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{82}{10}\) = \(\dfrac{820}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{450}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   54,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 547}
\item   32,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 280}
\item   0,057  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,57}
\item   96,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 680}
\item   0,052  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,2}
\item   6,82  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 820}
\item   0,036  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,36}
\item   75,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 540}
\item   73,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 370}
\item   0,974  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 974}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 938 ~ : ~ 1 000 ~ = ~{\color{red} 5,938}
\item   5 575 ~ : ~ 1 000 ~ = ~{\color{red} 5,575}
\item   90,59 ~ : ~ 100 ~ = ~{\color{red} 0,905 9}
\item   518,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,518 6}
\item   356,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,356 7}
\item   18,23 ~ : ~ 10 ~ = ~{\color{red} 1,823}
\item   609,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,609 4}
\item   6,209 ~ : ~ 100 ~ = ~{\color{red} 0,062 09}
\item   791,3 ~ : ~ 10 ~ = ~{\color{red} 79,13}
\item   7 280 ~ : ~ 1 000 ~ = ~{\color{red} 7,28}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~860
\item   1,72 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 720
\item   0,582 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~582
\item   0,089 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,89
\item   0,445 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~44,5
\item   93,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~93 800
\item   630 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~630 000
\item   0,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~800
\item   19,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~19 500
\item   0,545 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,45
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 086 ~ \(\times\)  0,1 ~ = ~{\color{red} 208,6
}\item   3,758 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 758
}\item   1 968 ~ \(\times\)  0,1 ~ = ~{\color{red} 196,8
}\item   7,104 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 104
}\item   967,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 96,74
}\item   33,89 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,033 89
}\item   573,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,739
}\item   745 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,745
}\item   7 553 ~ \(\times\)  0,1 ~ = ~{\color{red} 755,3
}\item   86,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,68
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 879 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,879
\item   742,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,423
\item   0,195 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,001 95
\item   4 344 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 43,44
\item   9 308 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 930,8
\item   63,44 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,344
\item   86,27 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,862 7
\item   4 802 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 48,02
\item   6,81 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 81
\item   7 591 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,591
\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}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   439,43 ~mg~ = {\color{red}  0,439 43 }~g
\item   647,2 ~mg~ = {\color{red}  0,006 472 }~hg
\item   5 492,8 ~dm~ = {\color{red}  549,28 }~m
\item   944,07 ~dag~ = {\color{red}  9 440,7 }~g
\item   672,82 ~dL~ = {\color{red}  0,672 82 }~hL
\item   9 534,9 ~daL~ = {\color{red}  9 534 900 }~cL
\item   812,7 ~dam~ = {\color{red}  81,27 }~hm
\item   586,85 ~dm~ = {\color{red}  5 868,5 }~cm
\item   3 912,9 ~hL~ = {\color{red}  39 129 }~daL
\item   1 703,6 ~dL~ = {\color{red}  170,36 }~L
\end{itemize}
\end{multicols}
\end{document}
