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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 318}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,6  ~ \(\times\)  ~ 100
\item   0,665  ~ \(\times\)  ~ 100
\item   76,6  ~ \(\times\)  ~ 100
\item   86,8  ~ \(\times\)  ~ 10
\item   770  ~ \(\times\)  ~ 1 000
\item   0,721  ~ \(\times\)  ~ 100
\item   0,719  ~ \(\times\)  ~ 100
\item   0,009  ~ \(\times\)  ~ 100
\item   961  ~ \(\times\)  ~ 100
\item   5,27  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 295  ~ : ~ 1 000
\item   37,18  ~ : ~ 10
\item   3 791  ~ : ~ 1 000
\item   1 330  ~ : ~ 10
\item   54,65  ~ : ~ 10
\item   7 191  ~ : ~ 10
\item   60,67  ~ : ~ 100
\item   19,63  ~ : ~ 10
\item   87,1  ~ : ~ 1 000
\item   12,16  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,011  ~ \(\times\)  ~ ... ~ = ~ 1,1
\item   0,172  ~ \(\times\)  ~ ... ~ = ~ 172
\item   46,6  ~ \(\times\)  ~ ... ~ = ~ 46 600
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 45
\item   110  ~ \(\times\)  ~ ... ~ = ~ 11 000
\item   5,16  ~ \(\times\)  ~ ... ~ = ~ 5 160
\item   0,053  ~ \(\times\)  ~ ... ~ = ~ 5,3
\item   52  ~ \(\times\)  ~ ... ~ = ~ 520
\item   9,84  ~ \(\times\)  ~ ... ~ = ~ 9 840
\item   5,65  ~ \(\times\)  ~ ... ~ = ~ 565
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 669  ~ \(\times\)  ~ 0,1
\item   9 640  ~ \(\times\)  ~ 0,01
\item   7 811  ~ \(\times\)  ~ 0,01
\item   1,86  ~ \(\times\)  ~ 0,01
\item   8,16  ~ \(\times\)  ~ 0,1
\item   5,797  ~ \(\times\)  ~ 0,001
\item   222,3  ~ \(\times\)  ~ 0,01
\item   21,9  ~ \(\times\)  ~ 0,001
\item   7 184  ~ \(\times\)  ~ 0,1
\item   6 077  ~ \(\times\)  ~ 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   6,102  ~ \(\times\)  ~ ... ~ = ~  0,061 02
\item   63,02  ~ \(\times\)  ~ ... ~ = ~  6,302
\item   1 513  ~ \(\times\)  ~ ... ~ = ~  15,13
\item   188,5  ~ \(\times\)  ~ ... ~ = ~  1,885
\item   351,6  ~ \(\times\)  ~ ... ~ = ~  3,516
\item   0,134  ~ \(\times\)  ~ ... ~ = ~  0,013 4
\item   2,044  ~ \(\times\)  ~ ... ~ = ~  0,020 44
\item   7,02  ~ \(\times\)  ~ ... ~ = ~  0,007 02
\item   8 810  ~ \(\times\)  ~ ... ~ = ~  88,1
\item   7,304  ~ \(\times\)  ~ ... ~ = ~  0,007 304
\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~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 624,2 ~mg~ = ...~cg
\item   557,67 ~hL~ = ...~daL
\item   5 406,6 ~dag~ = ...~hg
\item   9 650,4 ~dm~ = ...~hm
\item   621,06 ~hm~ = ...~m
\item   8 088,3 ~cm~ = ...~mm
\item   8 145,2 ~kL~ = ...~hL
\item   4 798,5 ~cm~ = ...~hm
\item   272,22 ~cg~ = ...~dag
\item   606,44 ~kL~ = ...~daL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{620}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{320}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{900}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 860}
\item   0,665  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66,5}
\item   76,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 660}
\item   86,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 868}
\item   770  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 770 000}
\item   0,721  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 72,1}
\item   0,719  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 71,9}
\item   0,009  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,9}
\item   961  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 96 100}
\item   5,27  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 52,7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 295 ~ : ~ 1 000 ~ = ~{\color{red} 2,295}
\item   37,18 ~ : ~ 10 ~ = ~{\color{red} 3,718}
\item   3 791 ~ : ~ 1 000 ~ = ~{\color{red} 3,791}
\item   1 330 ~ : ~ 10 ~ = ~{\color{red} 133}
\item   54,65 ~ : ~ 10 ~ = ~{\color{red} 5,465}
\item   7 191 ~ : ~ 10 ~ = ~{\color{red} 719,1}
\item   60,67 ~ : ~ 100 ~ = ~{\color{red} 0,606 7}
\item   19,63 ~ : ~ 10 ~ = ~{\color{red} 1,963}
\item   87,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,087 1}
\item   12,16 ~ : ~ 1 000 ~ = ~{\color{red} 0,012 16}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,011 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,1
\item   0,172 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~172
\item   46,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~46 600
\item   0,045 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~45
\item   110 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~11 000
\item   5,16 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 160
\item   0,053 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,3
\item   52 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~520
\item   9,84 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 840
\item   5,65 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~565
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 669 ~ \(\times\)  0,1 ~ = ~{\color{red} 366,9
}\item   9 640 ~ \(\times\)  0,01 ~ = ~{\color{red} 96,4
}\item   7 811 ~ \(\times\)  0,01 ~ = ~{\color{red} 78,11
}\item   1,86 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,018 6
}\item   8,16 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,816
}\item   5,797 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 797
}\item   222,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,223
}\item   21,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,021 9
}\item   7 184 ~ \(\times\)  0,1 ~ = ~{\color{red} 718,4
}\item   6 077 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,077
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,102 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,061 02
\item   63,02 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,302
\item   1 513 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 15,13
\item   188,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,885
\item   351,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,516
\item   0,134 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,013 4
\item   2,044 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,020 44
\item   7,02 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 02
\item   8 810 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 88,1
\item   7,304 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 304
\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~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\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   6 624,2 ~mg~ = {\color{red}  662,42 }~cg
\item   557,67 ~hL~ = {\color{red}  5 576,7 }~daL
\item   5 406,6 ~dag~ = {\color{red}  540,66 }~hg
\item   9 650,4 ~dm~ = {\color{red}  9,650 4 }~hm
\item   621,06 ~hm~ = {\color{red}  62 106 }~m
\item   8 088,3 ~cm~ = {\color{red}  80 883 }~mm
\item   8 145,2 ~kL~ = {\color{red}  81 452 }~hL
\item   4 798,5 ~cm~ = {\color{red}  0,479 85 }~hm
\item   272,22 ~cg~ = {\color{red}  0,272 22 }~dag
\item   606,44 ~kL~ = {\color{red}  60 644 }~daL
\end{itemize}
\end{multicols}
\end{document}
