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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 389}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{42}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,744  ~ \(\times\)  ~ 10
\item   41,2  ~ \(\times\)  ~ 1 000
\item   258  ~ \(\times\)  ~ 100
\item   238  ~ \(\times\)  ~ 1 000
\item   3,11  ~ \(\times\)  ~ 100
\item   157  ~ \(\times\)  ~ 1 000
\item   30,3  ~ \(\times\)  ~ 100
\item   0,081  ~ \(\times\)  ~ 100
\item   61  ~ \(\times\)  ~ 1 000
\item   0,769  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,58  ~ : ~ 10
\item   866  ~ : ~ 100
\item   88,51  ~ : ~ 100
\item   21,47  ~ : ~ 10
\item   500,1  ~ : ~ 10
\item   5,122  ~ : ~ 10
\item   9,857  ~ : ~ 100
\item   81,06  ~ : ~ 100
\item   0,367  ~ : ~ 1 000
\item   1,541  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   829  ~ \(\times\)  ~ ... ~ = ~ 82 900
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 0,61
\item   296  ~ \(\times\)  ~ ... ~ = ~ 2 960
\item   6,79  ~ \(\times\)  ~ ... ~ = ~ 6 790
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 0,02
\item   36,8  ~ \(\times\)  ~ ... ~ = ~ 36 800
\item   866  ~ \(\times\)  ~ ... ~ = ~ 866 000
\item   0,12  ~ \(\times\)  ~ ... ~ = ~ 1,2
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 6,1
\item   14  ~ \(\times\)  ~ ... ~ = ~ 14 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 739  ~ \(\times\)  ~ 0,01
\item   4,725  ~ \(\times\)  ~ 0,1
\item   18,55  ~ \(\times\)  ~ 0,001
\item   3,348  ~ \(\times\)  ~ 0,1
\item   8,22  ~ \(\times\)  ~ 0,1
\item   7,484  ~ \(\times\)  ~ 0,1
\item   14,54  ~ \(\times\)  ~ 0,1
\item   5 722  ~ \(\times\)  ~ 0,001
\item   4,118  ~ \(\times\)  ~ 0,1
\item   4,734  ~ \(\times\)  ~ 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   9 057  ~ \(\times\)  ~ ... ~ = ~  905,7
\item   8,287  ~ \(\times\)  ~ ... ~ = ~  0,082 87
\item   526,7  ~ \(\times\)  ~ ... ~ = ~  5,267
\item   561,7  ~ \(\times\)  ~ ... ~ = ~  56,17
\item   94,34  ~ \(\times\)  ~ ... ~ = ~  0,943 4
\item   563  ~ \(\times\)  ~ ... ~ = ~  56,3
\item   91,13  ~ \(\times\)  ~ ... ~ = ~  0,091 13
\item   158  ~ \(\times\)  ~ ... ~ = ~  15,8
\item   287,7  ~ \(\times\)  ~ ... ~ = ~  28,77
\item   8,82  ~ \(\times\)  ~ ... ~ = ~  0,088 2
\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 ~cm~ = ...~dam
\item   1 ~cm~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 787,9 ~dL~ = ...~kL
\item   3 524,6 ~mg~ = ...~cg
\item   9 984,2 ~dL~ = ...~hL
\item   562,89 ~hm~ = ...~km
\item   194,1 ~hg~ = ...~kg
\item   9 545,7 ~dag~ = ...~g
\item   372,15 ~mg~ = ...~dg
\item   9 150,7 ~dL~ = ...~L
\item   855,99 ~m~ = ...~mm
\item   499,41 ~hm~ = ...~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   6 = \(\dfrac{60}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{8000}{100}\) = \(\dfrac{800}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{42}{10}\) = \(\dfrac{420}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,744  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,44}
\item   41,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 41 200}
\item   258  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 25 800}
\item   238  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 238 000}
\item   3,11  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 311}
\item   157  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 157 000}
\item   30,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 030}
\item   0,081  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,1}
\item   61  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 61 000}
\item   0,769  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,69}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,58 ~ : ~ 10 ~ = ~{\color{red} 0,658}
\item   866 ~ : ~ 100 ~ = ~{\color{red} 8,66}
\item   88,51 ~ : ~ 100 ~ = ~{\color{red} 0,885 1}
\item   21,47 ~ : ~ 10 ~ = ~{\color{red} 2,147}
\item   500,1 ~ : ~ 10 ~ = ~{\color{red} 50,01}
\item   5,122 ~ : ~ 10 ~ = ~{\color{red} 0,512 2}
\item   9,857 ~ : ~ 100 ~ = ~{\color{red} 0,098 57}
\item   81,06 ~ : ~ 100 ~ = ~{\color{red} 0,810 6}
\item   0,367 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 367}
\item   1,541 ~ : ~ 100 ~ = ~{\color{red} 0,015 41}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   829 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~82 900
\item   0,061 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,61
\item   296 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 960
\item   6,79 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 790
\item   0,002 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,02
\item   36,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~36 800
\item   866 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~866 000
\item   0,12 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,2
\item   0,061 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,1
\item   14 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 739 ~ \(\times\)  0,01 ~ = ~{\color{red} 37,39
}\item   4,725 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,472 5
}\item   18,55 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,018 55
}\item   3,348 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,334 8
}\item   8,22 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,822
}\item   7,484 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,748 4
}\item   14,54 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,454
}\item   5 722 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,722
}\item   4,118 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,411 8
}\item   4,734 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,473 4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 057 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 905,7
\item   8,287 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,082 87
\item   526,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,267
\item   561,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 56,17
\item   94,34 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,943 4
\item   563 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 56,3
\item   91,13 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,091 13
\item   158 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 15,8
\item   287,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 28,77
\item   8,82 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,088 2
\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 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 787,9 ~dL~ = {\color{red}  0,178 79 }~kL
\item   3 524,6 ~mg~ = {\color{red}  352,46 }~cg
\item   9 984,2 ~dL~ = {\color{red}  9,984 2 }~hL
\item   562,89 ~hm~ = {\color{red}  56,289 }~km
\item   194,1 ~hg~ = {\color{red}  19,41 }~kg
\item   9 545,7 ~dag~ = {\color{red}  95 457 }~g
\item   372,15 ~mg~ = {\color{red}  3,721 5 }~dg
\item   9 150,7 ~dL~ = {\color{red}  915,07 }~L
\item   855,99 ~m~ = {\color{red}  855 990 }~mm
\item   499,41 ~hm~ = {\color{red}  4 994 100 }~cm
\end{itemize}
\end{multicols}
\end{document}
