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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 253}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{94}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{94}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   241  ~ \(\times\)  ~ 100
\item   7,3  ~ \(\times\)  ~ 100
\item   5,16  ~ \(\times\)  ~ 1 000
\item   570  ~ \(\times\)  ~ 100
\item   24,2  ~ \(\times\)  ~ 10
\item   0,907  ~ \(\times\)  ~ 1 000
\item   4,21  ~ \(\times\)  ~ 100
\item   515  ~ \(\times\)  ~ 1 000
\item   2,97  ~ \(\times\)  ~ 1 000
\item   0,21  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   961,2  ~ : ~ 10
\item   86,94  ~ : ~ 100
\item   2 983  ~ : ~ 100
\item   4,792  ~ : ~ 1 000
\item   9 571  ~ : ~ 100
\item   620,7  ~ : ~ 10
\item   88,08  ~ : ~ 100
\item   54  ~ : ~ 100
\item   340,2  ~ : ~ 10
\item   66,7  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,332  ~ \(\times\)  ~ ... ~ = ~ 33,2
\item   0,371  ~ \(\times\)  ~ ... ~ = ~ 371
\item   38,4  ~ \(\times\)  ~ ... ~ = ~ 38 400
\item   3,9  ~ \(\times\)  ~ ... ~ = ~ 3 900
\item   0,965  ~ \(\times\)  ~ ... ~ = ~ 9,65
\item   90  ~ \(\times\)  ~ ... ~ = ~ 90 000
\item   277  ~ \(\times\)  ~ ... ~ = ~ 277 000
\item   0,093  ~ \(\times\)  ~ ... ~ = ~ 0,93
\item   0,037  ~ \(\times\)  ~ ... ~ = ~ 0,37
\item   73  ~ \(\times\)  ~ ... ~ = ~ 730
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   76,14  ~ \(\times\)  ~ 0,001
\item   1,025  ~ \(\times\)  ~ 0,1
\item   6,539  ~ \(\times\)  ~ 0,001
\item   5,174  ~ \(\times\)  ~ 0,1
\item   70,74  ~ \(\times\)  ~ 0,01
\item   2,22  ~ \(\times\)  ~ 0,001
\item   865,8  ~ \(\times\)  ~ 0,01
\item   1,102  ~ \(\times\)  ~ 0,1
\item   922  ~ \(\times\)  ~ 0,01
\item   97,52  ~ \(\times\)  ~ 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   938,2  ~ \(\times\)  ~ ... ~ = ~  9,382
\item   40,34  ~ \(\times\)  ~ ... ~ = ~  0,403 4
\item   3 779  ~ \(\times\)  ~ ... ~ = ~  37,79
\item   6 333  ~ \(\times\)  ~ ... ~ = ~  633,3
\item   546,8  ~ \(\times\)  ~ ... ~ = ~  54,68
\item   172,1  ~ \(\times\)  ~ ... ~ = ~  1,721
\item   1 370  ~ \(\times\)  ~ ... ~ = ~  13,7
\item   6 253  ~ \(\times\)  ~ ... ~ = ~  62,53
\item   131,9  ~ \(\times\)  ~ ... ~ = ~  1,319
\item   88,39  ~ \(\times\)  ~ ... ~ = ~  0,088 39
\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 ~hm~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 655,4 ~mL~ = ...~hL
\item   688,2 ~g~ = ...~kg
\item   194,17 ~cm~ = ...~dam
\item   174,75 ~cg~ = ...~mg
\item   667,06 ~mg~ = ...~cg
\item   2 910,1 ~kg~ = ...~mg
\item   2 638,1 ~km~ = ...~cm
\item   8 382,4 ~cL~ = ...~daL
\item   6 296,7 ~dm~ = ...~m
\item   1 340,4 ~g~ = ...~mg
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{94}{10}\) = \(\dfrac{940}{100}\)
\item   \(\dfrac{94}{100}\) = \(\dfrac{940}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   241  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 24 100}
\item   7,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 730}
\item   5,16  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 160}
\item   570  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 57 000}
\item   24,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 242}
\item   0,907  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 907}
\item   4,21  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 421}
\item   515  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 515 000}
\item   2,97  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 970}
\item   0,21  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 210}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   961,2 ~ : ~ 10 ~ = ~{\color{red} 96,12}
\item   86,94 ~ : ~ 100 ~ = ~{\color{red} 0,869 4}
\item   2 983 ~ : ~ 100 ~ = ~{\color{red} 29,83}
\item   4,792 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 792}
\item   9 571 ~ : ~ 100 ~ = ~{\color{red} 95,71}
\item   620,7 ~ : ~ 10 ~ = ~{\color{red} 62,07}
\item   88,08 ~ : ~ 100 ~ = ~{\color{red} 0,880 8}
\item   54 ~ : ~ 100 ~ = ~{\color{red} 0,54}
\item   340,2 ~ : ~ 10 ~ = ~{\color{red} 34,02}
\item   66,7 ~ : ~ 10 ~ = ~{\color{red} 6,67}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,332 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~33,2
\item   0,371 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~371
\item   38,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~38 400
\item   3,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 900
\item   0,965 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,65
\item   90 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~90 000
\item   277 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~277 000
\item   0,093 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,93
\item   0,037 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,37
\item   73 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~730
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   76,14 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,076 14
}\item   1,025 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,102 5
}\item   6,539 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 539
}\item   5,174 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,517 4
}\item   70,74 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,707 4
}\item   2,22 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 22
}\item   865,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,658
}\item   1,102 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,110 2
}\item   922 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,22
}\item   97,52 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,097 52
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   938,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,382
\item   40,34 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,403 4
\item   3 779 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 37,79
\item   6 333 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 633,3
\item   546,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 54,68
\item   172,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,721
\item   1 370 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 13,7
\item   6 253 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 62,53
\item   131,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,319
\item   88,39 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,088 39
\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 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 655,4 ~mL~ = {\color{red}  0,066 554 }~hL
\item   688,2 ~g~ = {\color{red}  0,688 2 }~kg
\item   194,17 ~cm~ = {\color{red}  0,194 17 }~dam
\item   174,75 ~cg~ = {\color{red}  1 747,5 }~mg
\item   667,06 ~mg~ = {\color{red}  66,706 }~cg
\item   2 910,1 ~kg~ = {\color{red}  2 910 100 000 }~mg
\item   2 638,1 ~km~ = {\color{red}  263 810 000 }~cm
\item   8 382,4 ~cL~ = {\color{red}  8,382 4 }~daL
\item   6 296,7 ~dm~ = {\color{red}  629,67 }~m
\item   1 340,4 ~g~ = {\color{red}  1 340 400 }~mg
\end{itemize}
\end{multicols}
\end{document}
