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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 79}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,75  ~ \(\times\)  ~ 10
\item   0,76  ~ \(\times\)  ~ 10
\item   214  ~ \(\times\)  ~ 1 000
\item   5,11  ~ \(\times\)  ~ 10
\item   0,428  ~ \(\times\)  ~ 1 000
\item   0,039  ~ \(\times\)  ~ 10
\item   400  ~ \(\times\)  ~ 100
\item   0,807  ~ \(\times\)  ~ 10
\item   7,33  ~ \(\times\)  ~ 1 000
\item   0,766  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 391  ~ : ~ 100
\item   1 700  ~ : ~ 10
\item   3,142  ~ : ~ 100
\item   576,6  ~ : ~ 1 000
\item   5,338  ~ : ~ 100
\item   2 982  ~ : ~ 10
\item   96,69  ~ : ~ 10
\item   25,17  ~ : ~ 10
\item   45,68  ~ : ~ 10
\item   879,5  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 64
\item   0,003  ~ \(\times\)  ~ ... ~ = ~ 3
\item   0,082  ~ \(\times\)  ~ ... ~ = ~ 8,2
\item   0,026  ~ \(\times\)  ~ ... ~ = ~ 0,26
\item   676  ~ \(\times\)  ~ ... ~ = ~ 6 760
\item   74,2  ~ \(\times\)  ~ ... ~ = ~ 7 420
\item   0,704  ~ \(\times\)  ~ ... ~ = ~ 70,4
\item   24,4  ~ \(\times\)  ~ ... ~ = ~ 2 440
\item   83,5  ~ \(\times\)  ~ ... ~ = ~ 83 500
\item   0,057  ~ \(\times\)  ~ ... ~ = ~ 0,57
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,423  ~ \(\times\)  ~ 0,1
\item   8 925  ~ \(\times\)  ~ 0,01
\item   910,6  ~ \(\times\)  ~ 0,01
\item   9 613  ~ \(\times\)  ~ 0,1
\item   9,326  ~ \(\times\)  ~ 0,001
\item   3 326  ~ \(\times\)  ~ 0,1
\item   4,74  ~ \(\times\)  ~ 0,01
\item   750,4  ~ \(\times\)  ~ 0,1
\item   42,65  ~ \(\times\)  ~ 0,1
\item   3 008  ~ \(\times\)  ~ 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   97,64  ~ \(\times\)  ~ ... ~ = ~  0,976 4
\item   143  ~ \(\times\)  ~ ... ~ = ~  0,143
\item   0,184  ~ \(\times\)  ~ ... ~ = ~  0,000 184
\item   51,69  ~ \(\times\)  ~ ... ~ = ~  0,516 9
\item   62,61  ~ \(\times\)  ~ ... ~ = ~  0,626 1
\item   83,68  ~ \(\times\)  ~ ... ~ = ~  0,836 8
\item   21,67  ~ \(\times\)  ~ ... ~ = ~  0,021 67
\item   448,4  ~ \(\times\)  ~ ... ~ = ~  44,84
\item   3 752  ~ \(\times\)  ~ ... ~ = ~  3,752
\item   62,57  ~ \(\times\)  ~ ... ~ = ~  0,062 57
\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~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   349,55 ~km~ = ...~hm
\item   924,07 ~mg~ = ...~dag
\item   150,3 ~hL~ = ...~cL
\item   6 293,4 ~cL~ = ...~L
\item   3 208,8 ~L~ = ...~dL
\item   887,32 ~cm~ = ...~dm
\item   376,49 ~mm~ = ...~m
\item   958,67 ~km~ = ...~mm
\item   2 796,2 ~dag~ = ...~g
\item   7 098,6 ~hg~ = ...~kg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{5500}{100}\) = \(\dfrac{550}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{410}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{420}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,75  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,5}
\item   0,76  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,6}
\item   214  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 214 000}
\item   5,11  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 51,1}
\item   0,428  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 428}
\item   0,039  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,39}
\item   400  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 40 000}
\item   0,807  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,07}
\item   7,33  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 330}
\item   0,766  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 766}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 391 ~ : ~ 100 ~ = ~{\color{red} 13,91}
\item   1 700 ~ : ~ 10 ~ = ~{\color{red} 170}
\item   3,142 ~ : ~ 100 ~ = ~{\color{red} 0,031 42}
\item   576,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,576 6}
\item   5,338 ~ : ~ 100 ~ = ~{\color{red} 0,053 38}
\item   2 982 ~ : ~ 10 ~ = ~{\color{red} 298,2}
\item   96,69 ~ : ~ 10 ~ = ~{\color{red} 9,669}
\item   25,17 ~ : ~ 10 ~ = ~{\color{red} 2,517}
\item   45,68 ~ : ~ 10 ~ = ~{\color{red} 4,568}
\item   879,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,879 5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,064 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~64
\item   0,003 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3
\item   0,082 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,2
\item   0,026 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,26
\item   676 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 760
\item   74,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 420
\item   0,704 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~70,4
\item   24,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 440
\item   83,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~83 500
\item   0,057 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,57
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,423 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,242 3
}\item   8 925 ~ \(\times\)  0,01 ~ = ~{\color{red} 89,25
}\item   910,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,106
}\item   9 613 ~ \(\times\)  0,1 ~ = ~{\color{red} 961,3
}\item   9,326 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 326
}\item   3 326 ~ \(\times\)  0,1 ~ = ~{\color{red} 332,6
}\item   4,74 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,047 4
}\item   750,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 75,04
}\item   42,65 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,265
}\item   3 008 ~ \(\times\)  0,1 ~ = ~{\color{red} 300,8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   97,64 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,976 4
\item   143 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,143
\item   0,184 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 184
\item   51,69 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,516 9
\item   62,61 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,626 1
\item   83,68 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,836 8
\item   21,67 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,021 67
\item   448,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 44,84
\item   3 752 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,752
\item   62,57 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,062 57
\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}  10 ~ }hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   349,55 ~km~ = {\color{red}  3 495,5 }~hm
\item   924,07 ~mg~ = {\color{red}  0,092 407 }~dag
\item   150,3 ~hL~ = {\color{red}  1 503 000 }~cL
\item   6 293,4 ~cL~ = {\color{red}  62,934 }~L
\item   3 208,8 ~L~ = {\color{red}  32 088 }~dL
\item   887,32 ~cm~ = {\color{red}  88,732 }~dm
\item   376,49 ~mm~ = {\color{red}  0,376 49 }~m
\item   958,67 ~km~ = {\color{red}  958 670 000 }~mm
\item   2 796,2 ~dag~ = {\color{red}  27 962 }~g
\item   7 098,6 ~hg~ = {\color{red}  709,86 }~kg
\end{itemize}
\end{multicols}
\end{document}
