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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 42}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   763  ~ \(\times\)  ~ 1 000
\item   0,077  ~ \(\times\)  ~ 10
\item   0,613  ~ \(\times\)  ~ 10
\item   39  ~ \(\times\)  ~ 10
\item   0,025  ~ \(\times\)  ~ 1 000
\item   0,004  ~ \(\times\)  ~ 10
\item   0,074  ~ \(\times\)  ~ 100
\item   0,234  ~ \(\times\)  ~ 1 000
\item   293  ~ \(\times\)  ~ 10
\item   0,723  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   465,3  ~ : ~ 10
\item   5 615  ~ : ~ 10
\item   6 325  ~ : ~ 100
\item   57,36  ~ : ~ 10
\item   7 628  ~ : ~ 100
\item   13,92  ~ : ~ 1 000
\item   602,6  ~ : ~ 1 000
\item   1 240  ~ : ~ 1 000
\item   38,34  ~ : ~ 10
\item   3 915  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,293  ~ \(\times\)  ~ ... ~ = ~ 293
\item   8,63  ~ \(\times\)  ~ ... ~ = ~ 86,3
\item   3,88  ~ \(\times\)  ~ ... ~ = ~ 38,8
\item   6,95  ~ \(\times\)  ~ ... ~ = ~ 6 950
\item   968  ~ \(\times\)  ~ ... ~ = ~ 968 000
\item   65,9  ~ \(\times\)  ~ ... ~ = ~ 65 900
\item   75,5  ~ \(\times\)  ~ ... ~ = ~ 755
\item   0,482  ~ \(\times\)  ~ ... ~ = ~ 48,2
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 0,96
\item   7,1  ~ \(\times\)  ~ ... ~ = ~ 71
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 853  ~ \(\times\)  ~ 0,01
\item   66,73  ~ \(\times\)  ~ 0,1
\item   35,57  ~ \(\times\)  ~ 0,1
\item   8,28  ~ \(\times\)  ~ 0,001
\item   761,8  ~ \(\times\)  ~ 0,01
\item   238,8  ~ \(\times\)  ~ 0,001
\item   92,98  ~ \(\times\)  ~ 0,001
\item   9,678  ~ \(\times\)  ~ 0,001
\item   66,44  ~ \(\times\)  ~ 0,1
\item   2,367  ~ \(\times\)  ~ 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   872  ~ \(\times\)  ~ ... ~ = ~  87,2
\item   2,722  ~ \(\times\)  ~ ... ~ = ~  0,002 722
\item   1,141  ~ \(\times\)  ~ ... ~ = ~  0,011 41
\item   9,864  ~ \(\times\)  ~ ... ~ = ~  0,009 864
\item   4 220  ~ \(\times\)  ~ ... ~ = ~  4,22
\item   19,77  ~ \(\times\)  ~ ... ~ = ~  0,019 77
\item   5 674  ~ \(\times\)  ~ ... ~ = ~  56,74
\item   722,4  ~ \(\times\)  ~ ... ~ = ~  7,224
\item   1,54  ~ \(\times\)  ~ ... ~ = ~  0,001 54
\item   3 028  ~ \(\times\)  ~ ... ~ = ~  3,028
\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 ~dm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   574,68 ~kL~ = ...~cL
\item   190,55 ~g~ = ...~mg
\item   458,52 ~kg~ = ...~dag
\item   4 534,8 ~L~ = ...~cL
\item   2 347,4 ~g~ = ...~hg
\item   2 012,7 ~m~ = ...~dam
\item   2 624 ~dm~ = ...~m
\item   7 702 ~km~ = ...~dam
\item   5 890,6 ~kL~ = ...~daL
\item   1 612,5 ~dL~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{460}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{390}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{280}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   763  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 763 000}
\item   0,077  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,77}
\item   0,613  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,13}
\item   39  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 390}
\item   0,025  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 25}
\item   0,004  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,04}
\item   0,074  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,4}
\item   0,234  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 234}
\item   293  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 930}
\item   0,723  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 72,3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   465,3 ~ : ~ 10 ~ = ~{\color{red} 46,53}
\item   5 615 ~ : ~ 10 ~ = ~{\color{red} 561,5}
\item   6 325 ~ : ~ 100 ~ = ~{\color{red} 63,25}
\item   57,36 ~ : ~ 10 ~ = ~{\color{red} 5,736}
\item   7 628 ~ : ~ 100 ~ = ~{\color{red} 76,28}
\item   13,92 ~ : ~ 1 000 ~ = ~{\color{red} 0,013 92}
\item   602,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,602 6}
\item   1 240 ~ : ~ 1 000 ~ = ~{\color{red} 1,24}
\item   38,34 ~ : ~ 10 ~ = ~{\color{red} 3,834}
\item   3 915 ~ : ~ 100 ~ = ~{\color{red} 39,15}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,293 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~293
\item   8,63 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~86,3
\item   3,88 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~38,8
\item   6,95 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 950
\item   968 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~968 000
\item   65,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~65 900
\item   75,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~755
\item   0,482 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~48,2
\item   0,096 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,96
\item   7,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~71
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 853 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,53
}\item   66,73 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,673
}\item   35,57 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,557
}\item   8,28 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 28
}\item   761,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,618
}\item   238,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,238 8
}\item   92,98 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,092 98
}\item   9,678 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 678
}\item   66,44 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,644
}\item   2,367 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,236 7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   872 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 87,2
\item   2,722 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 722
\item   1,141 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,011 41
\item   9,864 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 864
\item   4 220 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,22
\item   19,77 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,019 77
\item   5 674 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 56,74
\item   722,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,224
\item   1,54 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 54
\item   3 028 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,028
\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 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   574,68 ~kL~ = {\color{red}  57 468 000 }~cL
\item   190,55 ~g~ = {\color{red}  190 550 }~mg
\item   458,52 ~kg~ = {\color{red}  45 852 }~dag
\item   4 534,8 ~L~ = {\color{red}  453 480 }~cL
\item   2 347,4 ~g~ = {\color{red}  23,474 }~hg
\item   2 012,7 ~m~ = {\color{red}  201,27 }~dam
\item   2 624 ~dm~ = {\color{red}  262,4 }~m
\item   7 702 ~km~ = {\color{red}  770 200 }~dam
\item   5 890,6 ~kL~ = {\color{red}  589 060 }~daL
\item   1 612,5 ~dL~ = {\color{red}  0,161 25 }~kL
\end{itemize}
\end{multicols}
\end{document}
