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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 49}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{52}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{81}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   532  ~ \(\times\)  ~ 1 000
\item   0,54  ~ \(\times\)  ~ 10
\item   474  ~ \(\times\)  ~ 1 000
\item   0,057  ~ \(\times\)  ~ 10
\item   0,089  ~ \(\times\)  ~ 100
\item   5,96  ~ \(\times\)  ~ 100
\item   4  ~ \(\times\)  ~ 1 000
\item   150  ~ \(\times\)  ~ 100
\item   0,755  ~ \(\times\)  ~ 100
\item   7,99  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 631  ~ : ~ 1 000
\item   686,5  ~ : ~ 1 000
\item   11,75  ~ : ~ 1 000
\item   98,61  ~ : ~ 10
\item   808,9  ~ : ~ 100
\item   4,281  ~ : ~ 1 000
\item   8,124  ~ : ~ 100
\item   4 515  ~ : ~ 1 000
\item   2 537  ~ : ~ 10
\item   14,89  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,63  ~ \(\times\)  ~ ... ~ = ~ 630
\item   688  ~ \(\times\)  ~ ... ~ = ~ 68 800
\item   8,83  ~ \(\times\)  ~ ... ~ = ~ 88,3
\item   49,5  ~ \(\times\)  ~ ... ~ = ~ 4 950
\item   0,313  ~ \(\times\)  ~ ... ~ = ~ 3,13
\item   0,276  ~ \(\times\)  ~ ... ~ = ~ 27,6
\item   115  ~ \(\times\)  ~ ... ~ = ~ 115 000
\item   0,425  ~ \(\times\)  ~ ... ~ = ~ 42,5
\item   675  ~ \(\times\)  ~ ... ~ = ~ 675 000
\item   627  ~ \(\times\)  ~ ... ~ = ~ 627 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   389,5  ~ \(\times\)  ~ 0,01
\item   5 659  ~ \(\times\)  ~ 0,001
\item   30,28  ~ \(\times\)  ~ 0,01
\item   1 782  ~ \(\times\)  ~ 0,1
\item   98,28  ~ \(\times\)  ~ 0,001
\item   7 124  ~ \(\times\)  ~ 0,01
\item   599,9  ~ \(\times\)  ~ 0,01
\item   2,102  ~ \(\times\)  ~ 0,001
\item   2,225  ~ \(\times\)  ~ 0,001
\item   5,38  ~ \(\times\)  ~ 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   19,2  ~ \(\times\)  ~ ... ~ = ~  0,019 2
\item   93,72  ~ \(\times\)  ~ ... ~ = ~  0,937 2
\item   859,9  ~ \(\times\)  ~ ... ~ = ~  85,99
\item   3 810  ~ \(\times\)  ~ ... ~ = ~  38,1
\item   1,376  ~ \(\times\)  ~ ... ~ = ~  0,013 76
\item   4 352  ~ \(\times\)  ~ ... ~ = ~  43,52
\item   85,49  ~ \(\times\)  ~ ... ~ = ~  8,549
\item   728,6  ~ \(\times\)  ~ ... ~ = ~  72,86
\item   793  ~ \(\times\)  ~ ... ~ = ~  7,93
\item   666,1  ~ \(\times\)  ~ ... ~ = ~  6,661
\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 ~cm~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 777 ~daL~ = ...~dL
\item   506,23 ~mm~ = ...~dm
\item   8 004,6 ~m~ = ...~dm
\item   2 258 ~g~ = ...~hg
\item   5 160,8 ~m~ = ...~km
\item   226,99 ~mL~ = ...~hL
\item   423,26 ~dL~ = ...~daL
\item   2 835,3 ~L~ = ...~kL
\item   548,34 ~kL~ = ...~hL
\item   603,17 ~m~ = ...~dam
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{52}{10}\) = \(\dfrac{520}{100}\)
\item   \(\dfrac{81}{100}\) = \(\dfrac{810}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   532  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 532 000}
\item   0,54  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,4}
\item   474  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 474 000}
\item   0,057  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,57}
\item   0,089  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,9}
\item   5,96  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 596}
\item   4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 000}
\item   150  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 15 000}
\item   0,755  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 75,5}
\item   7,99  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 799}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 631 ~ : ~ 1 000 ~ = ~{\color{red} 6,631}
\item   686,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,686 5}
\item   11,75 ~ : ~ 1 000 ~ = ~{\color{red} 0,011 75}
\item   98,61 ~ : ~ 10 ~ = ~{\color{red} 9,861}
\item   808,9 ~ : ~ 100 ~ = ~{\color{red} 8,089}
\item   4,281 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 281}
\item   8,124 ~ : ~ 100 ~ = ~{\color{red} 0,081 24}
\item   4 515 ~ : ~ 1 000 ~ = ~{\color{red} 4,515}
\item   2 537 ~ : ~ 10 ~ = ~{\color{red} 253,7}
\item   14,89 ~ : ~ 10 ~ = ~{\color{red} 1,489}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,63 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~630
\item   688 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~68 800
\item   8,83 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~88,3
\item   49,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 950
\item   0,313 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,13
\item   0,276 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~27,6
\item   115 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~115 000
\item   0,425 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~42,5
\item   675 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~675 000
\item   627 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~627 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   389,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,895
}\item   5 659 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,659
}\item   30,28 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,302 8
}\item   1 782 ~ \(\times\)  0,1 ~ = ~{\color{red} 178,2
}\item   98,28 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,098 28
}\item   7 124 ~ \(\times\)  0,01 ~ = ~{\color{red} 71,24
}\item   599,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,999
}\item   2,102 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 102
}\item   2,225 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 225
}\item   5,38 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 38
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   19,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,019 2
\item   93,72 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,937 2
\item   859,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 85,99
\item   3 810 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 38,1
\item   1,376 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,013 76
\item   4 352 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 43,52
\item   85,49 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,549
\item   728,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 72,86
\item   793 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,93
\item   666,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,661
\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 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 777 ~daL~ = {\color{red}  577 700 }~dL
\item   506,23 ~mm~ = {\color{red}  5,062 3 }~dm
\item   8 004,6 ~m~ = {\color{red}  80 046 }~dm
\item   2 258 ~g~ = {\color{red}  22,58 }~hg
\item   5 160,8 ~m~ = {\color{red}  5,160 8 }~km
\item   226,99 ~mL~ = {\color{red}  0,002 269 9 }~hL
\item   423,26 ~dL~ = {\color{red}  4,232 6 }~daL
\item   2 835,3 ~L~ = {\color{red}  2,835 3 }~kL
\item   548,34 ~kL~ = {\color{red}  5 483,4 }~hL
\item   603,17 ~m~ = {\color{red}  60,317 }~dam
\end{itemize}
\end{multicols}
\end{document}
