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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 125}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,8  ~ \(\times\)  ~ 1 000
\item   0,032  ~ \(\times\)  ~ 1 000
\item   13  ~ \(\times\)  ~ 1 000
\item   66,4  ~ \(\times\)  ~ 100
\item   0,525  ~ \(\times\)  ~ 1 000
\item   1,11  ~ \(\times\)  ~ 100
\item   0,17  ~ \(\times\)  ~ 10
\item   0,896  ~ \(\times\)  ~ 10
\item   934  ~ \(\times\)  ~ 100
\item   0,073  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,859  ~ : ~ 10
\item   977,3  ~ : ~ 10
\item   1 135  ~ : ~ 100
\item   9 828  ~ : ~ 100
\item   7 717  ~ : ~ 100
\item   3 326  ~ : ~ 1 000
\item   6,202  ~ : ~ 10
\item   0,231  ~ : ~ 1 000
\item   40,78  ~ : ~ 1 000
\item   811,9  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 6,3
\item   0,719  ~ \(\times\)  ~ ... ~ = ~ 719
\item   5,95  ~ \(\times\)  ~ ... ~ = ~ 5 950
\item   387  ~ \(\times\)  ~ ... ~ = ~ 3 870
\item   0,057  ~ \(\times\)  ~ ... ~ = ~ 5,7
\item   0,198  ~ \(\times\)  ~ ... ~ = ~ 198
\item   87,6  ~ \(\times\)  ~ ... ~ = ~ 8 760
\item   0,362  ~ \(\times\)  ~ ... ~ = ~ 3,62
\item   9,68  ~ \(\times\)  ~ ... ~ = ~ 96,8
\item   53  ~ \(\times\)  ~ ... ~ = ~ 53 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   60,1  ~ \(\times\)  ~ 0,001
\item   6 402  ~ \(\times\)  ~ 0,1
\item   400,7  ~ \(\times\)  ~ 0,1
\item   1,379  ~ \(\times\)  ~ 0,001
\item   945,1  ~ \(\times\)  ~ 0,01
\item   60,84  ~ \(\times\)  ~ 0,01
\item   88,74  ~ \(\times\)  ~ 0,001
\item   7,543  ~ \(\times\)  ~ 0,001
\item   680,4  ~ \(\times\)  ~ 0,001
\item   952,5  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   77,01  ~ \(\times\)  ~ ... ~ = ~  0,770 1
\item   4 050  ~ \(\times\)  ~ ... ~ = ~  4,05
\item   7,952  ~ \(\times\)  ~ ... ~ = ~  0,079 52
\item   2 833  ~ \(\times\)  ~ ... ~ = ~  2,833
\item   580,8  ~ \(\times\)  ~ ... ~ = ~  58,08
\item   655,1  ~ \(\times\)  ~ ... ~ = ~  6,551
\item   743,1  ~ \(\times\)  ~ ... ~ = ~  74,31
\item   9,578  ~ \(\times\)  ~ ... ~ = ~  0,095 78
\item   8,736  ~ \(\times\)  ~ ... ~ = ~  0,087 36
\item   8,922  ~ \(\times\)  ~ ... ~ = ~  0,008 922
\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~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 470,4 ~mL~ = ...~cL
\item   7 490,4 ~kL~ = ...~mL
\item   2 269,6 ~kL~ = ...~daL
\item   1 334,9 ~g~ = ...~dg
\item   3 436,8 ~m~ = ...~dm
\item   313,38 ~daL~ = ...~hL
\item   4 243,6 ~dag~ = ...~mg
\item   4 825,3 ~mL~ = ...~daL
\item   9 826,2 ~dg~ = ...~g
\item   6 096,9 ~mm~ = ...~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   4 = \(\dfrac{40}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{8700}{100}\) = \(\dfrac{870}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{340}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 36 800}
\item   0,032  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32}
\item   13  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 13 000}
\item   66,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 640}
\item   0,525  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 525}
\item   1,11  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 111}
\item   0,17  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,7}
\item   0,896  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,96}
\item   934  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 93 400}
\item   0,073  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 73}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,859 ~ : ~ 10 ~ = ~{\color{red} 0,885 9}
\item   977,3 ~ : ~ 10 ~ = ~{\color{red} 97,73}
\item   1 135 ~ : ~ 100 ~ = ~{\color{red} 11,35}
\item   9 828 ~ : ~ 100 ~ = ~{\color{red} 98,28}
\item   7 717 ~ : ~ 100 ~ = ~{\color{red} 77,17}
\item   3 326 ~ : ~ 1 000 ~ = ~{\color{red} 3,326}
\item   6,202 ~ : ~ 10 ~ = ~{\color{red} 0,620 2}
\item   0,231 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 231}
\item   40,78 ~ : ~ 1 000 ~ = ~{\color{red} 0,040 78}
\item   811,9 ~ : ~ 100 ~ = ~{\color{red} 8,119}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,063 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,3
\item   0,719 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~719
\item   5,95 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 950
\item   387 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 870
\item   0,057 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,7
\item   0,198 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~198
\item   87,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 760
\item   0,362 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,62
\item   9,68 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~96,8
\item   53 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~53 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   60,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,060 1
}\item   6 402 ~ \(\times\)  0,1 ~ = ~{\color{red} 640,2
}\item   400,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 40,07
}\item   1,379 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 379
}\item   945,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,451
}\item   60,84 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,608 4
}\item   88,74 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,088 74
}\item   7,543 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 543
}\item   680,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,680 4
}\item   952,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,525
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   77,01 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,770 1
\item   4 050 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,05
\item   7,952 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,079 52
\item   2 833 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,833
\item   580,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 58,08
\item   655,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,551
\item   743,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 74,31
\item   9,578 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,095 78
\item   8,736 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,087 36
\item   8,922 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 922
\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~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 470,4 ~mL~ = {\color{red}  547,04 }~cL
\item   7 490,4 ~kL~ = {\color{red}  7 490 400 000 }~mL
\item   2 269,6 ~kL~ = {\color{red}  226 960 }~daL
\item   1 334,9 ~g~ = {\color{red}  13 349 }~dg
\item   3 436,8 ~m~ = {\color{red}  34 368 }~dm
\item   313,38 ~daL~ = {\color{red}  31,338 }~hL
\item   4 243,6 ~dag~ = {\color{red}  42 436 000 }~mg
\item   4 825,3 ~mL~ = {\color{red}  0,482 53 }~daL
\item   9 826,2 ~dg~ = {\color{red}  982,62 }~g
\item   6 096,9 ~mm~ = {\color{red}  0,609 69 }~dam
\end{itemize}
\end{multicols}
\end{document}
