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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 397}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{11}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,029  ~ \(\times\)  ~ 10
\item   0,251  ~ \(\times\)  ~ 100
\item   1,23  ~ \(\times\)  ~ 100
\item   0,088  ~ \(\times\)  ~ 100
\item   0,088  ~ \(\times\)  ~ 100
\item   432  ~ \(\times\)  ~ 1 000
\item   0,348  ~ \(\times\)  ~ 1 000
\item   6,68  ~ \(\times\)  ~ 100
\item   0,4  ~ \(\times\)  ~ 100
\item   0,82  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,06  ~ : ~ 1 000
\item   403,9  ~ : ~ 100
\item   3 211  ~ : ~ 100
\item   8,879  ~ : ~ 1 000
\item   62,91  ~ : ~ 10
\item   367  ~ : ~ 100
\item   39,82  ~ : ~ 100
\item   46,18  ~ : ~ 10
\item   40,7  ~ : ~ 100
\item   785,9  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,437  ~ \(\times\)  ~ ... ~ = ~ 437
\item   2,12  ~ \(\times\)  ~ ... ~ = ~ 21,2
\item   66  ~ \(\times\)  ~ ... ~ = ~ 66 000
\item   0,573  ~ \(\times\)  ~ ... ~ = ~ 573
\item   542  ~ \(\times\)  ~ ... ~ = ~ 54 200
\item   240  ~ \(\times\)  ~ ... ~ = ~ 2 400
\item   5,05  ~ \(\times\)  ~ ... ~ = ~ 50,5
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 0,97
\item   0,614  ~ \(\times\)  ~ ... ~ = ~ 61,4
\item   9  ~ \(\times\)  ~ ... ~ = ~ 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,07  ~ \(\times\)  ~ 0,01
\item   1,688  ~ \(\times\)  ~ 0,001
\item   967,5  ~ \(\times\)  ~ 0,1
\item   78  ~ \(\times\)  ~ 0,001
\item   98,45  ~ \(\times\)  ~ 0,001
\item   40,09  ~ \(\times\)  ~ 0,1
\item   4 941  ~ \(\times\)  ~ 0,001
\item   3,605  ~ \(\times\)  ~ 0,01
\item   1,89  ~ \(\times\)  ~ 0,01
\item   62,55  ~ \(\times\)  ~ 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   8,896  ~ \(\times\)  ~ ... ~ = ~  0,008 896
\item   66,36  ~ \(\times\)  ~ ... ~ = ~  6,636
\item   1 045  ~ \(\times\)  ~ ... ~ = ~  1,045
\item   519  ~ \(\times\)  ~ ... ~ = ~  51,9
\item   7,821  ~ \(\times\)  ~ ... ~ = ~  0,078 21
\item   554  ~ \(\times\)  ~ ... ~ = ~  5,54
\item   831,8  ~ \(\times\)  ~ ... ~ = ~  8,318
\item   7 550  ~ \(\times\)  ~ ... ~ = ~  75,5
\item   34,19  ~ \(\times\)  ~ ... ~ = ~  0,034 19
\item   688,7  ~ \(\times\)  ~ ... ~ = ~  68,87
\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 ~dam~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 002,4 ~km~ = ...~m
\item   3 127,7 ~mL~ = ...~hL
\item   1 982,9 ~dL~ = ...~daL
\item   249,46 ~m~ = ...~dam
\item   3 388,3 ~dL~ = ...~hL
\item   3 318,2 ~mm~ = ...~dm
\item   243,23 ~hg~ = ...~g
\item   8 333,6 ~daL~ = ...~dL
\item   7 882,9 ~dg~ = ...~mg
\item   328,55 ~cm~ = ...~mm
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{6100}{100}\) = \(\dfrac{610}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{11}{10}\) = \(\dfrac{110}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{990}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,029  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,29}
\item   0,251  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 25,1}
\item   1,23  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 123}
\item   0,088  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,8}
\item   0,088  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,8}
\item   432  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 432 000}
\item   0,348  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 348}
\item   6,68  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 668}
\item   0,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 40}
\item   0,82  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 820}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,06 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 06}
\item   403,9 ~ : ~ 100 ~ = ~{\color{red} 4,039}
\item   3 211 ~ : ~ 100 ~ = ~{\color{red} 32,11}
\item   8,879 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 879}
\item   62,91 ~ : ~ 10 ~ = ~{\color{red} 6,291}
\item   367 ~ : ~ 100 ~ = ~{\color{red} 3,67}
\item   39,82 ~ : ~ 100 ~ = ~{\color{red} 0,398 2}
\item   46,18 ~ : ~ 10 ~ = ~{\color{red} 4,618}
\item   40,7 ~ : ~ 100 ~ = ~{\color{red} 0,407}
\item   785,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,785 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,437 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~437
\item   2,12 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~21,2
\item   66 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~66 000
\item   0,573 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~573
\item   542 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~54 200
\item   240 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 400
\item   5,05 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~50,5
\item   0,097 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,97
\item   0,614 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~61,4
\item   9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,07 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,080 7
}\item   1,688 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 688
}\item   967,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 96,75
}\item   78 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,078
}\item   98,45 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,098 45
}\item   40,09 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,009
}\item   4 941 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,941
}\item   3,605 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,036 05
}\item   1,89 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,018 9
}\item   62,55 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,625 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,896 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 896
\item   66,36 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,636
\item   1 045 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,045
\item   519 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 51,9
\item   7,821 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,078 21
\item   554 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,54
\item   831,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,318
\item   7 550 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 75,5
\item   34,19 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,034 19
\item   688,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 68,87
\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 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 002,4 ~km~ = {\color{red}  9 002 400 }~m
\item   3 127,7 ~mL~ = {\color{red}  0,031 277 }~hL
\item   1 982,9 ~dL~ = {\color{red}  19,829 }~daL
\item   249,46 ~m~ = {\color{red}  24,946 }~dam
\item   3 388,3 ~dL~ = {\color{red}  3,388 3 }~hL
\item   3 318,2 ~mm~ = {\color{red}  33,182 }~dm
\item   243,23 ~hg~ = {\color{red}  24 323 }~g
\item   8 333,6 ~daL~ = {\color{red}  833 360 }~dL
\item   7 882,9 ~dg~ = {\color{red}  788 290 }~mg
\item   328,55 ~cm~ = {\color{red}  3 285,5 }~mm
\end{itemize}
\end{multicols}
\end{document}
