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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 228}

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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   \(\dfrac{3900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{88}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,722  ~ \(\times\)  ~ 10
\item   834  ~ \(\times\)  ~ 1 000
\item   94  ~ \(\times\)  ~ 100
\item   0,714  ~ \(\times\)  ~ 100
\item   8,63  ~ \(\times\)  ~ 1 000
\item   0,852  ~ \(\times\)  ~ 1 000
\item   0,021  ~ \(\times\)  ~ 1 000
\item   977  ~ \(\times\)  ~ 1 000
\item   0,06  ~ \(\times\)  ~ 1 000
\item   0,455  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,98  ~ : ~ 1 000
\item   683,7  ~ : ~ 100
\item   5,732  ~ : ~ 100
\item   5 592  ~ : ~ 10
\item   15,44  ~ : ~ 100
\item   23,38  ~ : ~ 100
\item   620,2  ~ : ~ 10
\item   1,515  ~ : ~ 10
\item   1,848  ~ : ~ 1 000
\item   4 185  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   327  ~ \(\times\)  ~ ... ~ = ~ 32 700
\item   11,3  ~ \(\times\)  ~ ... ~ = ~ 11 300
\item   2,67  ~ \(\times\)  ~ ... ~ = ~ 267
\item   1,94  ~ \(\times\)  ~ ... ~ = ~ 19,4
\item   0,687  ~ \(\times\)  ~ ... ~ = ~ 68,7
\item   0,011  ~ \(\times\)  ~ ... ~ = ~ 1,1
\item   8,07  ~ \(\times\)  ~ ... ~ = ~ 807
\item   845  ~ \(\times\)  ~ ... ~ = ~ 845 000
\item   2,85  ~ \(\times\)  ~ ... ~ = ~ 28,5
\item   0,094  ~ \(\times\)  ~ ... ~ = ~ 94
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   459,4  ~ \(\times\)  ~ 0,001
\item   8,39  ~ \(\times\)  ~ 0,1
\item   3,372  ~ \(\times\)  ~ 0,001
\item   9,608  ~ \(\times\)  ~ 0,1
\item   145,9  ~ \(\times\)  ~ 0,001
\item   3 867  ~ \(\times\)  ~ 0,01
\item   6,996  ~ \(\times\)  ~ 0,01
\item   21,82  ~ \(\times\)  ~ 0,01
\item   5,08  ~ \(\times\)  ~ 0,1
\item   2 272  ~ \(\times\)  ~ 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   3 919  ~ \(\times\)  ~ ... ~ = ~  391,9
\item   74,91  ~ \(\times\)  ~ ... ~ = ~  0,074 91
\item   605,4  ~ \(\times\)  ~ ... ~ = ~  6,054
\item   72,51  ~ \(\times\)  ~ ... ~ = ~  0,072 51
\item   67,84  ~ \(\times\)  ~ ... ~ = ~  0,678 4
\item   189,1  ~ \(\times\)  ~ ... ~ = ~  18,91
\item   4,999  ~ \(\times\)  ~ ... ~ = ~  0,499 9
\item   104,2  ~ \(\times\)  ~ ... ~ = ~  0,104 2
\item   8,118  ~ \(\times\)  ~ ... ~ = ~  0,008 118
\item   64,95  ~ \(\times\)  ~ ... ~ = ~  0,649 5
\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 ~cm~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   837,29 ~L~ = ...~mL
\item   5 678,6 ~g~ = ...~hg
\item   465,76 ~daL~ = ...~dL
\item   818,03 ~hm~ = ...~m
\item   2 941,9 ~m~ = ...~dm
\item   4 156,5 ~L~ = ...~cL
\item   337,09 ~L~ = ...~dL
\item   283,83 ~mL~ = ...~L
\item   3 542,1 ~kg~ = ...~g
\item   862,2 ~cg~ = ...~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   4 = \(\dfrac{40}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{3900}{100}\) = \(\dfrac{390}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{88}{100}\) = \(\dfrac{880}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,722  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,22}
\item   834  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 834 000}
\item   94  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 400}
\item   0,714  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 71,4}
\item   8,63  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 630}
\item   0,852  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 852}
\item   0,021  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 21}
\item   977  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 977 000}
\item   0,06  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 60}
\item   0,455  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,55}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,98 ~ : ~ 1 000 ~ = ~{\color{red} 0,056 98}
\item   683,7 ~ : ~ 100 ~ = ~{\color{red} 6,837}
\item   5,732 ~ : ~ 100 ~ = ~{\color{red} 0,057 32}
\item   5 592 ~ : ~ 10 ~ = ~{\color{red} 559,2}
\item   15,44 ~ : ~ 100 ~ = ~{\color{red} 0,154 4}
\item   23,38 ~ : ~ 100 ~ = ~{\color{red} 0,233 8}
\item   620,2 ~ : ~ 10 ~ = ~{\color{red} 62,02}
\item   1,515 ~ : ~ 10 ~ = ~{\color{red} 0,151 5}
\item   1,848 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 848}
\item   4 185 ~ : ~ 100 ~ = ~{\color{red} 41,85}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   327 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~32 700
\item   11,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~11 300
\item   2,67 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~267
\item   1,94 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~19,4
\item   0,687 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~68,7
\item   0,011 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,1
\item   8,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~807
\item   845 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~845 000
\item   2,85 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~28,5
\item   0,094 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~94
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   459,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,459 4
}\item   8,39 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,839
}\item   3,372 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 372
}\item   9,608 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,960 8
}\item   145,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,145 9
}\item   3 867 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,67
}\item   6,996 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,069 96
}\item   21,82 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,218 2
}\item   5,08 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,508
}\item   2 272 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,272
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 919 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 391,9
\item   74,91 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,074 91
\item   605,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,054
\item   72,51 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,072 51
\item   67,84 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,678 4
\item   189,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 18,91
\item   4,999 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,499 9
\item   104,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,104 2
\item   8,118 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 118
\item   64,95 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,649 5
\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 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   837,29 ~L~ = {\color{red}  837 290 }~mL
\item   5 678,6 ~g~ = {\color{red}  56,786 }~hg
\item   465,76 ~daL~ = {\color{red}  46 576 }~dL
\item   818,03 ~hm~ = {\color{red}  81 803 }~m
\item   2 941,9 ~m~ = {\color{red}  29 419 }~dm
\item   4 156,5 ~L~ = {\color{red}  415 650 }~cL
\item   337,09 ~L~ = {\color{red}  3 370,9 }~dL
\item   283,83 ~mL~ = {\color{red}  0,283 83 }~L
\item   3 542,1 ~kg~ = {\color{red}  3 542 100 }~g
\item   862,2 ~cg~ = {\color{red}  0,008 622 }~kg
\end{itemize}
\end{multicols}
\end{document}
