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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 398}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{69}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,4  ~ \(\times\)  ~ 1 000
\item   75  ~ \(\times\)  ~ 100
\item   5,77  ~ \(\times\)  ~ 10
\item   0,297  ~ \(\times\)  ~ 100
\item   5,67  ~ \(\times\)  ~ 10
\item   0,012  ~ \(\times\)  ~ 10
\item   9,77  ~ \(\times\)  ~ 10
\item   0,218  ~ \(\times\)  ~ 1 000
\item   571  ~ \(\times\)  ~ 100
\item   0,053  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,137  ~ : ~ 1 000
\item   9 385  ~ : ~ 100
\item   3,977  ~ : ~ 1 000
\item   0,98  ~ : ~ 100
\item   37,64  ~ : ~ 10
\item   408,5  ~ : ~ 100
\item   1 872  ~ : ~ 10
\item   5 504  ~ : ~ 1 000
\item   9,23  ~ : ~ 10
\item   2 921  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 0,43
\item   76,5  ~ \(\times\)  ~ ... ~ = ~ 7 650
\item   52  ~ \(\times\)  ~ ... ~ = ~ 520
\item   21,3  ~ \(\times\)  ~ ... ~ = ~ 21 300
\item   0,233  ~ \(\times\)  ~ ... ~ = ~ 233
\item   86,2  ~ \(\times\)  ~ ... ~ = ~ 86 200
\item   0,281  ~ \(\times\)  ~ ... ~ = ~ 28,1
\item   0,056  ~ \(\times\)  ~ ... ~ = ~ 0,56
\item   91,7  ~ \(\times\)  ~ ... ~ = ~ 917
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 69
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,475  ~ \(\times\)  ~ 0,001
\item   4,224  ~ \(\times\)  ~ 0,001
\item   8 356  ~ \(\times\)  ~ 0,1
\item   84,89  ~ \(\times\)  ~ 0,001
\item   3 584  ~ \(\times\)  ~ 0,001
\item   153,6  ~ \(\times\)  ~ 0,001
\item   3 535  ~ \(\times\)  ~ 0,001
\item   829,8  ~ \(\times\)  ~ 0,001
\item   8 388  ~ \(\times\)  ~ 0,1
\item   46,8  ~ \(\times\)  ~ 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   2 469  ~ \(\times\)  ~ ... ~ = ~  246,9
\item   40,92  ~ \(\times\)  ~ ... ~ = ~  4,092
\item   66,5  ~ \(\times\)  ~ ... ~ = ~  0,665
\item   7 773  ~ \(\times\)  ~ ... ~ = ~  7,773
\item   4 531  ~ \(\times\)  ~ ... ~ = ~  453,1
\item   7,212  ~ \(\times\)  ~ ... ~ = ~  0,072 12
\item   88,54  ~ \(\times\)  ~ ... ~ = ~  0,885 4
\item   2 576  ~ \(\times\)  ~ ... ~ = ~  25,76
\item   367,8  ~ \(\times\)  ~ ... ~ = ~  0,367 8
\item   92,91  ~ \(\times\)  ~ ... ~ = ~  0,929 1
\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~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   354,2 ~dam~ = ...~mm
\item   4 251,9 ~dag~ = ...~dg
\item   822,34 ~dg~ = ...~mg
\item   3 238,2 ~kL~ = ...~cL
\item   3 687,2 ~km~ = ...~dam
\item   322,77 ~hL~ = ...~mL
\item   2 661 ~dL~ = ...~hL
\item   743,52 ~cg~ = ...~hg
\item   741 ~dg~ = ...~cg
\item   6 518,2 ~cg~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{410}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{580}{100}\)
\item   \(\dfrac{69}{100}\) = \(\dfrac{690}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 74 400}
\item   75  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 500}
\item   5,77  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 57,7}
\item   0,297  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 29,7}
\item   5,67  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 56,7}
\item   0,012  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,12}
\item   9,77  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 97,7}
\item   0,218  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 218}
\item   571  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 57 100}
\item   0,053  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 53}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,137 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 137}
\item   9 385 ~ : ~ 100 ~ = ~{\color{red} 93,85}
\item   3,977 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 977}
\item   0,98 ~ : ~ 100 ~ = ~{\color{red} 0,009 8}
\item   37,64 ~ : ~ 10 ~ = ~{\color{red} 3,764}
\item   408,5 ~ : ~ 100 ~ = ~{\color{red} 4,085}
\item   1 872 ~ : ~ 10 ~ = ~{\color{red} 187,2}
\item   5 504 ~ : ~ 1 000 ~ = ~{\color{red} 5,504}
\item   9,23 ~ : ~ 10 ~ = ~{\color{red} 0,923}
\item   2 921 ~ : ~ 1 000 ~ = ~{\color{red} 2,921}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,043 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,43
\item   76,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 650
\item   52 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~520
\item   21,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~21 300
\item   0,233 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~233
\item   86,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~86 200
\item   0,281 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~28,1
\item   0,056 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,56
\item   91,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~917
\item   0,069 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~69
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,475 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 475
}\item   4,224 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 224
}\item   8 356 ~ \(\times\)  0,1 ~ = ~{\color{red} 835,6
}\item   84,89 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,084 89
}\item   3 584 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,584
}\item   153,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,153 6
}\item   3 535 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,535
}\item   829,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,829 8
}\item   8 388 ~ \(\times\)  0,1 ~ = ~{\color{red} 838,8
}\item   46,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,68
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 469 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 246,9
\item   40,92 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,092
\item   66,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,665
\item   7 773 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,773
\item   4 531 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 453,1
\item   7,212 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,072 12
\item   88,54 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,885 4
\item   2 576 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 25,76
\item   367,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,367 8
\item   92,91 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,929 1
\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~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   354,2 ~dam~ = {\color{red}  3 542 000 }~mm
\item   4 251,9 ~dag~ = {\color{red}  425 190 }~dg
\item   822,34 ~dg~ = {\color{red}  82 234 }~mg
\item   3 238,2 ~kL~ = {\color{red}  323 820 000 }~cL
\item   3 687,2 ~km~ = {\color{red}  368 720 }~dam
\item   322,77 ~hL~ = {\color{red}  32 277 000 }~mL
\item   2 661 ~dL~ = {\color{red}  2,661 }~hL
\item   743,52 ~cg~ = {\color{red}  0,074 352 }~hg
\item   741 ~dg~ = {\color{red}  7 410 }~cg
\item   6 518,2 ~cg~ = {\color{red}  65 182 }~mg
\end{itemize}
\end{multicols}
\end{document}
