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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 378}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{67}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   446  ~ \(\times\)  ~ 10
\item   2,44  ~ \(\times\)  ~ 10
\item   0,624  ~ \(\times\)  ~ 10
\item   0,087  ~ \(\times\)  ~ 100
\item   0,821  ~ \(\times\)  ~ 1 000
\item   0,385  ~ \(\times\)  ~ 1 000
\item   49,7  ~ \(\times\)  ~ 10
\item   0,06  ~ \(\times\)  ~ 1 000
\item   0,053  ~ \(\times\)  ~ 1 000
\item   0,514  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,95  ~ : ~ 10
\item   847  ~ : ~ 1 000
\item   8,781  ~ : ~ 100
\item   7 598  ~ : ~ 10
\item   12,22  ~ : ~ 1 000
\item   25,35  ~ : ~ 10
\item   2,253  ~ : ~ 100
\item   7 913  ~ : ~ 1 000
\item   1,467  ~ : ~ 10
\item   6,581  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,733  ~ \(\times\)  ~ ... ~ = ~ 733
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 43
\item   6,27  ~ \(\times\)  ~ ... ~ = ~ 6 270
\item   33,5  ~ \(\times\)  ~ ... ~ = ~ 33 500
\item   8,56  ~ \(\times\)  ~ ... ~ = ~ 85,6
\item   0,44  ~ \(\times\)  ~ ... ~ = ~ 44
\item   0,175  ~ \(\times\)  ~ ... ~ = ~ 175
\item   801  ~ \(\times\)  ~ ... ~ = ~ 801 000
\item   0,015  ~ \(\times\)  ~ ... ~ = ~ 0,15
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 69
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 739  ~ \(\times\)  ~ 0,1
\item   55,45  ~ \(\times\)  ~ 0,1
\item   40,34  ~ \(\times\)  ~ 0,01
\item   2,553  ~ \(\times\)  ~ 0,001
\item   12,75  ~ \(\times\)  ~ 0,001
\item   29,55  ~ \(\times\)  ~ 0,01
\item   614,6  ~ \(\times\)  ~ 0,001
\item   5 763  ~ \(\times\)  ~ 0,01
\item   429,4  ~ \(\times\)  ~ 0,1
\item   3 595  ~ \(\times\)  ~ 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   57  ~ \(\times\)  ~ ... ~ = ~  0,057
\item   2,368  ~ \(\times\)  ~ ... ~ = ~  0,002 368
\item   8 810  ~ \(\times\)  ~ ... ~ = ~  88,1
\item   9,528  ~ \(\times\)  ~ ... ~ = ~  0,009 528
\item   53,55  ~ \(\times\)  ~ ... ~ = ~  5,355
\item   4 997  ~ \(\times\)  ~ ... ~ = ~  49,97
\item   4 291  ~ \(\times\)  ~ ... ~ = ~  429,1
\item   23,97  ~ \(\times\)  ~ ... ~ = ~  0,023 97
\item   1,176  ~ \(\times\)  ~ ... ~ = ~  0,011 76
\item   720,6  ~ \(\times\)  ~ ... ~ = ~  72,06
\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 ~m~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   663,39 ~cL~ = ...~daL
\item   751,78 ~kL~ = ...~daL
\item   6 345,7 ~hg~ = ...~dg
\item   376,92 ~dm~ = ...~cm
\item   348,63 ~kg~ = ...~cg
\item   347,46 ~L~ = ...~dL
\item   877,61 ~km~ = ...~cm
\item   926,68 ~cL~ = ...~dL
\item   8 572,7 ~dm~ = ...~km
\item   5 417,2 ~kg~ = ...~dag
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{620}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{290}{100}\)
\item   \(\dfrac{67}{100}\) = \(\dfrac{670}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   446  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 460}
\item   2,44  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 24,4}
\item   0,624  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,24}
\item   0,087  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,7}
\item   0,821  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 821}
\item   0,385  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 385}
\item   49,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 497}
\item   0,06  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 60}
\item   0,053  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 53}
\item   0,514  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,14}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,95 ~ : ~ 10 ~ = ~{\color{red} 1,895}
\item   847 ~ : ~ 1 000 ~ = ~{\color{red} 0,847}
\item   8,781 ~ : ~ 100 ~ = ~{\color{red} 0,087 81}
\item   7 598 ~ : ~ 10 ~ = ~{\color{red} 759,8}
\item   12,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,012 22}
\item   25,35 ~ : ~ 10 ~ = ~{\color{red} 2,535}
\item   2,253 ~ : ~ 100 ~ = ~{\color{red} 0,022 53}
\item   7 913 ~ : ~ 1 000 ~ = ~{\color{red} 7,913}
\item   1,467 ~ : ~ 10 ~ = ~{\color{red} 0,146 7}
\item   6,581 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 581}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,733 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~733
\item   0,043 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43
\item   6,27 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 270
\item   33,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33 500
\item   8,56 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~85,6
\item   0,44 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~44
\item   0,175 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~175
\item   801 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~801 000
\item   0,015 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,15
\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   3 739 ~ \(\times\)  0,1 ~ = ~{\color{red} 373,9
}\item   55,45 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,545
}\item   40,34 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,403 4
}\item   2,553 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 553
}\item   12,75 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,012 75
}\item   29,55 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,295 5
}\item   614,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,614 6
}\item   5 763 ~ \(\times\)  0,01 ~ = ~{\color{red} 57,63
}\item   429,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 42,94
}\item   3 595 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,595
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   57 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,057
\item   2,368 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 368
\item   8 810 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 88,1
\item   9,528 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 528
\item   53,55 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,355
\item   4 997 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 49,97
\item   4 291 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 429,1
\item   23,97 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,023 97
\item   1,176 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,011 76
\item   720,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 72,06
\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 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   663,39 ~cL~ = {\color{red}  0,663 39 }~daL
\item   751,78 ~kL~ = {\color{red}  75 178 }~daL
\item   6 345,7 ~hg~ = {\color{red}  6 345 700 }~dg
\item   376,92 ~dm~ = {\color{red}  3 769,2 }~cm
\item   348,63 ~kg~ = {\color{red}  34 863 000 }~cg
\item   347,46 ~L~ = {\color{red}  3 474,6 }~dL
\item   877,61 ~km~ = {\color{red}  87 761 000 }~cm
\item   926,68 ~cL~ = {\color{red}  92,668 }~dL
\item   8 572,7 ~dm~ = {\color{red}  0,857 27 }~km
\item   5 417,2 ~kg~ = {\color{red}  541 720 }~dag
\end{itemize}
\end{multicols}
\end{document}
