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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 292}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{82}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,02  ~ \(\times\)  ~ 100
\item   88,5  ~ \(\times\)  ~ 1 000
\item   439  ~ \(\times\)  ~ 10
\item   0,005  ~ \(\times\)  ~ 1 000
\item   49,4  ~ \(\times\)  ~ 10
\item   0,651  ~ \(\times\)  ~ 1 000
\item   0,011  ~ \(\times\)  ~ 10
\item   0,42  ~ \(\times\)  ~ 10
\item   0,009  ~ \(\times\)  ~ 100
\item   25,1  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   46,78  ~ : ~ 100
\item   539  ~ : ~ 100
\item   0,375  ~ : ~ 10
\item   76,99  ~ : ~ 1 000
\item   23,35  ~ : ~ 10
\item   0,524  ~ : ~ 1 000
\item   3,384  ~ : ~ 10
\item   8,241  ~ : ~ 1 000
\item   0,556  ~ : ~ 100
\item   42,55  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,987  ~ \(\times\)  ~ ... ~ = ~ 9,87
\item   0,775  ~ \(\times\)  ~ ... ~ = ~ 775
\item   0,585  ~ \(\times\)  ~ ... ~ = ~ 58,5
\item   74,8  ~ \(\times\)  ~ ... ~ = ~ 7 480
\item   4,22  ~ \(\times\)  ~ ... ~ = ~ 422
\item   0,523  ~ \(\times\)  ~ ... ~ = ~ 52,3
\item   68,3  ~ \(\times\)  ~ ... ~ = ~ 68 300
\item   459  ~ \(\times\)  ~ ... ~ = ~ 45 900
\item   3,1  ~ \(\times\)  ~ ... ~ = ~ 310
\item   22  ~ \(\times\)  ~ ... ~ = ~ 2 200
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   98,42  ~ \(\times\)  ~ 0,001
\item   6,762  ~ \(\times\)  ~ 0,1
\item   805  ~ \(\times\)  ~ 0,001
\item   2,784  ~ \(\times\)  ~ 0,01
\item   561,4  ~ \(\times\)  ~ 0,01
\item   420,5  ~ \(\times\)  ~ 0,1
\item   5 316  ~ \(\times\)  ~ 0,1
\item   91,91  ~ \(\times\)  ~ 0,1
\item   321,3  ~ \(\times\)  ~ 0,01
\item   70,1  ~ \(\times\)  ~ 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   0,683  ~ \(\times\)  ~ ... ~ = ~  0,000 683
\item   4,644  ~ \(\times\)  ~ ... ~ = ~  0,464 4
\item   2 438  ~ \(\times\)  ~ ... ~ = ~  24,38
\item   589,8  ~ \(\times\)  ~ ... ~ = ~  58,98
\item   4 640  ~ \(\times\)  ~ ... ~ = ~  4,64
\item   4,866  ~ \(\times\)  ~ ... ~ = ~  0,004 866
\item   323,3  ~ \(\times\)  ~ ... ~ = ~  3,233
\item   910,6  ~ \(\times\)  ~ ... ~ = ~  9,106
\item   629,5  ~ \(\times\)  ~ ... ~ = ~  6,295
\item   9,483  ~ \(\times\)  ~ ... ~ = ~  0,009 483
\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~ = ...~dm
\item   1 ~km~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   117,59 ~cg~ = ...~g
\item   9 196,6 ~mg~ = ...~dg
\item   872,91 ~km~ = ...~cm
\item   8 203,7 ~mL~ = ...~dL
\item   6 147,7 ~mg~ = ...~kg
\item   7 812,7 ~dm~ = ...~km
\item   427,34 ~mL~ = ...~cL
\item   8 142,3 ~daL~ = ...~cL
\item   461,62 ~km~ = ...~hm
\item   5 905,3 ~hg~ = ...~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   3 = \(\dfrac{30}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{3000}{100}\) = \(\dfrac{300}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{82}{100}\) = \(\dfrac{820}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,02  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 602}
\item   88,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 88 500}
\item   439  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 390}
\item   0,005  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5}
\item   49,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 494}
\item   0,651  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 651}
\item   0,011  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,11}
\item   0,42  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,2}
\item   0,009  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,9}
\item   25,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 25 100}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   46,78 ~ : ~ 100 ~ = ~{\color{red} 0,467 8}
\item   539 ~ : ~ 100 ~ = ~{\color{red} 5,39}
\item   0,375 ~ : ~ 10 ~ = ~{\color{red} 0,037 5}
\item   76,99 ~ : ~ 1 000 ~ = ~{\color{red} 0,076 99}
\item   23,35 ~ : ~ 10 ~ = ~{\color{red} 2,335}
\item   0,524 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 524}
\item   3,384 ~ : ~ 10 ~ = ~{\color{red} 0,338 4}
\item   8,241 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 241}
\item   0,556 ~ : ~ 100 ~ = ~{\color{red} 0,005 56}
\item   42,55 ~ : ~ 10 ~ = ~{\color{red} 4,255}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,987 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,87
\item   0,775 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~775
\item   0,585 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~58,5
\item   74,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 480
\item   4,22 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~422
\item   0,523 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~52,3
\item   68,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~68 300
\item   459 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~45 900
\item   3,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~310
\item   22 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 200
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   98,42 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,098 42
}\item   6,762 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,676 2
}\item   805 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,805
}\item   2,784 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,027 84
}\item   561,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,614
}\item   420,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 42,05
}\item   5 316 ~ \(\times\)  0,1 ~ = ~{\color{red} 531,6
}\item   91,91 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,191
}\item   321,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,213
}\item   70,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,701
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,683 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 683
\item   4,644 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,464 4
\item   2 438 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 24,38
\item   589,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 58,98
\item   4 640 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,64
\item   4,866 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 866
\item   323,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,233
\item   910,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,106
\item   629,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,295
\item   9,483 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 483
\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~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   117,59 ~cg~ = {\color{red}  1,175 9 }~g
\item   9 196,6 ~mg~ = {\color{red}  91,966 }~dg
\item   872,91 ~km~ = {\color{red}  87 291 000 }~cm
\item   8 203,7 ~mL~ = {\color{red}  82,037 }~dL
\item   6 147,7 ~mg~ = {\color{red}  0,006 147 7 }~kg
\item   7 812,7 ~dm~ = {\color{red}  0,781 27 }~km
\item   427,34 ~mL~ = {\color{red}  42,734 }~cL
\item   8 142,3 ~daL~ = {\color{red}  8 142 300 }~cL
\item   461,62 ~km~ = {\color{red}  4 616,2 }~hm
\item   5 905,3 ~hg~ = {\color{red}  59 053 }~dag
\end{itemize}
\end{multicols}
\end{document}
