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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 74}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{50}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,5  ~ \(\times\)  ~ 100
\item   0,131  ~ \(\times\)  ~ 100
\item   5,45  ~ \(\times\)  ~ 100
\item   1,83  ~ \(\times\)  ~ 100
\item   0,052  ~ \(\times\)  ~ 10
\item   0,071  ~ \(\times\)  ~ 10
\item   13,9  ~ \(\times\)  ~ 100
\item   0,017  ~ \(\times\)  ~ 100
\item   2,49  ~ \(\times\)  ~ 100
\item   0,688  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   913  ~ : ~ 1 000
\item   2 715  ~ : ~ 1 000
\item   36,58  ~ : ~ 10
\item   435  ~ : ~ 1 000
\item   1,829  ~ : ~ 1 000
\item   9,388  ~ : ~ 1 000
\item   658,7  ~ : ~ 1 000
\item   289,8  ~ : ~ 100
\item   7,677  ~ : ~ 100
\item   176,8  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   946  ~ \(\times\)  ~ ... ~ = ~ 94 600
\item   0,866  ~ \(\times\)  ~ ... ~ = ~ 8,66
\item   49,2  ~ \(\times\)  ~ ... ~ = ~ 492
\item   322  ~ \(\times\)  ~ ... ~ = ~ 32 200
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 6,8
\item   5,31  ~ \(\times\)  ~ ... ~ = ~ 531
\item   1,9  ~ \(\times\)  ~ ... ~ = ~ 19
\item   0,021  ~ \(\times\)  ~ ... ~ = ~ 0,21
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 6,7
\item   43,1  ~ \(\times\)  ~ ... ~ = ~ 43 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 379  ~ \(\times\)  ~ 0,001
\item   2,094  ~ \(\times\)  ~ 0,1
\item   21,87  ~ \(\times\)  ~ 0,01
\item   900  ~ \(\times\)  ~ 0,1
\item   9,266  ~ \(\times\)  ~ 0,001
\item   15,12  ~ \(\times\)  ~ 0,01
\item   1,494  ~ \(\times\)  ~ 0,001
\item   73,6  ~ \(\times\)  ~ 0,1
\item   6,963  ~ \(\times\)  ~ 0,001
\item   2,254  ~ \(\times\)  ~ 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   24,74  ~ \(\times\)  ~ ... ~ = ~  0,024 74
\item   86,42  ~ \(\times\)  ~ ... ~ = ~  0,864 2
\item   9,27  ~ \(\times\)  ~ ... ~ = ~  0,927
\item   955,6  ~ \(\times\)  ~ ... ~ = ~  95,56
\item   479,1  ~ \(\times\)  ~ ... ~ = ~  47,91
\item   64,14  ~ \(\times\)  ~ ... ~ = ~  6,414
\item   448,6  ~ \(\times\)  ~ ... ~ = ~  0,448 6
\item   641,3  ~ \(\times\)  ~ ... ~ = ~  6,413
\item   175,1  ~ \(\times\)  ~ ... ~ = ~  17,51
\item   571,5  ~ \(\times\)  ~ ... ~ = ~  57,15
\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 ~dam~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   381,87 ~g~ = ...~mg
\item   7 019 ~kL~ = ...~mL
\item   6 107,5 ~dam~ = ...~cm
\item   1 996,5 ~kg~ = ...~cg
\item   312,73 ~g~ = ...~kg
\item   9 071,8 ~g~ = ...~dag
\item   130,89 ~hg~ = ...~mg
\item   5 662,4 ~dg~ = ...~mg
\item   639,11 ~km~ = ...~dm
\item   2 780,3 ~cg~ = ...~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   9 = \(\dfrac{90}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{510}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{50}{10}\) = \(\dfrac{500}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{340}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 050}
\item   0,131  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 13,1}
\item   5,45  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 545}
\item   1,83  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 183}
\item   0,052  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,52}
\item   0,071  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,71}
\item   13,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 390}
\item   0,017  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,7}
\item   2,49  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 249}
\item   0,688  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,88}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   913 ~ : ~ 1 000 ~ = ~{\color{red} 0,913}
\item   2 715 ~ : ~ 1 000 ~ = ~{\color{red} 2,715}
\item   36,58 ~ : ~ 10 ~ = ~{\color{red} 3,658}
\item   435 ~ : ~ 1 000 ~ = ~{\color{red} 0,435}
\item   1,829 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 829}
\item   9,388 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 388}
\item   658,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,658 7}
\item   289,8 ~ : ~ 100 ~ = ~{\color{red} 2,898}
\item   7,677 ~ : ~ 100 ~ = ~{\color{red} 0,076 77}
\item   176,8 ~ : ~ 10 ~ = ~{\color{red} 17,68}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   946 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~94 600
\item   0,866 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,66
\item   49,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~492
\item   322 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~32 200
\item   0,068 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,8
\item   5,31 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~531
\item   1,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~19
\item   0,021 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,21
\item   0,067 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,7
\item   43,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 379 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,379
}\item   2,094 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,209 4
}\item   21,87 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,218 7
}\item   900 ~ \(\times\)  0,1 ~ = ~{\color{red} 90
}\item   9,266 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 266
}\item   15,12 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,151 2
}\item   1,494 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 494
}\item   73,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,36
}\item   6,963 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 963
}\item   2,254 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 254
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24,74 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,024 74
\item   86,42 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,864 2
\item   9,27 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,927
\item   955,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 95,56
\item   479,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 47,91
\item   64,14 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,414
\item   448,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,448 6
\item   641,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,413
\item   175,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 17,51
\item   571,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 57,15
\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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   381,87 ~g~ = {\color{red}  381 870 }~mg
\item   7 019 ~kL~ = {\color{red}  7 019 000 000 }~mL
\item   6 107,5 ~dam~ = {\color{red}  6 107 500 }~cm
\item   1 996,5 ~kg~ = {\color{red}  199 650 000 }~cg
\item   312,73 ~g~ = {\color{red}  0,312 73 }~kg
\item   9 071,8 ~g~ = {\color{red}  907,18 }~dag
\item   130,89 ~hg~ = {\color{red}  13 089 000 }~mg
\item   5 662,4 ~dg~ = {\color{red}  566 240 }~mg
\item   639,11 ~km~ = {\color{red}  6 391 100 }~dm
\item   2 780,3 ~cg~ = {\color{red}  2,780 3 }~dag
\end{itemize}
\end{multicols}
\end{document}
