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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 67}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{64}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,098  ~ \(\times\)  ~ 100
\item   0,051  ~ \(\times\)  ~ 100
\item   95  ~ \(\times\)  ~ 1 000
\item   4,9  ~ \(\times\)  ~ 100
\item   4,4  ~ \(\times\)  ~ 100
\item   194  ~ \(\times\)  ~ 1 000
\item   0,106  ~ \(\times\)  ~ 100
\item   0,259  ~ \(\times\)  ~ 1 000
\item   0,091  ~ \(\times\)  ~ 10
\item   0,042  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   273,2  ~ : ~ 100
\item   8 608  ~ : ~ 1 000
\item   738  ~ : ~ 1 000
\item   6 471  ~ : ~ 100
\item   2,724  ~ : ~ 1 000
\item   0,147  ~ : ~ 100
\item   3 964  ~ : ~ 10
\item   12,2  ~ : ~ 1 000
\item   4,029  ~ : ~ 10
\item   6 589  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,09  ~ \(\times\)  ~ ... ~ = ~ 9
\item   14,5  ~ \(\times\)  ~ ... ~ = ~ 14 500
\item   559  ~ \(\times\)  ~ ... ~ = ~ 559 000
\item   0,66  ~ \(\times\)  ~ ... ~ = ~ 66
\item   569  ~ \(\times\)  ~ ... ~ = ~ 569 000
\item   401  ~ \(\times\)  ~ ... ~ = ~ 40 100
\item   0,457  ~ \(\times\)  ~ ... ~ = ~ 4,57
\item   905  ~ \(\times\)  ~ ... ~ = ~ 9 050
\item   0,523  ~ \(\times\)  ~ ... ~ = ~ 52,3
\item   2,6  ~ \(\times\)  ~ ... ~ = ~ 26
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,93  ~ \(\times\)  ~ 0,01
\item   9,706  ~ \(\times\)  ~ 0,001
\item   86,19  ~ \(\times\)  ~ 0,1
\item   17,36  ~ \(\times\)  ~ 0,1
\item   834,8  ~ \(\times\)  ~ 0,01
\item   211,7  ~ \(\times\)  ~ 0,001
\item   48,69  ~ \(\times\)  ~ 0,001
\item   4 061  ~ \(\times\)  ~ 0,01
\item   9 018  ~ \(\times\)  ~ 0,001
\item   45,28  ~ \(\times\)  ~ 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   378,7  ~ \(\times\)  ~ ... ~ = ~  37,87
\item   7 437  ~ \(\times\)  ~ ... ~ = ~  74,37
\item   83,38  ~ \(\times\)  ~ ... ~ = ~  8,338
\item   19,31  ~ \(\times\)  ~ ... ~ = ~  0,019 31
\item   11,4  ~ \(\times\)  ~ ... ~ = ~  0,011 4
\item   10,8  ~ \(\times\)  ~ ... ~ = ~  0,010 8
\item   3 357  ~ \(\times\)  ~ ... ~ = ~  335,7
\item   7 962  ~ \(\times\)  ~ ... ~ = ~  796,2
\item   9 174  ~ \(\times\)  ~ ... ~ = ~  91,74
\item   48,36  ~ \(\times\)  ~ ... ~ = ~  0,048 36
\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~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 008,1 ~mL~ = ...~hL
\item   8 170,5 ~dag~ = ...~dg
\item   710,55 ~kg~ = ...~cg
\item   9 137,2 ~dg~ = ...~kg
\item   522,11 ~cg~ = ...~hg
\item   941,27 ~dL~ = ...~hL
\item   5 361,4 ~mL~ = ...~L
\item   9 165,2 ~dm~ = ...~hm
\item   875,99 ~kL~ = ...~cL
\item   143,11 ~cm~ = ...~dam
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{64}{10}\) = \(\dfrac{640}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{450}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,098  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,8}
\item   0,051  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,1}
\item   95  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 95 000}
\item   4,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 490}
\item   4,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 440}
\item   194  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 194 000}
\item   0,106  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 10,6}
\item   0,259  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 259}
\item   0,091  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,91}
\item   0,042  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 42}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   273,2 ~ : ~ 100 ~ = ~{\color{red} 2,732}
\item   8 608 ~ : ~ 1 000 ~ = ~{\color{red} 8,608}
\item   738 ~ : ~ 1 000 ~ = ~{\color{red} 0,738}
\item   6 471 ~ : ~ 100 ~ = ~{\color{red} 64,71}
\item   2,724 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 724}
\item   0,147 ~ : ~ 100 ~ = ~{\color{red} 0,001 47}
\item   3 964 ~ : ~ 10 ~ = ~{\color{red} 396,4}
\item   12,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,012 2}
\item   4,029 ~ : ~ 10 ~ = ~{\color{red} 0,402 9}
\item   6 589 ~ : ~ 100 ~ = ~{\color{red} 65,89}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,09 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9
\item   14,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14 500
\item   559 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~559 000
\item   0,66 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~66
\item   569 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~569 000
\item   401 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~40 100
\item   0,457 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,57
\item   905 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 050
\item   0,523 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~52,3
\item   2,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~26
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,93 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,799 3
}\item   9,706 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 706
}\item   86,19 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,619
}\item   17,36 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,736
}\item   834,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,348
}\item   211,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,211 7
}\item   48,69 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,048 69
}\item   4 061 ~ \(\times\)  0,01 ~ = ~{\color{red} 40,61
}\item   9 018 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,018
}\item   45,28 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,528
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   378,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 37,87
\item   7 437 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 74,37
\item   83,38 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,338
\item   19,31 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,019 31
\item   11,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,011 4
\item   10,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,010 8
\item   3 357 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 335,7
\item   7 962 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 796,2
\item   9 174 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 91,74
\item   48,36 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,048 36
\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~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\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   6 008,1 ~mL~ = {\color{red}  0,060 081 }~hL
\item   8 170,5 ~dag~ = {\color{red}  817 050 }~dg
\item   710,55 ~kg~ = {\color{red}  71 055 000 }~cg
\item   9 137,2 ~dg~ = {\color{red}  0,913 72 }~kg
\item   522,11 ~cg~ = {\color{red}  0,052 211 }~hg
\item   941,27 ~dL~ = {\color{red}  0,941 27 }~hL
\item   5 361,4 ~mL~ = {\color{red}  5,361 4 }~L
\item   9 165,2 ~dm~ = {\color{red}  9,165 2 }~hm
\item   875,99 ~kL~ = {\color{red}  87 599 000 }~cL
\item   143,11 ~cm~ = {\color{red}  0,143 11 }~dam
\end{itemize}
\end{multicols}
\end{document}
