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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 97}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{84}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   580  ~ \(\times\)  ~ 10
\item   9,18  ~ \(\times\)  ~ 100
\item   35  ~ \(\times\)  ~ 1 000
\item   0,457  ~ \(\times\)  ~ 1 000
\item   1,24  ~ \(\times\)  ~ 10
\item   9,31  ~ \(\times\)  ~ 10
\item   0,267  ~ \(\times\)  ~ 1 000
\item   20,1  ~ \(\times\)  ~ 10
\item   0,025  ~ \(\times\)  ~ 1 000
\item   140  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 392  ~ : ~ 10
\item   89,72  ~ : ~ 1 000
\item   1 434  ~ : ~ 100
\item   135,8  ~ : ~ 10
\item   44,1  ~ : ~ 1 000
\item   33,4  ~ : ~ 10
\item   982,5  ~ : ~ 10
\item   2 407  ~ : ~ 10
\item   8 219  ~ : ~ 1 000
\item   8,517  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   772  ~ \(\times\)  ~ ... ~ = ~ 772 000
\item   0,953  ~ \(\times\)  ~ ... ~ = ~ 953
\item   450  ~ \(\times\)  ~ ... ~ = ~ 4 500
\item   0,075  ~ \(\times\)  ~ ... ~ = ~ 0,75
\item   867  ~ \(\times\)  ~ ... ~ = ~ 867 000
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 70
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 0,58
\item   0,57  ~ \(\times\)  ~ ... ~ = ~ 57
\item   37,5  ~ \(\times\)  ~ ... ~ = ~ 3 750
\item   0,013  ~ \(\times\)  ~ ... ~ = ~ 13
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,48  ~ \(\times\)  ~ 0,01
\item   87,1  ~ \(\times\)  ~ 0,1
\item   31,69  ~ \(\times\)  ~ 0,01
\item   1 462  ~ \(\times\)  ~ 0,001
\item   3,533  ~ \(\times\)  ~ 0,1
\item   0,475  ~ \(\times\)  ~ 0,1
\item   75,27  ~ \(\times\)  ~ 0,001
\item   75,7  ~ \(\times\)  ~ 0,001
\item   5 010  ~ \(\times\)  ~ 0,1
\item   88,45  ~ \(\times\)  ~ 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   31,78  ~ \(\times\)  ~ ... ~ = ~  0,031 78
\item   150,1  ~ \(\times\)  ~ ... ~ = ~  1,501
\item   8 347  ~ \(\times\)  ~ ... ~ = ~  834,7
\item   731,4  ~ \(\times\)  ~ ... ~ = ~  0,731 4
\item   7 230  ~ \(\times\)  ~ ... ~ = ~  723
\item   323,3  ~ \(\times\)  ~ ... ~ = ~  3,233
\item   2 996  ~ \(\times\)  ~ ... ~ = ~  29,96
\item   499,4  ~ \(\times\)  ~ ... ~ = ~  49,94
\item   621  ~ \(\times\)  ~ ... ~ = ~  6,21
\item   32,28  ~ \(\times\)  ~ ... ~ = ~  0,032 28
\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~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   722,41 ~daL~ = ...~dL
\item   664,4 ~daL~ = ...~kL
\item   175,42 ~hm~ = ...~cm
\item   476,65 ~hm~ = ...~dm
\item   3 208 ~dm~ = ...~mm
\item   4 982,4 ~mg~ = ...~dg
\item   738,08 ~kg~ = ...~hg
\item   6 375,4 ~kg~ = ...~dag
\item   757,49 ~m~ = ...~cm
\item   1 484,8 ~m~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{5800}{100}\) = \(\dfrac{580}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{84}{10}\) = \(\dfrac{840}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{130}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   580  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 800}
\item   9,18  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 918}
\item   35  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 35 000}
\item   0,457  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 457}
\item   1,24  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 12,4}
\item   9,31  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 93,1}
\item   0,267  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 267}
\item   20,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 201}
\item   0,025  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 25}
\item   140  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 140 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 392 ~ : ~ 10 ~ = ~{\color{red} 239,2}
\item   89,72 ~ : ~ 1 000 ~ = ~{\color{red} 0,089 72}
\item   1 434 ~ : ~ 100 ~ = ~{\color{red} 14,34}
\item   135,8 ~ : ~ 10 ~ = ~{\color{red} 13,58}
\item   44,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,044 1}
\item   33,4 ~ : ~ 10 ~ = ~{\color{red} 3,34}
\item   982,5 ~ : ~ 10 ~ = ~{\color{red} 98,25}
\item   2 407 ~ : ~ 10 ~ = ~{\color{red} 240,7}
\item   8 219 ~ : ~ 1 000 ~ = ~{\color{red} 8,219}
\item   8,517 ~ : ~ 10 ~ = ~{\color{red} 0,851 7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   772 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~772 000
\item   0,953 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~953
\item   450 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 500
\item   0,075 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,75
\item   867 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~867 000
\item   0,07 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~70
\item   0,058 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,58
\item   0,57 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~57
\item   37,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 750
\item   0,013 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~13
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,48 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,594 8
}\item   87,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,71
}\item   31,69 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,316 9
}\item   1 462 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,462
}\item   3,533 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,353 3
}\item   0,475 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,047 5
}\item   75,27 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,075 27
}\item   75,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,075 7
}\item   5 010 ~ \(\times\)  0,1 ~ = ~{\color{red} 501
}\item   88,45 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,884 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   31,78 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,031 78
\item   150,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,501
\item   8 347 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 834,7
\item   731,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,731 4
\item   7 230 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 723
\item   323,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,233
\item   2 996 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 29,96
\item   499,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 49,94
\item   621 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,21
\item   32,28 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,032 28
\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~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   722,41 ~daL~ = {\color{red}  72 241 }~dL
\item   664,4 ~daL~ = {\color{red}  6,644 }~kL
\item   175,42 ~hm~ = {\color{red}  1 754 200 }~cm
\item   476,65 ~hm~ = {\color{red}  476 650 }~dm
\item   3 208 ~dm~ = {\color{red}  320 800 }~mm
\item   4 982,4 ~mg~ = {\color{red}  49,824 }~dg
\item   738,08 ~kg~ = {\color{red}  7 380,8 }~hg
\item   6 375,4 ~kg~ = {\color{red}  637 540 }~dag
\item   757,49 ~m~ = {\color{red}  75 749 }~cm
\item   1 484,8 ~m~ = {\color{red}  14 848 }~dm
\end{itemize}
\end{multicols}
\end{document}
