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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 51}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{43}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,957  ~ \(\times\)  ~ 1 000
\item   0,048  ~ \(\times\)  ~ 1 000
\item   6,53  ~ \(\times\)  ~ 1 000
\item   6,85  ~ \(\times\)  ~ 100
\item   0,293  ~ \(\times\)  ~ 1 000
\item   16  ~ \(\times\)  ~ 10
\item   5,6  ~ \(\times\)  ~ 10
\item   49,8  ~ \(\times\)  ~ 100
\item   6,39  ~ \(\times\)  ~ 100
\item   46,8  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   727,9  ~ : ~ 100
\item   310  ~ : ~ 10
\item   9 802  ~ : ~ 10
\item   9,099  ~ : ~ 10
\item   7,219  ~ : ~ 10
\item   6 160  ~ : ~ 100
\item   910,8  ~ : ~ 1 000
\item   5,97  ~ : ~ 100
\item   2,027  ~ : ~ 1 000
\item   0,27  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   813  ~ \(\times\)  ~ ... ~ = ~ 81 300
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 96
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 0,88
\item   5,45  ~ \(\times\)  ~ ... ~ = ~ 5 450
\item   0,859  ~ \(\times\)  ~ ... ~ = ~ 859
\item   0,37  ~ \(\times\)  ~ ... ~ = ~ 37
\item   550  ~ \(\times\)  ~ ... ~ = ~ 550 000
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 8,9
\item   5,83  ~ \(\times\)  ~ ... ~ = ~ 58,3
\item   0,936  ~ \(\times\)  ~ ... ~ = ~ 936
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   803,4  ~ \(\times\)  ~ 0,001
\item   9,78  ~ \(\times\)  ~ 0,01
\item   5,142  ~ \(\times\)  ~ 0,1
\item   91,36  ~ \(\times\)  ~ 0,001
\item   49,25  ~ \(\times\)  ~ 0,01
\item   2,507  ~ \(\times\)  ~ 0,1
\item   19,43  ~ \(\times\)  ~ 0,01
\item   28,5  ~ \(\times\)  ~ 0,001
\item   7 003  ~ \(\times\)  ~ 0,001
\item   84,06  ~ \(\times\)  ~ 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   9,818  ~ \(\times\)  ~ ... ~ = ~  0,009 818
\item   7,415  ~ \(\times\)  ~ ... ~ = ~  0,074 15
\item   3,76  ~ \(\times\)  ~ ... ~ = ~  0,376
\item   6,664  ~ \(\times\)  ~ ... ~ = ~  0,006 664
\item   64,23  ~ \(\times\)  ~ ... ~ = ~  0,642 3
\item   66,79  ~ \(\times\)  ~ ... ~ = ~  0,066 79
\item   7,599  ~ \(\times\)  ~ ... ~ = ~  0,007 599
\item   98,02  ~ \(\times\)  ~ ... ~ = ~  0,980 2
\item   2 142  ~ \(\times\)  ~ ... ~ = ~  214,2
\item   652  ~ \(\times\)  ~ ... ~ = ~  6,52
\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 ~dm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   405,39 ~dag~ = ...~g
\item   796,77 ~dL~ = ...~hL
\item   265,36 ~hg~ = ...~dg
\item   119,11 ~mL~ = ...~cL
\item   888,67 ~kL~ = ...~hL
\item   9 022,9 ~dag~ = ...~hg
\item   4 672,2 ~cL~ = ...~hL
\item   8 336,5 ~hg~ = ...~g
\item   8 550,5 ~daL~ = ...~mL
\item   5 411,1 ~cg~ = ...~dg
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{81}{10}\) = \(\dfrac{810}{100}\)
\item   \(\dfrac{43}{100}\) = \(\dfrac{430}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,957  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 957}
\item   0,048  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 48}
\item   6,53  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 530}
\item   6,85  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 685}
\item   0,293  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 293}
\item   16  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 160}
\item   5,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 56}
\item   49,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 980}
\item   6,39  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 639}
\item   46,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 468}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   727,9 ~ : ~ 100 ~ = ~{\color{red} 7,279}
\item   310 ~ : ~ 10 ~ = ~{\color{red} 31}
\item   9 802 ~ : ~ 10 ~ = ~{\color{red} 980,2}
\item   9,099 ~ : ~ 10 ~ = ~{\color{red} 0,909 9}
\item   7,219 ~ : ~ 10 ~ = ~{\color{red} 0,721 9}
\item   6 160 ~ : ~ 100 ~ = ~{\color{red} 61,6}
\item   910,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,910 8}
\item   5,97 ~ : ~ 100 ~ = ~{\color{red} 0,059 7}
\item   2,027 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 027}
\item   0,27 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 27}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   813 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~81 300
\item   0,096 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~96
\item   0,088 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,88
\item   5,45 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 450
\item   0,859 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~859
\item   0,37 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~37
\item   550 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~550 000
\item   0,089 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,9
\item   5,83 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~58,3
\item   0,936 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~936
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   803,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,803 4
}\item   9,78 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,097 8
}\item   5,142 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,514 2
}\item   91,36 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,091 36
}\item   49,25 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,492 5
}\item   2,507 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,250 7
}\item   19,43 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,194 3
}\item   28,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,028 5
}\item   7 003 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,003
}\item   84,06 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,084 06
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,818 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 818
\item   7,415 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,074 15
\item   3,76 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,376
\item   6,664 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 664
\item   64,23 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,642 3
\item   66,79 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,066 79
\item   7,599 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 599
\item   98,02 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,980 2
\item   2 142 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 214,2
\item   652 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,52
\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 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   405,39 ~dag~ = {\color{red}  4 053,9 }~g
\item   796,77 ~dL~ = {\color{red}  0,796 77 }~hL
\item   265,36 ~hg~ = {\color{red}  265 360 }~dg
\item   119,11 ~mL~ = {\color{red}  11,911 }~cL
\item   888,67 ~kL~ = {\color{red}  8 886,7 }~hL
\item   9 022,9 ~dag~ = {\color{red}  902,29 }~hg
\item   4 672,2 ~cL~ = {\color{red}  0,467 22 }~hL
\item   8 336,5 ~hg~ = {\color{red}  833 650 }~g
\item   8 550,5 ~daL~ = {\color{red}  85 505 000 }~mL
\item   5 411,1 ~cg~ = {\color{red}  541,11 }~dg
\end{itemize}
\end{multicols}
\end{document}
