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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 148}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{55}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   288  ~ \(\times\)  ~ 10
\item   518  ~ \(\times\)  ~ 100
\item   0,085  ~ \(\times\)  ~ 1 000
\item   59,9  ~ \(\times\)  ~ 100
\item   0,336  ~ \(\times\)  ~ 1 000
\item   0,021  ~ \(\times\)  ~ 100
\item   8,31  ~ \(\times\)  ~ 10
\item   274  ~ \(\times\)  ~ 100
\item   0,062  ~ \(\times\)  ~ 10
\item   529  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,191  ~ : ~ 1 000
\item   7,137  ~ : ~ 1 000
\item   2,187  ~ : ~ 1 000
\item   61,11  ~ : ~ 10
\item   6,983  ~ : ~ 10
\item   70,1  ~ : ~ 10
\item   79,78  ~ : ~ 100
\item   4,052  ~ : ~ 100
\item   7,611  ~ : ~ 10
\item   89,97  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   275  ~ \(\times\)  ~ ... ~ = ~ 275 000
\item   945  ~ \(\times\)  ~ ... ~ = ~ 94 500
\item   0,023  ~ \(\times\)  ~ ... ~ = ~ 23
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 9,6
\item   0,206  ~ \(\times\)  ~ ... ~ = ~ 20,6
\item   4,67  ~ \(\times\)  ~ ... ~ = ~ 467
\item   0,051  ~ \(\times\)  ~ ... ~ = ~ 0,51
\item   0,38  ~ \(\times\)  ~ ... ~ = ~ 3,8
\item   8,09  ~ \(\times\)  ~ ... ~ = ~ 809
\item   0,05  ~ \(\times\)  ~ ... ~ = ~ 0,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 657  ~ \(\times\)  ~ 0,001
\item   508,5  ~ \(\times\)  ~ 0,01
\item   1 515  ~ \(\times\)  ~ 0,1
\item   4,966  ~ \(\times\)  ~ 0,001
\item   25,94  ~ \(\times\)  ~ 0,1
\item   9 398  ~ \(\times\)  ~ 0,001
\item   52,48  ~ \(\times\)  ~ 0,1
\item   211,3  ~ \(\times\)  ~ 0,1
\item   6,94  ~ \(\times\)  ~ 0,001
\item   8 909  ~ \(\times\)  ~ 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   142,9  ~ \(\times\)  ~ ... ~ = ~  1,429
\item   634,7  ~ \(\times\)  ~ ... ~ = ~  63,47
\item   142,4  ~ \(\times\)  ~ ... ~ = ~  0,142 4
\item   54,19  ~ \(\times\)  ~ ... ~ = ~  5,419
\item   39,67  ~ \(\times\)  ~ ... ~ = ~  0,039 67
\item   278,6  ~ \(\times\)  ~ ... ~ = ~  27,86
\item   8,864  ~ \(\times\)  ~ ... ~ = ~  0,088 64
\item   1,14  ~ \(\times\)  ~ ... ~ = ~  0,001 14
\item   7,714  ~ \(\times\)  ~ ... ~ = ~  0,771 4
\item   14,04  ~ \(\times\)  ~ ... ~ = ~  1,404
\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~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   991,54 ~dam~ = ...~hm
\item   657,34 ~cL~ = ...~L
\item   8 990,4 ~kg~ = ...~cg
\item   984,98 ~dag~ = ...~hg
\item   197,52 ~dg~ = ...~cg
\item   954,23 ~L~ = ...~dL
\item   7 873,5 ~dam~ = ...~cm
\item   556,85 ~mm~ = ...~dam
\item   795,83 ~hm~ = ...~km
\item   7 996,6 ~g~ = ...~hg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{970}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{55}{10}\) = \(\dfrac{550}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{470}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   288  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 880}
\item   518  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 51 800}
\item   0,085  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 85}
\item   59,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 990}
\item   0,336  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 336}
\item   0,021  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,1}
\item   8,31  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 83,1}
\item   274  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 27 400}
\item   0,062  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,62}
\item   529  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 52 900}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,191 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 191}
\item   7,137 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 137}
\item   2,187 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 187}
\item   61,11 ~ : ~ 10 ~ = ~{\color{red} 6,111}
\item   6,983 ~ : ~ 10 ~ = ~{\color{red} 0,698 3}
\item   70,1 ~ : ~ 10 ~ = ~{\color{red} 7,01}
\item   79,78 ~ : ~ 100 ~ = ~{\color{red} 0,797 8}
\item   4,052 ~ : ~ 100 ~ = ~{\color{red} 0,040 52}
\item   7,611 ~ : ~ 10 ~ = ~{\color{red} 0,761 1}
\item   89,97 ~ : ~ 100 ~ = ~{\color{red} 0,899 7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   275 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~275 000
\item   945 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~94 500
\item   0,023 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~23
\item   0,096 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,6
\item   0,206 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~20,6
\item   4,67 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~467
\item   0,051 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,51
\item   0,38 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,8
\item   8,09 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~809
\item   0,05 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 657 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,657
}\item   508,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,085
}\item   1 515 ~ \(\times\)  0,1 ~ = ~{\color{red} 151,5
}\item   4,966 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 966
}\item   25,94 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,594
}\item   9 398 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,398
}\item   52,48 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,248
}\item   211,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 21,13
}\item   6,94 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 94
}\item   8 909 ~ \(\times\)  0,01 ~ = ~{\color{red} 89,09
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   142,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,429
\item   634,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 63,47
\item   142,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,142 4
\item   54,19 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,419
\item   39,67 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,039 67
\item   278,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 27,86
\item   8,864 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,088 64
\item   1,14 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 14
\item   7,714 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,771 4
\item   14,04 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,404
\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~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   991,54 ~dam~ = {\color{red}  99,154 }~hm
\item   657,34 ~cL~ = {\color{red}  6,573 4 }~L
\item   8 990,4 ~kg~ = {\color{red}  899 040 000 }~cg
\item   984,98 ~dag~ = {\color{red}  98,498 }~hg
\item   197,52 ~dg~ = {\color{red}  1 975,2 }~cg
\item   954,23 ~L~ = {\color{red}  9 542,3 }~dL
\item   7 873,5 ~dam~ = {\color{red}  7 873 500 }~cm
\item   556,85 ~mm~ = {\color{red}  0,055 685 }~dam
\item   795,83 ~hm~ = {\color{red}  79,583 }~km
\item   7 996,6 ~g~ = {\color{red}  79,966 }~hg
\end{itemize}
\end{multicols}
\end{document}
