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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 157}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{14}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,3  ~ \(\times\)  ~ 100
\item   84,4  ~ \(\times\)  ~ 10
\item   19,2  ~ \(\times\)  ~ 1 000
\item   117  ~ \(\times\)  ~ 10
\item   0,94  ~ \(\times\)  ~ 100
\item   3,98  ~ \(\times\)  ~ 1 000
\item   0,071  ~ \(\times\)  ~ 10
\item   0,449  ~ \(\times\)  ~ 10
\item   794  ~ \(\times\)  ~ 1 000
\item   757  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,48  ~ : ~ 1 000
\item   599  ~ : ~ 100
\item   16,07  ~ : ~ 100
\item   814  ~ : ~ 1 000
\item   1 181  ~ : ~ 1 000
\item   24,01  ~ : ~ 10
\item   617,6  ~ : ~ 1 000
\item   788,1  ~ : ~ 100
\item   46,15  ~ : ~ 100
\item   853  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,731  ~ \(\times\)  ~ ... ~ = ~ 731
\item   685  ~ \(\times\)  ~ ... ~ = ~ 685 000
\item   87,6  ~ \(\times\)  ~ ... ~ = ~ 8 760
\item   4,23  ~ \(\times\)  ~ ... ~ = ~ 4 230
\item   0,398  ~ \(\times\)  ~ ... ~ = ~ 398
\item   83,9  ~ \(\times\)  ~ ... ~ = ~ 83 900
\item   2,52  ~ \(\times\)  ~ ... ~ = ~ 252
\item   9,34  ~ \(\times\)  ~ ... ~ = ~ 93,4
\item   0,576  ~ \(\times\)  ~ ... ~ = ~ 57,6
\item   780  ~ \(\times\)  ~ ... ~ = ~ 78 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,28  ~ \(\times\)  ~ 0,001
\item   493  ~ \(\times\)  ~ 0,001
\item   9 220  ~ \(\times\)  ~ 0,01
\item   7,771  ~ \(\times\)  ~ 0,1
\item   26,1  ~ \(\times\)  ~ 0,001
\item   57,19  ~ \(\times\)  ~ 0,1
\item   6,887  ~ \(\times\)  ~ 0,1
\item   865,3  ~ \(\times\)  ~ 0,001
\item   4 731  ~ \(\times\)  ~ 0,01
\item   80  ~ \(\times\)  ~ 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   676,5  ~ \(\times\)  ~ ... ~ = ~  67,65
\item   5,75  ~ \(\times\)  ~ ... ~ = ~  0,005 75
\item   52,18  ~ \(\times\)  ~ ... ~ = ~  0,052 18
\item   692,6  ~ \(\times\)  ~ ... ~ = ~  0,692 6
\item   3 476  ~ \(\times\)  ~ ... ~ = ~  347,6
\item   52,43  ~ \(\times\)  ~ ... ~ = ~  5,243
\item   3 644  ~ \(\times\)  ~ ... ~ = ~  3,644
\item   1 945  ~ \(\times\)  ~ ... ~ = ~  194,5
\item   41,45  ~ \(\times\)  ~ ... ~ = ~  0,414 5
\item   27,2  ~ \(\times\)  ~ ... ~ = ~  0,027 2
\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 ~dam~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   670,45 ~cg~ = ...~hg
\item   509,71 ~L~ = ...~hL
\item   2 568,1 ~dag~ = ...~mg
\item   795,81 ~hg~ = ...~kg
\item   554,32 ~dg~ = ...~dag
\item   1 691,4 ~dam~ = ...~cm
\item   486,51 ~mg~ = ...~cg
\item   4 448,4 ~dg~ = ...~g
\item   529,47 ~dL~ = ...~L
\item   7 679,8 ~hL~ = ...~L
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{3100}{100}\) = \(\dfrac{310}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{14}{10}\) = \(\dfrac{140}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{550}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 630}
\item   84,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 844}
\item   19,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 19 200}
\item   117  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 170}
\item   0,94  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 94}
\item   3,98  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 980}
\item   0,071  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,71}
\item   0,449  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,49}
\item   794  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 794 000}
\item   757  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 75 700}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,48 ~ : ~ 1 000 ~ = ~{\color{red} 0,056 48}
\item   599 ~ : ~ 100 ~ = ~{\color{red} 5,99}
\item   16,07 ~ : ~ 100 ~ = ~{\color{red} 0,160 7}
\item   814 ~ : ~ 1 000 ~ = ~{\color{red} 0,814}
\item   1 181 ~ : ~ 1 000 ~ = ~{\color{red} 1,181}
\item   24,01 ~ : ~ 10 ~ = ~{\color{red} 2,401}
\item   617,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,617 6}
\item   788,1 ~ : ~ 100 ~ = ~{\color{red} 7,881}
\item   46,15 ~ : ~ 100 ~ = ~{\color{red} 0,461 5}
\item   853 ~ : ~ 100 ~ = ~{\color{red} 8,53}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,731 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~731
\item   685 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~685 000
\item   87,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 760
\item   4,23 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 230
\item   0,398 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~398
\item   83,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~83 900
\item   2,52 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~252
\item   9,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~93,4
\item   0,576 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~57,6
\item   780 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~78 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,28 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,011 28
}\item   493 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,493
}\item   9 220 ~ \(\times\)  0,01 ~ = ~{\color{red} 92,2
}\item   7,771 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,777 1
}\item   26,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,026 1
}\item   57,19 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,719
}\item   6,887 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,688 7
}\item   865,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,865 3
}\item   4 731 ~ \(\times\)  0,01 ~ = ~{\color{red} 47,31
}\item   80 ~ \(\times\)  0,1 ~ = ~{\color{red} 8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   676,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 67,65
\item   5,75 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 75
\item   52,18 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,052 18
\item   692,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,692 6
\item   3 476 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 347,6
\item   52,43 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,243
\item   3 644 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,644
\item   1 945 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 194,5
\item   41,45 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,414 5
\item   27,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,027 2
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   670,45 ~cg~ = {\color{red}  0,067 045 }~hg
\item   509,71 ~L~ = {\color{red}  5,097 1 }~hL
\item   2 568,1 ~dag~ = {\color{red}  25 681 000 }~mg
\item   795,81 ~hg~ = {\color{red}  79,581 }~kg
\item   554,32 ~dg~ = {\color{red}  5,543 2 }~dag
\item   1 691,4 ~dam~ = {\color{red}  1 691 400 }~cm
\item   486,51 ~mg~ = {\color{red}  48,651 }~cg
\item   4 448,4 ~dg~ = {\color{red}  444,84 }~g
\item   529,47 ~dL~ = {\color{red}  52,947 }~L
\item   7 679,8 ~hL~ = {\color{red}  767 980 }~L
\end{itemize}
\end{multicols}
\end{document}
