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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 147}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{34}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,05  ~ \(\times\)  ~ 100
\item   0,872  ~ \(\times\)  ~ 1 000
\item   0,114  ~ \(\times\)  ~ 100
\item   0,079  ~ \(\times\)  ~ 100
\item   3,61  ~ \(\times\)  ~ 1 000
\item   0,066  ~ \(\times\)  ~ 10
\item   98,6  ~ \(\times\)  ~ 10
\item   0,072  ~ \(\times\)  ~ 10
\item   524  ~ \(\times\)  ~ 100
\item   77,2  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   63,7  ~ : ~ 100
\item   4,382  ~ : ~ 100
\item   3 603  ~ : ~ 10
\item   9,388  ~ : ~ 1 000
\item   3 567  ~ : ~ 10
\item   26,09  ~ : ~ 1 000
\item   4 892  ~ : ~ 1 000
\item   62,53  ~ : ~ 100
\item   79,3  ~ : ~ 1 000
\item   3 824  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,59  ~ \(\times\)  ~ ... ~ = ~ 959
\item   91,5  ~ \(\times\)  ~ ... ~ = ~ 9 150
\item   0,015  ~ \(\times\)  ~ ... ~ = ~ 15
\item   0,399  ~ \(\times\)  ~ ... ~ = ~ 39,9
\item   0,029  ~ \(\times\)  ~ ... ~ = ~ 0,29
\item   0,075  ~ \(\times\)  ~ ... ~ = ~ 75
\item   411  ~ \(\times\)  ~ ... ~ = ~ 41 100
\item   7,18  ~ \(\times\)  ~ ... ~ = ~ 718
\item   0,224  ~ \(\times\)  ~ ... ~ = ~ 224
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 22
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   450,8  ~ \(\times\)  ~ 0,001
\item   58,11  ~ \(\times\)  ~ 0,001
\item   4 963  ~ \(\times\)  ~ 0,01
\item   1 439  ~ \(\times\)  ~ 0,1
\item   30,43  ~ \(\times\)  ~ 0,001
\item   2,189  ~ \(\times\)  ~ 0,1
\item   3,166  ~ \(\times\)  ~ 0,001
\item   5 919  ~ \(\times\)  ~ 0,01
\item   778,9  ~ \(\times\)  ~ 0,1
\item   4 475  ~ \(\times\)  ~ 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   84,63  ~ \(\times\)  ~ ... ~ = ~  0,846 3
\item   6,419  ~ \(\times\)  ~ ... ~ = ~  0,064 19
\item   38,42  ~ \(\times\)  ~ ... ~ = ~  0,384 2
\item   1 342  ~ \(\times\)  ~ ... ~ = ~  1,342
\item   4,682  ~ \(\times\)  ~ ... ~ = ~  0,046 82
\item   821,3  ~ \(\times\)  ~ ... ~ = ~  82,13
\item   834,1  ~ \(\times\)  ~ ... ~ = ~  83,41
\item   1,244  ~ \(\times\)  ~ ... ~ = ~  0,001 244
\item   42,01  ~ \(\times\)  ~ ... ~ = ~  4,201
\item   5,464  ~ \(\times\)  ~ ... ~ = ~  0,054 64
\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~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   210,61 ~kg~ = ...~dg
\item   765,45 ~dag~ = ...~dg
\item   645,13 ~dag~ = ...~mg
\item   5 340,3 ~g~ = ...~kg
\item   621,11 ~hg~ = ...~mg
\item   181,62 ~dL~ = ...~L
\item   2 069,2 ~kL~ = ...~dL
\item   651,13 ~cm~ = ...~hm
\item   3 422,7 ~cg~ = ...~g
\item   7 595,7 ~hg~ = ...~kg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{6700}{100}\) = \(\dfrac{670}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{34}{10}\) = \(\dfrac{340}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{910}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,05  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 905}
\item   0,872  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 872}
\item   0,114  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 11,4}
\item   0,079  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,9}
\item   3,61  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 610}
\item   0,066  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,66}
\item   98,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 986}
\item   0,072  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,72}
\item   524  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 52 400}
\item   77,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 772}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   63,7 ~ : ~ 100 ~ = ~{\color{red} 0,637}
\item   4,382 ~ : ~ 100 ~ = ~{\color{red} 0,043 82}
\item   3 603 ~ : ~ 10 ~ = ~{\color{red} 360,3}
\item   9,388 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 388}
\item   3 567 ~ : ~ 10 ~ = ~{\color{red} 356,7}
\item   26,09 ~ : ~ 1 000 ~ = ~{\color{red} 0,026 09}
\item   4 892 ~ : ~ 1 000 ~ = ~{\color{red} 4,892}
\item   62,53 ~ : ~ 100 ~ = ~{\color{red} 0,625 3}
\item   79,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,079 3}
\item   3 824 ~ : ~ 1 000 ~ = ~{\color{red} 3,824}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,59 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~959
\item   91,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 150
\item   0,015 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~15
\item   0,399 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~39,9
\item   0,029 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,29
\item   0,075 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~75
\item   411 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~41 100
\item   7,18 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~718
\item   0,224 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~224
\item   0,022 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~22
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   450,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,450 8
}\item   58,11 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,058 11
}\item   4 963 ~ \(\times\)  0,01 ~ = ~{\color{red} 49,63
}\item   1 439 ~ \(\times\)  0,1 ~ = ~{\color{red} 143,9
}\item   30,43 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 43
}\item   2,189 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,218 9
}\item   3,166 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 166
}\item   5 919 ~ \(\times\)  0,01 ~ = ~{\color{red} 59,19
}\item   778,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 77,89
}\item   4 475 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,475
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   84,63 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,846 3
\item   6,419 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,064 19
\item   38,42 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,384 2
\item   1 342 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,342
\item   4,682 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,046 82
\item   821,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 82,13
\item   834,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 83,41
\item   1,244 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 244
\item   42,01 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,201
\item   5,464 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,054 64
\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~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\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   210,61 ~kg~ = {\color{red}  2 106 100 }~dg
\item   765,45 ~dag~ = {\color{red}  76 545 }~dg
\item   645,13 ~dag~ = {\color{red}  6 451 300 }~mg
\item   5 340,3 ~g~ = {\color{red}  5,340 3 }~kg
\item   621,11 ~hg~ = {\color{red}  62 111 000 }~mg
\item   181,62 ~dL~ = {\color{red}  18,162 }~L
\item   2 069,2 ~kL~ = {\color{red}  20 692 000 }~dL
\item   651,13 ~cm~ = {\color{red}  0,065 113 }~hm
\item   3 422,7 ~cg~ = {\color{red}  34,227 }~g
\item   7 595,7 ~hg~ = {\color{red}  759,57 }~kg
\end{itemize}
\end{multicols}
\end{document}
