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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 188}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,284  ~ \(\times\)  ~ 100
\item   9,33  ~ \(\times\)  ~ 100
\item   281  ~ \(\times\)  ~ 10
\item   0,004  ~ \(\times\)  ~ 1 000
\item   0,52  ~ \(\times\)  ~ 100
\item   12,3  ~ \(\times\)  ~ 100
\item   855  ~ \(\times\)  ~ 100
\item   41,9  ~ \(\times\)  ~ 1 000
\item   0,05  ~ \(\times\)  ~ 10
\item   212  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   914,8  ~ : ~ 1 000
\item   56,74  ~ : ~ 1 000
\item   43,46  ~ : ~ 1 000
\item   195,6  ~ : ~ 10
\item   8,752  ~ : ~ 100
\item   3,791  ~ : ~ 1 000
\item   273  ~ : ~ 100
\item   0,835  ~ : ~ 100
\item   2,942  ~ : ~ 1 000
\item   0,615  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   341  ~ \(\times\)  ~ ... ~ = ~ 341 000
\item   4,44  ~ \(\times\)  ~ ... ~ = ~ 44,4
\item   824  ~ \(\times\)  ~ ... ~ = ~ 824 000
\item   571  ~ \(\times\)  ~ ... ~ = ~ 5 710
\item   803  ~ \(\times\)  ~ ... ~ = ~ 8 030
\item   0,435  ~ \(\times\)  ~ ... ~ = ~ 435
\item   0,633  ~ \(\times\)  ~ ... ~ = ~ 6,33
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 3,3
\item   813  ~ \(\times\)  ~ ... ~ = ~ 8 130
\item   0,039  ~ \(\times\)  ~ ... ~ = ~ 39
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,762  ~ \(\times\)  ~ 0,01
\item   6 169  ~ \(\times\)  ~ 0,1
\item   583,9  ~ \(\times\)  ~ 0,01
\item   524  ~ \(\times\)  ~ 0,1
\item   4,868  ~ \(\times\)  ~ 0,01
\item   1 946  ~ \(\times\)  ~ 0,001
\item   5,05  ~ \(\times\)  ~ 0,01
\item   193,8  ~ \(\times\)  ~ 0,1
\item   2 511  ~ \(\times\)  ~ 0,1
\item   613  ~ \(\times\)  ~ 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   9,18  ~ \(\times\)  ~ ... ~ = ~  0,091 8
\item   83,29  ~ \(\times\)  ~ ... ~ = ~  0,083 29
\item   216,1  ~ \(\times\)  ~ ... ~ = ~  21,61
\item   50,18  ~ \(\times\)  ~ ... ~ = ~  0,050 18
\item   712,6  ~ \(\times\)  ~ ... ~ = ~  7,126
\item   61,37  ~ \(\times\)  ~ ... ~ = ~  0,613 7
\item   72,85  ~ \(\times\)  ~ ... ~ = ~  0,728 5
\item   733,1  ~ \(\times\)  ~ ... ~ = ~  73,31
\item   4,464  ~ \(\times\)  ~ ... ~ = ~  0,044 64
\item   6 817  ~ \(\times\)  ~ ... ~ = ~  681,7
\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 ~hm~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 801,7 ~cL~ = ...~L
\item   8 697,2 ~dm~ = ...~hm
\item   402,15 ~hm~ = ...~mm
\item   887,42 ~kg~ = ...~mg
\item   2 879,9 ~m~ = ...~mm
\item   5 939,7 ~daL~ = ...~kL
\item   8 962,4 ~cm~ = ...~mm
\item   208,44 ~dL~ = ...~mL
\item   989,35 ~dL~ = ...~kL
\item   893,16 ~dag~ = ...~g
\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   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{110}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{200}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{990}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,284  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 28,4}
\item   9,33  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 933}
\item   281  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 810}
\item   0,004  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4}
\item   0,52  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 52}
\item   12,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 230}
\item   855  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 85 500}
\item   41,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 41 900}
\item   0,05  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,5}
\item   212  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 120}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   914,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,914 8}
\item   56,74 ~ : ~ 1 000 ~ = ~{\color{red} 0,056 74}
\item   43,46 ~ : ~ 1 000 ~ = ~{\color{red} 0,043 46}
\item   195,6 ~ : ~ 10 ~ = ~{\color{red} 19,56}
\item   8,752 ~ : ~ 100 ~ = ~{\color{red} 0,087 52}
\item   3,791 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 791}
\item   273 ~ : ~ 100 ~ = ~{\color{red} 2,73}
\item   0,835 ~ : ~ 100 ~ = ~{\color{red} 0,008 35}
\item   2,942 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 942}
\item   0,615 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 615}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   341 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~341 000
\item   4,44 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~44,4
\item   824 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~824 000
\item   571 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 710
\item   803 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 030
\item   0,435 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~435
\item   0,633 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,33
\item   0,033 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,3
\item   813 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 130
\item   0,039 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~39
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,762 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,087 62
}\item   6 169 ~ \(\times\)  0,1 ~ = ~{\color{red} 616,9
}\item   583,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,839
}\item   524 ~ \(\times\)  0,1 ~ = ~{\color{red} 52,4
}\item   4,868 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,048 68
}\item   1 946 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,946
}\item   5,05 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,050 5
}\item   193,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 19,38
}\item   2 511 ~ \(\times\)  0,1 ~ = ~{\color{red} 251,1
}\item   613 ~ \(\times\)  0,1 ~ = ~{\color{red} 61,3
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,18 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,091 8
\item   83,29 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,083 29
\item   216,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 21,61
\item   50,18 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,050 18
\item   712,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,126
\item   61,37 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,613 7
\item   72,85 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,728 5
\item   733,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 73,31
\item   4,464 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,044 64
\item   6 817 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 681,7
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 801,7 ~cL~ = {\color{red}  28,017 }~L
\item   8 697,2 ~dm~ = {\color{red}  8,697 2 }~hm
\item   402,15 ~hm~ = {\color{red}  40 215 000 }~mm
\item   887,42 ~kg~ = {\color{red}  887 420 000 }~mg
\item   2 879,9 ~m~ = {\color{red}  2 879 900 }~mm
\item   5 939,7 ~daL~ = {\color{red}  59,397 }~kL
\item   8 962,4 ~cm~ = {\color{red}  89 624 }~mm
\item   208,44 ~dL~ = {\color{red}  20 844 }~mL
\item   989,35 ~dL~ = {\color{red}  0,098 935 }~kL
\item   893,16 ~dag~ = {\color{red}  8 931,6 }~g
\end{itemize}
\end{multicols}
\end{document}
