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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 127}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{45}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{36}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42,6  ~ \(\times\)  ~ 100
\item   6,99  ~ \(\times\)  ~ 100
\item   983  ~ \(\times\)  ~ 100
\item   0,031  ~ \(\times\)  ~ 1 000
\item   856  ~ \(\times\)  ~ 100
\item   119  ~ \(\times\)  ~ 1 000
\item   6,15  ~ \(\times\)  ~ 100
\item   0,031  ~ \(\times\)  ~ 10
\item   0,076  ~ \(\times\)  ~ 1 000
\item   0,39  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 736  ~ : ~ 1 000
\item   20,96  ~ : ~ 1 000
\item   16,86  ~ : ~ 100
\item   8 690  ~ : ~ 100
\item   3,448  ~ : ~ 100
\item   714,2  ~ : ~ 1 000
\item   6,45  ~ : ~ 10
\item   946,5  ~ : ~ 10
\item   732,8  ~ : ~ 100
\item   2 517  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 0,88
\item   1,08  ~ \(\times\)  ~ ... ~ = ~ 1 080
\item   59,2  ~ \(\times\)  ~ ... ~ = ~ 5 920
\item   0,604  ~ \(\times\)  ~ ... ~ = ~ 6,04
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 60
\item   0,743  ~ \(\times\)  ~ ... ~ = ~ 7,43
\item   487  ~ \(\times\)  ~ ... ~ = ~ 487 000
\item   253  ~ \(\times\)  ~ ... ~ = ~ 253 000
\item   4,46  ~ \(\times\)  ~ ... ~ = ~ 44,6
\item   208  ~ \(\times\)  ~ ... ~ = ~ 20 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   260,5  ~ \(\times\)  ~ 0,001
\item   4,932  ~ \(\times\)  ~ 0,001
\item   50,75  ~ \(\times\)  ~ 0,01
\item   5,981  ~ \(\times\)  ~ 0,001
\item   7 630  ~ \(\times\)  ~ 0,1
\item   105,6  ~ \(\times\)  ~ 0,1
\item   3 810  ~ \(\times\)  ~ 0,1
\item   26,87  ~ \(\times\)  ~ 0,01
\item   4 053  ~ \(\times\)  ~ 0,001
\item   55,42  ~ \(\times\)  ~ 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   4 339  ~ \(\times\)  ~ ... ~ = ~  433,9
\item   926,2  ~ \(\times\)  ~ ... ~ = ~  92,62
\item   1,318  ~ \(\times\)  ~ ... ~ = ~  0,013 18
\item   0,561  ~ \(\times\)  ~ ... ~ = ~  0,005 61
\item   6,274  ~ \(\times\)  ~ ... ~ = ~  0,627 4
\item   42,13  ~ \(\times\)  ~ ... ~ = ~  0,421 3
\item   8,524  ~ \(\times\)  ~ ... ~ = ~  0,852 4
\item   40,37  ~ \(\times\)  ~ ... ~ = ~  4,037
\item   0,136  ~ \(\times\)  ~ ... ~ = ~  0,013 6
\item   530,6  ~ \(\times\)  ~ ... ~ = ~  5,306
\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~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   203,07 ~mm~ = ...~dam
\item   2 461,8 ~hm~ = ...~m
\item   996,19 ~dg~ = ...~g
\item   4 261,7 ~dL~ = ...~cL
\item   669,63 ~kg~ = ...~hg
\item   8 877,5 ~dL~ = ...~mL
\item   7 801,5 ~kg~ = ...~g
\item   9 471 ~L~ = ...~cL
\item   6 082,8 ~km~ = ...~hm
\item   787,6 ~hL~ = ...~cL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{1400}{100}\) = \(\dfrac{140}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{45}{10}\) = \(\dfrac{450}{100}\)
\item   \(\dfrac{36}{100}\) = \(\dfrac{360}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 260}
\item   6,99  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 699}
\item   983  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 98 300}
\item   0,031  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 31}
\item   856  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 85 600}
\item   119  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 119 000}
\item   6,15  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 615}
\item   0,031  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,31}
\item   0,076  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 76}
\item   0,39  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 390}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 736 ~ : ~ 1 000 ~ = ~{\color{red} 4,736}
\item   20,96 ~ : ~ 1 000 ~ = ~{\color{red} 0,020 96}
\item   16,86 ~ : ~ 100 ~ = ~{\color{red} 0,168 6}
\item   8 690 ~ : ~ 100 ~ = ~{\color{red} 86,9}
\item   3,448 ~ : ~ 100 ~ = ~{\color{red} 0,034 48}
\item   714,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,714 2}
\item   6,45 ~ : ~ 10 ~ = ~{\color{red} 0,645}
\item   946,5 ~ : ~ 10 ~ = ~{\color{red} 94,65}
\item   732,8 ~ : ~ 100 ~ = ~{\color{red} 7,328}
\item   2 517 ~ : ~ 100 ~ = ~{\color{red} 25,17}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,088 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,88
\item   1,08 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 080
\item   59,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 920
\item   0,604 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,04
\item   0,06 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~60
\item   0,743 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,43
\item   487 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~487 000
\item   253 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~253 000
\item   4,46 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~44,6
\item   208 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~20 800
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   260,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,260 5
}\item   4,932 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 932
}\item   50,75 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,507 5
}\item   5,981 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 981
}\item   7 630 ~ \(\times\)  0,1 ~ = ~{\color{red} 763
}\item   105,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 10,56
}\item   3 810 ~ \(\times\)  0,1 ~ = ~{\color{red} 381
}\item   26,87 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,268 7
}\item   4 053 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,053
}\item   55,42 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,055 42
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 339 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 433,9
\item   926,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 92,62
\item   1,318 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,013 18
\item   0,561 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,005 61
\item   6,274 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,627 4
\item   42,13 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,421 3
\item   8,524 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,852 4
\item   40,37 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,037
\item   0,136 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,013 6
\item   530,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,306
\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~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   203,07 ~mm~ = {\color{red}  0,020 307 }~dam
\item   2 461,8 ~hm~ = {\color{red}  246 180 }~m
\item   996,19 ~dg~ = {\color{red}  99,619 }~g
\item   4 261,7 ~dL~ = {\color{red}  42 617 }~cL
\item   669,63 ~kg~ = {\color{red}  6 696,3 }~hg
\item   8 877,5 ~dL~ = {\color{red}  887 750 }~mL
\item   7 801,5 ~kg~ = {\color{red}  7 801 500 }~g
\item   9 471 ~L~ = {\color{red}  947 100 }~cL
\item   6 082,8 ~km~ = {\color{red}  60 828 }~hm
\item   787,6 ~hL~ = {\color{red}  7 876 000 }~cL
\end{itemize}
\end{multicols}
\end{document}
