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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 399}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{89}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   10,6  ~ \(\times\)  ~ 1 000
\item   0,01  ~ \(\times\)  ~ 10
\item   5,4  ~ \(\times\)  ~ 100
\item   0,037  ~ \(\times\)  ~ 100
\item   0,058  ~ \(\times\)  ~ 10
\item   0,688  ~ \(\times\)  ~ 1 000
\item   0,037  ~ \(\times\)  ~ 10
\item   92,1  ~ \(\times\)  ~ 10
\item   0,321  ~ \(\times\)  ~ 100
\item   0,556  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   40,95  ~ : ~ 100
\item   14,37  ~ : ~ 10
\item   1 529  ~ : ~ 1 000
\item   1,17  ~ : ~ 100
\item   5,902  ~ : ~ 100
\item   4,013  ~ : ~ 1 000
\item   317,2  ~ : ~ 1 000
\item   75,53  ~ : ~ 10
\item   7,381  ~ : ~ 100
\item   5,17  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,87  ~ \(\times\)  ~ ... ~ = ~ 87
\item   397  ~ \(\times\)  ~ ... ~ = ~ 397 000
\item   26,2  ~ \(\times\)  ~ ... ~ = ~ 26 200
\item   848  ~ \(\times\)  ~ ... ~ = ~ 848 000
\item   0,098  ~ \(\times\)  ~ ... ~ = ~ 9,8
\item   0,67  ~ \(\times\)  ~ ... ~ = ~ 67
\item   0,386  ~ \(\times\)  ~ ... ~ = ~ 3,86
\item   0,051  ~ \(\times\)  ~ ... ~ = ~ 5,1
\item   33,9  ~ \(\times\)  ~ ... ~ = ~ 3 390
\item   0,709  ~ \(\times\)  ~ ... ~ = ~ 709
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,24  ~ \(\times\)  ~ 0,001
\item   3 050  ~ \(\times\)  ~ 0,01
\item   6 483  ~ \(\times\)  ~ 0,001
\item   7 889  ~ \(\times\)  ~ 0,1
\item   5,084  ~ \(\times\)  ~ 0,001
\item   45,56  ~ \(\times\)  ~ 0,001
\item   781,9  ~ \(\times\)  ~ 0,01
\item   1,279  ~ \(\times\)  ~ 0,01
\item   851,5  ~ \(\times\)  ~ 0,001
\item   9 854  ~ \(\times\)  ~ 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   50,32  ~ \(\times\)  ~ ... ~ = ~  5,032
\item   98,41  ~ \(\times\)  ~ ... ~ = ~  0,098 41
\item   89,55  ~ \(\times\)  ~ ... ~ = ~  8,955
\item   7,51  ~ \(\times\)  ~ ... ~ = ~  0,007 51
\item   87,7  ~ \(\times\)  ~ ... ~ = ~  8,77
\item   110,9  ~ \(\times\)  ~ ... ~ = ~  0,110 9
\item   1,071  ~ \(\times\)  ~ ... ~ = ~  0,001 071
\item   687,6  ~ \(\times\)  ~ ... ~ = ~  6,876
\item   7 047  ~ \(\times\)  ~ ... ~ = ~  704,7
\item   28,64  ~ \(\times\)  ~ ... ~ = ~  0,028 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 ~dm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   173,68 ~dg~ = ...~kg
\item   429,32 ~dam~ = ...~dm
\item   5 888 ~mL~ = ...~kL
\item   6 762,5 ~hm~ = ...~dm
\item   717,79 ~km~ = ...~dm
\item   556,86 ~dL~ = ...~kL
\item   7 342,9 ~cm~ = ...~km
\item   7 096 ~hm~ = ...~cm
\item   8 081,8 ~hL~ = ...~kL
\item   5 886,6 ~dag~ = ...~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   1 = \(\dfrac{10}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{8900}{100}\) = \(\dfrac{890}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{89}{10}\) = \(\dfrac{890}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{400}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   10,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 10 600}
\item   0,01  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,1}
\item   5,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 540}
\item   0,037  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,7}
\item   0,058  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,58}
\item   0,688  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 688}
\item   0,037  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,37}
\item   92,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 921}
\item   0,321  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 32,1}
\item   0,556  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,56}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   40,95 ~ : ~ 100 ~ = ~{\color{red} 0,409 5}
\item   14,37 ~ : ~ 10 ~ = ~{\color{red} 1,437}
\item   1 529 ~ : ~ 1 000 ~ = ~{\color{red} 1,529}
\item   1,17 ~ : ~ 100 ~ = ~{\color{red} 0,011 7}
\item   5,902 ~ : ~ 100 ~ = ~{\color{red} 0,059 02}
\item   4,013 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 013}
\item   317,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,317 2}
\item   75,53 ~ : ~ 10 ~ = ~{\color{red} 7,553}
\item   7,381 ~ : ~ 100 ~ = ~{\color{red} 0,073 81}
\item   5,17 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 17}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,87 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~87
\item   397 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~397 000
\item   26,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~26 200
\item   848 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~848 000
\item   0,098 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,8
\item   0,67 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~67
\item   0,386 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,86
\item   0,051 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,1
\item   33,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 390
\item   0,709 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~709
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,24 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,080 24
}\item   3 050 ~ \(\times\)  0,01 ~ = ~{\color{red} 30,5
}\item   6 483 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,483
}\item   7 889 ~ \(\times\)  0,1 ~ = ~{\color{red} 788,9
}\item   5,084 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 084
}\item   45,56 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,045 56
}\item   781,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,819
}\item   1,279 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,012 79
}\item   851,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,851 5
}\item   9 854 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,854
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   50,32 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,032
\item   98,41 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,098 41
\item   89,55 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,955
\item   7,51 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 51
\item   87,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,77
\item   110,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,110 9
\item   1,071 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 071
\item   687,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,876
\item   7 047 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 704,7
\item   28,64 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,028 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 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   173,68 ~dg~ = {\color{red}  0,017 368 }~kg
\item   429,32 ~dam~ = {\color{red}  42 932 }~dm
\item   5 888 ~mL~ = {\color{red}  0,005 888 }~kL
\item   6 762,5 ~hm~ = {\color{red}  6 762 500 }~dm
\item   717,79 ~km~ = {\color{red}  7 177 900 }~dm
\item   556,86 ~dL~ = {\color{red}  0,055 686 }~kL
\item   7 342,9 ~cm~ = {\color{red}  0,073 429 }~km
\item   7 096 ~hm~ = {\color{red}  70 960 000 }~cm
\item   8 081,8 ~hL~ = {\color{red}  808,18 }~kL
\item   5 886,6 ~dag~ = {\color{red}  58,866 }~kg
\end{itemize}
\end{multicols}
\end{document}
