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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 280}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,047  ~ \(\times\)  ~ 100
\item   577  ~ \(\times\)  ~ 100
\item   697  ~ \(\times\)  ~ 1 000
\item   68,1  ~ \(\times\)  ~ 100
\item   48,8  ~ \(\times\)  ~ 1 000
\item   0,64  ~ \(\times\)  ~ 1 000
\item   0,674  ~ \(\times\)  ~ 1 000
\item   3,65  ~ \(\times\)  ~ 100
\item   7,35  ~ \(\times\)  ~ 1 000
\item   356  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 088  ~ : ~ 100
\item   73,65  ~ : ~ 10
\item   6,899  ~ : ~ 100
\item   49,95  ~ : ~ 100
\item   9,202  ~ : ~ 100
\item   16,22  ~ : ~ 10
\item   9,5  ~ : ~ 1 000
\item   9 431  ~ : ~ 10
\item   3 498  ~ : ~ 1 000
\item   83,29  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,014  ~ \(\times\)  ~ ... ~ = ~ 0,14
\item   8,27  ~ \(\times\)  ~ ... ~ = ~ 827
\item   4,6  ~ \(\times\)  ~ ... ~ = ~ 460
\item   0,95  ~ \(\times\)  ~ ... ~ = ~ 950
\item   0,428  ~ \(\times\)  ~ ... ~ = ~ 42,8
\item   863  ~ \(\times\)  ~ ... ~ = ~ 86 300
\item   371  ~ \(\times\)  ~ ... ~ = ~ 37 100
\item   108  ~ \(\times\)  ~ ... ~ = ~ 108 000
\item   7,06  ~ \(\times\)  ~ ... ~ = ~ 706
\item   529  ~ \(\times\)  ~ ... ~ = ~ 52 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 951  ~ \(\times\)  ~ 0,1
\item   926,7  ~ \(\times\)  ~ 0,1
\item   7,791  ~ \(\times\)  ~ 0,001
\item   4 080  ~ \(\times\)  ~ 0,01
\item   1 651  ~ \(\times\)  ~ 0,01
\item   2,489  ~ \(\times\)  ~ 0,1
\item   9 193  ~ \(\times\)  ~ 0,01
\item   69,42  ~ \(\times\)  ~ 0,01
\item   9 396  ~ \(\times\)  ~ 0,1
\item   5 041  ~ \(\times\)  ~ 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   568,3  ~ \(\times\)  ~ ... ~ = ~  0,568 3
\item   90,35  ~ \(\times\)  ~ ... ~ = ~  0,903 5
\item   13,69  ~ \(\times\)  ~ ... ~ = ~  0,013 69
\item   3,047  ~ \(\times\)  ~ ... ~ = ~  0,003 047
\item   5,43  ~ \(\times\)  ~ ... ~ = ~  0,543
\item   28,96  ~ \(\times\)  ~ ... ~ = ~  0,289 6
\item   0,356  ~ \(\times\)  ~ ... ~ = ~  0,003 56
\item   95,51  ~ \(\times\)  ~ ... ~ = ~  0,095 51
\item   53,38  ~ \(\times\)  ~ ... ~ = ~  0,533 8
\item   802,7  ~ \(\times\)  ~ ... ~ = ~  80,27
\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~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   549,17 ~dm~ = ...~m
\item   8 653,3 ~cm~ = ...~km
\item   3 166,5 ~hL~ = ...~L
\item   8 597,1 ~m~ = ...~hm
\item   813,34 ~daL~ = ...~hL
\item   652,91 ~dL~ = ...~kL
\item   8 509,7 ~daL~ = ...~cL
\item   8 375,7 ~mL~ = ...~kL
\item   744,69 ~hL~ = ...~cL
\item   223,11 ~g~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{9400}{100}\) = \(\dfrac{940}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{910}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{440}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,047  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,7}
\item   577  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 57 700}
\item   697  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 697 000}
\item   68,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 810}
\item   48,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 48 800}
\item   0,64  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 640}
\item   0,674  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 674}
\item   3,65  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 365}
\item   7,35  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 350}
\item   356  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 356 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 088 ~ : ~ 100 ~ = ~{\color{red} 10,88}
\item   73,65 ~ : ~ 10 ~ = ~{\color{red} 7,365}
\item   6,899 ~ : ~ 100 ~ = ~{\color{red} 0,068 99}
\item   49,95 ~ : ~ 100 ~ = ~{\color{red} 0,499 5}
\item   9,202 ~ : ~ 100 ~ = ~{\color{red} 0,092 02}
\item   16,22 ~ : ~ 10 ~ = ~{\color{red} 1,622}
\item   9,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 5}
\item   9 431 ~ : ~ 10 ~ = ~{\color{red} 943,1}
\item   3 498 ~ : ~ 1 000 ~ = ~{\color{red} 3,498}
\item   83,29 ~ : ~ 1 000 ~ = ~{\color{red} 0,083 29}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,014 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,14
\item   8,27 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~827
\item   4,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~460
\item   0,95 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~950
\item   0,428 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~42,8
\item   863 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~86 300
\item   371 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~37 100
\item   108 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~108 000
\item   7,06 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~706
\item   529 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~52 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 951 ~ \(\times\)  0,1 ~ = ~{\color{red} 495,1
}\item   926,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 92,67
}\item   7,791 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 791
}\item   4 080 ~ \(\times\)  0,01 ~ = ~{\color{red} 40,8
}\item   1 651 ~ \(\times\)  0,01 ~ = ~{\color{red} 16,51
}\item   2,489 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,248 9
}\item   9 193 ~ \(\times\)  0,01 ~ = ~{\color{red} 91,93
}\item   69,42 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,694 2
}\item   9 396 ~ \(\times\)  0,1 ~ = ~{\color{red} 939,6
}\item   5 041 ~ \(\times\)  0,1 ~ = ~{\color{red} 504,1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   568,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,568 3
\item   90,35 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,903 5
\item   13,69 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,013 69
\item   3,047 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 047
\item   5,43 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,543
\item   28,96 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,289 6
\item   0,356 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,003 56
\item   95,51 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,095 51
\item   53,38 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,533 8
\item   802,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 80,27
\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 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   549,17 ~dm~ = {\color{red}  54,917 }~m
\item   8 653,3 ~cm~ = {\color{red}  0,086 533 }~km
\item   3 166,5 ~hL~ = {\color{red}  316 650 }~L
\item   8 597,1 ~m~ = {\color{red}  85,971 }~hm
\item   813,34 ~daL~ = {\color{red}  81,334 }~hL
\item   652,91 ~dL~ = {\color{red}  0,065 291 }~kL
\item   8 509,7 ~daL~ = {\color{red}  8 509 700 }~cL
\item   8 375,7 ~mL~ = {\color{red}  0,008 375 7 }~kL
\item   744,69 ~hL~ = {\color{red}  7 446 900 }~cL
\item   223,11 ~g~ = {\color{red}  2 231,1 }~dg
\end{itemize}
\end{multicols}
\end{document}
