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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 366}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{60}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,709  ~ \(\times\)  ~ 100
\item   65,3  ~ \(\times\)  ~ 1 000
\item   851  ~ \(\times\)  ~ 10
\item   0,418  ~ \(\times\)  ~ 1 000
\item   81  ~ \(\times\)  ~ 10
\item   7,83  ~ \(\times\)  ~ 10
\item   153  ~ \(\times\)  ~ 1 000
\item   215  ~ \(\times\)  ~ 10
\item   84,6  ~ \(\times\)  ~ 100
\item   512  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,233  ~ : ~ 100
\item   5 870  ~ : ~ 10
\item   7 529  ~ : ~ 100
\item   537  ~ : ~ 10
\item   459,1  ~ : ~ 1 000
\item   38,83  ~ : ~ 100
\item   7,339  ~ : ~ 10
\item   34,7  ~ : ~ 10
\item   128,1  ~ : ~ 100
\item   4,72  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,804  ~ \(\times\)  ~ ... ~ = ~ 804
\item   475  ~ \(\times\)  ~ ... ~ = ~ 47 500
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 0,6
\item   0,025  ~ \(\times\)  ~ ... ~ = ~ 25
\item   68,9  ~ \(\times\)  ~ ... ~ = ~ 68 900
\item   0,161  ~ \(\times\)  ~ ... ~ = ~ 161
\item   0,756  ~ \(\times\)  ~ ... ~ = ~ 7,56
\item   567  ~ \(\times\)  ~ ... ~ = ~ 567 000
\item   274  ~ \(\times\)  ~ ... ~ = ~ 2 740
\item   0,63  ~ \(\times\)  ~ ... ~ = ~ 63
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   141,3  ~ \(\times\)  ~ 0,1
\item   2,142  ~ \(\times\)  ~ 0,001
\item   4 700  ~ \(\times\)  ~ 0,001
\item   50,8  ~ \(\times\)  ~ 0,001
\item   7 713  ~ \(\times\)  ~ 0,1
\item   23,34  ~ \(\times\)  ~ 0,01
\item   8,838  ~ \(\times\)  ~ 0,01
\item   81,12  ~ \(\times\)  ~ 0,001
\item   4,652  ~ \(\times\)  ~ 0,1
\item   3,972  ~ \(\times\)  ~ 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   87,45  ~ \(\times\)  ~ ... ~ = ~  0,087 45
\item   6,195  ~ \(\times\)  ~ ... ~ = ~  0,061 95
\item   107,6  ~ \(\times\)  ~ ... ~ = ~  1,076
\item   27,65  ~ \(\times\)  ~ ... ~ = ~  2,765
\item   7 890  ~ \(\times\)  ~ ... ~ = ~  78,9
\item   6,885  ~ \(\times\)  ~ ... ~ = ~  0,688 5
\item   76,37  ~ \(\times\)  ~ ... ~ = ~  0,076 37
\item   13,52  ~ \(\times\)  ~ ... ~ = ~  0,135 2
\item   4 532  ~ \(\times\)  ~ ... ~ = ~  45,32
\item   2,492  ~ \(\times\)  ~ ... ~ = ~  0,002 492
\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 ~km~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 998,5 ~hg~ = ...~cg
\item   852,44 ~m~ = ...~mm
\item   673,24 ~mg~ = ...~g
\item   512,27 ~hL~ = ...~daL
\item   533,32 ~mL~ = ...~hL
\item   944,75 ~mL~ = ...~kL
\item   9 698,4 ~kL~ = ...~dL
\item   1 813,9 ~kg~ = ...~dg
\item   7 177,5 ~kL~ = ...~mL
\item   6 335,9 ~hg~ = ...~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   2 = \(\dfrac{20}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{2600}{100}\) = \(\dfrac{260}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{780}{100}\)
\item   \(\dfrac{60}{100}\) = \(\dfrac{600}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,709  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 70,9}
\item   65,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 65 300}
\item   851  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 510}
\item   0,418  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 418}
\item   81  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 810}
\item   7,83  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 78,3}
\item   153  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 153 000}
\item   215  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 150}
\item   84,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 460}
\item   512  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 120}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,233 ~ : ~ 100 ~ = ~{\color{red} 0,062 33}
\item   5 870 ~ : ~ 10 ~ = ~{\color{red} 587}
\item   7 529 ~ : ~ 100 ~ = ~{\color{red} 75,29}
\item   537 ~ : ~ 10 ~ = ~{\color{red} 53,7}
\item   459,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,459 1}
\item   38,83 ~ : ~ 100 ~ = ~{\color{red} 0,388 3}
\item   7,339 ~ : ~ 10 ~ = ~{\color{red} 0,733 9}
\item   34,7 ~ : ~ 10 ~ = ~{\color{red} 3,47}
\item   128,1 ~ : ~ 100 ~ = ~{\color{red} 1,281}
\item   4,72 ~ : ~ 100 ~ = ~{\color{red} 0,047 2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,804 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~804
\item   475 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~47 500
\item   0,06 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,6
\item   0,025 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~25
\item   68,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~68 900
\item   0,161 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~161
\item   0,756 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,56
\item   567 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~567 000
\item   274 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 740
\item   0,63 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~63
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   141,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 14,13
}\item   2,142 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 142
}\item   4 700 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,7
}\item   50,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,050 8
}\item   7 713 ~ \(\times\)  0,1 ~ = ~{\color{red} 771,3
}\item   23,34 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,233 4
}\item   8,838 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,088 38
}\item   81,12 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,081 12
}\item   4,652 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,465 2
}\item   3,972 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,397 2
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,45 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,087 45
\item   6,195 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,061 95
\item   107,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,076
\item   27,65 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,765
\item   7 890 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 78,9
\item   6,885 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,688 5
\item   76,37 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,076 37
\item   13,52 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,135 2
\item   4 532 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 45,32
\item   2,492 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 492
\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 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 998,5 ~hg~ = {\color{red}  79 985 000 }~cg
\item   852,44 ~m~ = {\color{red}  852 440 }~mm
\item   673,24 ~mg~ = {\color{red}  0,673 24 }~g
\item   512,27 ~hL~ = {\color{red}  5 122,7 }~daL
\item   533,32 ~mL~ = {\color{red}  0,005 333 2 }~hL
\item   944,75 ~mL~ = {\color{red}  0,000 944 75 }~kL
\item   9 698,4 ~kL~ = {\color{red}  96 984 000 }~dL
\item   1 813,9 ~kg~ = {\color{red}  18 139 000 }~dg
\item   7 177,5 ~kL~ = {\color{red}  7 177 500 000 }~mL
\item   6 335,9 ~hg~ = {\color{red}  6 335 900 }~dg
\end{itemize}
\end{multicols}
\end{document}
