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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 264}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{52}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   920  ~ \(\times\)  ~ 100
\item   644  ~ \(\times\)  ~ 1 000
\item   7,53  ~ \(\times\)  ~ 1 000
\item   0,865  ~ \(\times\)  ~ 10
\item   0,945  ~ \(\times\)  ~ 10
\item   57,6  ~ \(\times\)  ~ 10
\item   0,94  ~ \(\times\)  ~ 10
\item   4,57  ~ \(\times\)  ~ 10
\item   291  ~ \(\times\)  ~ 10
\item   0,021  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   676,1  ~ : ~ 100
\item   35,12  ~ : ~ 1 000
\item   4 418  ~ : ~ 100
\item   1,038  ~ : ~ 10
\item   2,066  ~ : ~ 10
\item   220,4  ~ : ~ 10
\item   8,11  ~ : ~ 1 000
\item   1 267  ~ : ~ 1 000
\item   50,22  ~ : ~ 1 000
\item   412,5  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   131  ~ \(\times\)  ~ ... ~ = ~ 13 100
\item   0,081  ~ \(\times\)  ~ ... ~ = ~ 0,81
\item   260  ~ \(\times\)  ~ ... ~ = ~ 26 000
\item   80,6  ~ \(\times\)  ~ ... ~ = ~ 80 600
\item   0,026  ~ \(\times\)  ~ ... ~ = ~ 0,26
\item   970  ~ \(\times\)  ~ ... ~ = ~ 9 700
\item   8,77  ~ \(\times\)  ~ ... ~ = ~ 877
\item   380  ~ \(\times\)  ~ ... ~ = ~ 380 000
\item   30,6  ~ \(\times\)  ~ ... ~ = ~ 3 060
\item   309  ~ \(\times\)  ~ ... ~ = ~ 30 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,425  ~ \(\times\)  ~ 0,01
\item   1 764  ~ \(\times\)  ~ 0,1
\item   82,21  ~ \(\times\)  ~ 0,01
\item   6,791  ~ \(\times\)  ~ 0,1
\item   52,86  ~ \(\times\)  ~ 0,001
\item   21,99  ~ \(\times\)  ~ 0,1
\item   34,18  ~ \(\times\)  ~ 0,01
\item   7,91  ~ \(\times\)  ~ 0,01
\item   90,23  ~ \(\times\)  ~ 0,01
\item   2,473  ~ \(\times\)  ~ 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   8 195  ~ \(\times\)  ~ ... ~ = ~  819,5
\item   2 142  ~ \(\times\)  ~ ... ~ = ~  21,42
\item   2 694  ~ \(\times\)  ~ ... ~ = ~  269,4
\item   328,1  ~ \(\times\)  ~ ... ~ = ~  3,281
\item   8,32  ~ \(\times\)  ~ ... ~ = ~  0,832
\item   58  ~ \(\times\)  ~ ... ~ = ~  0,58
\item   0,127  ~ \(\times\)  ~ ... ~ = ~  0,012 7
\item   51,57  ~ \(\times\)  ~ ... ~ = ~  0,051 57
\item   7 154  ~ \(\times\)  ~ ... ~ = ~  71,54
\item   68,82  ~ \(\times\)  ~ ... ~ = ~  0,688 2
\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 ~cm~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 922,2 ~mg~ = ...~g
\item   217,48 ~daL~ = ...~cL
\item   9 035,5 ~g~ = ...~mg
\item   3 044,9 ~g~ = ...~kg
\item   9 853,2 ~cL~ = ...~dL
\item   320,84 ~dg~ = ...~hg
\item   5 962,5 ~g~ = ...~cg
\item   2 291,5 ~mm~ = ...~dam
\item   6 501,4 ~kL~ = ...~dL
\item   279,6 ~hm~ = ...~km
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{7700}{100}\) = \(\dfrac{770}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{52}{10}\) = \(\dfrac{520}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{390}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   920  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 92 000}
\item   644  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 644 000}
\item   7,53  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 530}
\item   0,865  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,65}
\item   0,945  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,45}
\item   57,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 576}
\item   0,94  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,4}
\item   4,57  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 45,7}
\item   291  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 910}
\item   0,021  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   676,1 ~ : ~ 100 ~ = ~{\color{red} 6,761}
\item   35,12 ~ : ~ 1 000 ~ = ~{\color{red} 0,035 12}
\item   4 418 ~ : ~ 100 ~ = ~{\color{red} 44,18}
\item   1,038 ~ : ~ 10 ~ = ~{\color{red} 0,103 8}
\item   2,066 ~ : ~ 10 ~ = ~{\color{red} 0,206 6}
\item   220,4 ~ : ~ 10 ~ = ~{\color{red} 22,04}
\item   8,11 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 11}
\item   1 267 ~ : ~ 1 000 ~ = ~{\color{red} 1,267}
\item   50,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,050 22}
\item   412,5 ~ : ~ 10 ~ = ~{\color{red} 41,25}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   131 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~13 100
\item   0,081 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,81
\item   260 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~26 000
\item   80,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~80 600
\item   0,026 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,26
\item   970 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 700
\item   8,77 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~877
\item   380 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~380 000
\item   30,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 060
\item   309 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,425 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,074 25
}\item   1 764 ~ \(\times\)  0,1 ~ = ~{\color{red} 176,4
}\item   82,21 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,822 1
}\item   6,791 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,679 1
}\item   52,86 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,052 86
}\item   21,99 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,199
}\item   34,18 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,341 8
}\item   7,91 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,079 1
}\item   90,23 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,902 3
}\item   2,473 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 473
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 195 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 819,5
\item   2 142 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 21,42
\item   2 694 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 269,4
\item   328,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,281
\item   8,32 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,832
\item   58 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,58
\item   0,127 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,012 7
\item   51,57 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,051 57
\item   7 154 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 71,54
\item   68,82 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,688 2
\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 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 922,2 ~mg~ = {\color{red}  6,922 2 }~g
\item   217,48 ~daL~ = {\color{red}  217 480 }~cL
\item   9 035,5 ~g~ = {\color{red}  9 035 500 }~mg
\item   3 044,9 ~g~ = {\color{red}  3,044 9 }~kg
\item   9 853,2 ~cL~ = {\color{red}  985,32 }~dL
\item   320,84 ~dg~ = {\color{red}  0,320 84 }~hg
\item   5 962,5 ~g~ = {\color{red}  596 250 }~cg
\item   2 291,5 ~mm~ = {\color{red}  0,229 15 }~dam
\item   6 501,4 ~kL~ = {\color{red}  65 014 000 }~dL
\item   279,6 ~hm~ = {\color{red}  27,96 }~km
\end{itemize}
\end{multicols}
\end{document}
