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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 275}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{51}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9  ~ \(\times\)  ~ 1 000
\item   89,4  ~ \(\times\)  ~ 1 000
\item   3,71  ~ \(\times\)  ~ 100
\item   0,046  ~ \(\times\)  ~ 1 000
\item   0,933  ~ \(\times\)  ~ 100
\item   72,5  ~ \(\times\)  ~ 10
\item   0,064  ~ \(\times\)  ~ 10
\item   5,45  ~ \(\times\)  ~ 10
\item   33  ~ \(\times\)  ~ 1 000
\item   9,32  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,823  ~ : ~ 1 000
\item   751,9  ~ : ~ 100
\item   8 263  ~ : ~ 10
\item   3,351  ~ : ~ 1 000
\item   6 978  ~ : ~ 100
\item   207,7  ~ : ~ 1 000
\item   5,502  ~ : ~ 100
\item   3 171  ~ : ~ 10
\item   3 723  ~ : ~ 10
\item   4 454  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,426  ~ \(\times\)  ~ ... ~ = ~ 42,6
\item   6,97  ~ \(\times\)  ~ ... ~ = ~ 69,7
\item   0,003  ~ \(\times\)  ~ ... ~ = ~ 0,3
\item   0,121  ~ \(\times\)  ~ ... ~ = ~ 1,21
\item   975  ~ \(\times\)  ~ ... ~ = ~ 97 500
\item   9,53  ~ \(\times\)  ~ ... ~ = ~ 9 530
\item   636  ~ \(\times\)  ~ ... ~ = ~ 63 600
\item   4,25  ~ \(\times\)  ~ ... ~ = ~ 425
\item   349  ~ \(\times\)  ~ ... ~ = ~ 3 490
\item   59,6  ~ \(\times\)  ~ ... ~ = ~ 596
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 560  ~ \(\times\)  ~ 0,001
\item   8,571  ~ \(\times\)  ~ 0,01
\item   93,75  ~ \(\times\)  ~ 0,001
\item   25,95  ~ \(\times\)  ~ 0,001
\item   828,5  ~ \(\times\)  ~ 0,001
\item   9 102  ~ \(\times\)  ~ 0,1
\item   2 779  ~ \(\times\)  ~ 0,1
\item   36,55  ~ \(\times\)  ~ 0,001
\item   6 074  ~ \(\times\)  ~ 0,01
\item   5 228  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 558  ~ \(\times\)  ~ ... ~ = ~  755,8
\item   918,6  ~ \(\times\)  ~ ... ~ = ~  0,918 6
\item   3 915  ~ \(\times\)  ~ ... ~ = ~  391,5
\item   1 648  ~ \(\times\)  ~ ... ~ = ~  164,8
\item   282,7  ~ \(\times\)  ~ ... ~ = ~  2,827
\item   8,6  ~ \(\times\)  ~ ... ~ = ~  0,008 6
\item   87,1  ~ \(\times\)  ~ ... ~ = ~  8,71
\item   165  ~ \(\times\)  ~ ... ~ = ~  1,65
\item   806,9  ~ \(\times\)  ~ ... ~ = ~  80,69
\item   899,1  ~ \(\times\)  ~ ... ~ = ~  8,991
\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 ~m~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   641,24 ~km~ = ...~hm
\item   3 956,8 ~cm~ = ...~m
\item   3 324,6 ~dam~ = ...~km
\item   887,71 ~g~ = ...~hg
\item   5 995,1 ~mg~ = ...~g
\item   473,16 ~mL~ = ...~kL
\item   205,19 ~kL~ = ...~cL
\item   391,64 ~dg~ = ...~mg
\item   132,26 ~cg~ = ...~dag
\item   120,81 ~daL~ = ...~kL
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{8200}{100}\) = \(\dfrac{820}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{51}{10}\) = \(\dfrac{510}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{330}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 000}
\item   89,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 89 400}
\item   3,71  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 371}
\item   0,046  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 46}
\item   0,933  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 93,3}
\item   72,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 725}
\item   0,064  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,64}
\item   5,45  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 54,5}
\item   33  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 33 000}
\item   9,32  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 932}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,823 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 823}
\item   751,9 ~ : ~ 100 ~ = ~{\color{red} 7,519}
\item   8 263 ~ : ~ 10 ~ = ~{\color{red} 826,3}
\item   3,351 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 351}
\item   6 978 ~ : ~ 100 ~ = ~{\color{red} 69,78}
\item   207,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,207 7}
\item   5,502 ~ : ~ 100 ~ = ~{\color{red} 0,055 02}
\item   3 171 ~ : ~ 10 ~ = ~{\color{red} 317,1}
\item   3 723 ~ : ~ 10 ~ = ~{\color{red} 372,3}
\item   4 454 ~ : ~ 1 000 ~ = ~{\color{red} 4,454}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,426 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~42,6
\item   6,97 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~69,7
\item   0,003 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,3
\item   0,121 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,21
\item   975 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~97 500
\item   9,53 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 530
\item   636 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~63 600
\item   4,25 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~425
\item   349 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 490
\item   59,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~596
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 560 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,56
}\item   8,571 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,085 71
}\item   93,75 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,093 75
}\item   25,95 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,025 95
}\item   828,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,828 5
}\item   9 102 ~ \(\times\)  0,1 ~ = ~{\color{red} 910,2
}\item   2 779 ~ \(\times\)  0,1 ~ = ~{\color{red} 277,9
}\item   36,55 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,036 55
}\item   6 074 ~ \(\times\)  0,01 ~ = ~{\color{red} 60,74
}\item   5 228 ~ \(\times\)  0,01 ~ = ~{\color{red} 52,28
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 558 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 755,8
\item   918,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,918 6
\item   3 915 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 391,5
\item   1 648 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 164,8
\item   282,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,827
\item   8,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 6
\item   87,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,71
\item   165 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,65
\item   806,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 80,69
\item   899,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,991
\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 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\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   641,24 ~km~ = {\color{red}  6 412,4 }~hm
\item   3 956,8 ~cm~ = {\color{red}  39,568 }~m
\item   3 324,6 ~dam~ = {\color{red}  33,246 }~km
\item   887,71 ~g~ = {\color{red}  8,877 1 }~hg
\item   5 995,1 ~mg~ = {\color{red}  5,995 1 }~g
\item   473,16 ~mL~ = {\color{red}  0,000 473 16 }~kL
\item   205,19 ~kL~ = {\color{red}  20 519 000 }~cL
\item   391,64 ~dg~ = {\color{red}  39 164 }~mg
\item   132,26 ~cg~ = {\color{red}  0,132 26 }~dag
\item   120,81 ~daL~ = {\color{red}  1,208 1 }~kL
\end{itemize}
\end{multicols}
\end{document}
