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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 326}

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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   \(\dfrac{5000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{70}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{62}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   86  ~ \(\times\)  ~ 1 000
\item   2,77  ~ \(\times\)  ~ 1 000
\item   59,5  ~ \(\times\)  ~ 10
\item   390  ~ \(\times\)  ~ 100
\item   777  ~ \(\times\)  ~ 1 000
\item   805  ~ \(\times\)  ~ 100
\item   1,39  ~ \(\times\)  ~ 1 000
\item   0,055  ~ \(\times\)  ~ 10
\item   0,415  ~ \(\times\)  ~ 100
\item   705  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   629  ~ : ~ 100
\item   341,4  ~ : ~ 1 000
\item   833,2  ~ : ~ 1 000
\item   731,7  ~ : ~ 1 000
\item   53,14  ~ : ~ 100
\item   8,174  ~ : ~ 100
\item   2,864  ~ : ~ 100
\item   5 671  ~ : ~ 1 000
\item   829,5  ~ : ~ 1 000
\item   3,039  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,4  ~ \(\times\)  ~ ... ~ = ~ 840
\item   65  ~ \(\times\)  ~ ... ~ = ~ 65 000
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 0,96
\item   0,021  ~ \(\times\)  ~ ... ~ = ~ 2,1
\item   0,914  ~ \(\times\)  ~ ... ~ = ~ 91,4
\item   8,27  ~ \(\times\)  ~ ... ~ = ~ 82,7
\item   0,014  ~ \(\times\)  ~ ... ~ = ~ 14
\item   2,8  ~ \(\times\)  ~ ... ~ = ~ 2 800
\item   565  ~ \(\times\)  ~ ... ~ = ~ 5 650
\item   5,74  ~ \(\times\)  ~ ... ~ = ~ 57,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   95,4  ~ \(\times\)  ~ 0,001
\item   81,6  ~ \(\times\)  ~ 0,1
\item   2 848  ~ \(\times\)  ~ 0,001
\item   3,01  ~ \(\times\)  ~ 0,01
\item   8 869  ~ \(\times\)  ~ 0,1
\item   9,424  ~ \(\times\)  ~ 0,1
\item   53,67  ~ \(\times\)  ~ 0,01
\item   7 947  ~ \(\times\)  ~ 0,01
\item   888,3  ~ \(\times\)  ~ 0,001
\item   282,8  ~ \(\times\)  ~ 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   4 870  ~ \(\times\)  ~ ... ~ = ~  48,7
\item   6 318  ~ \(\times\)  ~ ... ~ = ~  631,8
\item   706,5  ~ \(\times\)  ~ ... ~ = ~  7,065
\item   52,35  ~ \(\times\)  ~ ... ~ = ~  0,523 5
\item   9,287  ~ \(\times\)  ~ ... ~ = ~  0,009 287
\item   9 668  ~ \(\times\)  ~ ... ~ = ~  966,8
\item   6 804  ~ \(\times\)  ~ ... ~ = ~  68,04
\item   8 398  ~ \(\times\)  ~ ... ~ = ~  8,398
\item   6,459  ~ \(\times\)  ~ ... ~ = ~  0,006 459
\item   8,82  ~ \(\times\)  ~ ... ~ = ~  0,008 82
\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 ~dam~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   797,43 ~dL~ = ...~kL
\item   720,15 ~dL~ = ...~cL
\item   2 674,1 ~kg~ = ...~hg
\item   373,48 ~dam~ = ...~mm
\item   582,09 ~cm~ = ...~dm
\item   8 510,4 ~m~ = ...~dam
\item   2 365,1 ~cm~ = ...~dam
\item   306,13 ~kg~ = ...~g
\item   672,2 ~mm~ = ...~km
\item   7 049,8 ~g~ = ...~mg
\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   \(\dfrac{5000}{100}\) = \(\dfrac{500}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{70}{10}\) = \(\dfrac{700}{100}\)
\item   \(\dfrac{62}{100}\) = \(\dfrac{620}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   86  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 86 000}
\item   2,77  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 770}
\item   59,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 595}
\item   390  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 39 000}
\item   777  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 777 000}
\item   805  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80 500}
\item   1,39  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 390}
\item   0,055  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,55}
\item   0,415  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 41,5}
\item   705  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 705 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   629 ~ : ~ 100 ~ = ~{\color{red} 6,29}
\item   341,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,341 4}
\item   833,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,833 2}
\item   731,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,731 7}
\item   53,14 ~ : ~ 100 ~ = ~{\color{red} 0,531 4}
\item   8,174 ~ : ~ 100 ~ = ~{\color{red} 0,081 74}
\item   2,864 ~ : ~ 100 ~ = ~{\color{red} 0,028 64}
\item   5 671 ~ : ~ 1 000 ~ = ~{\color{red} 5,671}
\item   829,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,829 5}
\item   3,039 ~ : ~ 10 ~ = ~{\color{red} 0,303 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~840
\item   65 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~65 000
\item   0,096 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,96
\item   0,021 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,1
\item   0,914 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~91,4
\item   8,27 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~82,7
\item   0,014 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14
\item   2,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 800
\item   565 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 650
\item   5,74 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~57,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   95,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,095 4
}\item   81,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,16
}\item   2 848 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,848
}\item   3,01 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,030 1
}\item   8 869 ~ \(\times\)  0,1 ~ = ~{\color{red} 886,9
}\item   9,424 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,942 4
}\item   53,67 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,536 7
}\item   7 947 ~ \(\times\)  0,01 ~ = ~{\color{red} 79,47
}\item   888,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,888 3
}\item   282,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 28,28
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 870 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 48,7
\item   6 318 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 631,8
\item   706,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,065
\item   52,35 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,523 5
\item   9,287 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 287
\item   9 668 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 966,8
\item   6 804 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 68,04
\item   8 398 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,398
\item   6,459 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 459
\item   8,82 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 82
\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 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   797,43 ~dL~ = {\color{red}  0,079 743 }~kL
\item   720,15 ~dL~ = {\color{red}  7 201,5 }~cL
\item   2 674,1 ~kg~ = {\color{red}  26 741 }~hg
\item   373,48 ~dam~ = {\color{red}  3 734 800 }~mm
\item   582,09 ~cm~ = {\color{red}  58,209 }~dm
\item   8 510,4 ~m~ = {\color{red}  851,04 }~dam
\item   2 365,1 ~cm~ = {\color{red}  2,365 1 }~dam
\item   306,13 ~kg~ = {\color{red}  306 130 }~g
\item   672,2 ~mm~ = {\color{red}  0,000 672 2 }~km
\item   7 049,8 ~g~ = {\color{red}  7 049 800 }~mg
\end{itemize}
\end{multicols}
\end{document}
