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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 222}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{15}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{14}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   50,2  ~ \(\times\)  ~ 100
\item   0,766  ~ \(\times\)  ~ 100
\item   85  ~ \(\times\)  ~ 10
\item   0,967  ~ \(\times\)  ~ 10
\item   0,985  ~ \(\times\)  ~ 1 000
\item   53,6  ~ \(\times\)  ~ 100
\item   72,5  ~ \(\times\)  ~ 1 000
\item   0,353  ~ \(\times\)  ~ 100
\item   21  ~ \(\times\)  ~ 10
\item   8,41  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   49,3  ~ : ~ 1 000
\item   6 453  ~ : ~ 100
\item   537,3  ~ : ~ 10
\item   297,9  ~ : ~ 100
\item   338,6  ~ : ~ 1 000
\item   873,4  ~ : ~ 100
\item   9 106  ~ : ~ 10
\item   33,52  ~ : ~ 100
\item   4 511  ~ : ~ 100
\item   60,7  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,775  ~ \(\times\)  ~ ... ~ = ~ 77,5
\item   0,899  ~ \(\times\)  ~ ... ~ = ~ 89,9
\item   512  ~ \(\times\)  ~ ... ~ = ~ 51 200
\item   8,22  ~ \(\times\)  ~ ... ~ = ~ 822
\item   0,852  ~ \(\times\)  ~ ... ~ = ~ 852
\item   0,185  ~ \(\times\)  ~ ... ~ = ~ 18,5
\item   0,086  ~ \(\times\)  ~ ... ~ = ~ 86
\item   3,66  ~ \(\times\)  ~ ... ~ = ~ 36,6
\item   153  ~ \(\times\)  ~ ... ~ = ~ 153 000
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 0,67
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   746,7  ~ \(\times\)  ~ 0,1
\item   403,2  ~ \(\times\)  ~ 0,1
\item   6,467  ~ \(\times\)  ~ 0,1
\item   1 479  ~ \(\times\)  ~ 0,1
\item   19,25  ~ \(\times\)  ~ 0,1
\item   2 951  ~ \(\times\)  ~ 0,01
\item   8,269  ~ \(\times\)  ~ 0,01
\item   896,8  ~ \(\times\)  ~ 0,001
\item   831,5  ~ \(\times\)  ~ 0,01
\item   3,534  ~ \(\times\)  ~ 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   5,365  ~ \(\times\)  ~ ... ~ = ~  0,053 65
\item   5,722  ~ \(\times\)  ~ ... ~ = ~  0,057 22
\item   9 206  ~ \(\times\)  ~ ... ~ = ~  9,206
\item   8,777  ~ \(\times\)  ~ ... ~ = ~  0,087 77
\item   68,6  ~ \(\times\)  ~ ... ~ = ~  0,068 6
\item   8 914  ~ \(\times\)  ~ ... ~ = ~  8,914
\item   1,63  ~ \(\times\)  ~ ... ~ = ~  0,001 63
\item   9 872  ~ \(\times\)  ~ ... ~ = ~  9,872
\item   2 935  ~ \(\times\)  ~ ... ~ = ~  2,935
\item   4 098  ~ \(\times\)  ~ ... ~ = ~  4,098
\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 ~m~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 674 ~kg~ = ...~hg
\item   823,48 ~kL~ = ...~dL
\item   2 688,9 ~hg~ = ...~dg
\item   741,8 ~L~ = ...~cL
\item   200,68 ~kg~ = ...~dag
\item   6 952,4 ~dg~ = ...~g
\item   4 406,7 ~dL~ = ...~hL
\item   6 421,2 ~hg~ = ...~cg
\item   2 796,5 ~kL~ = ...~daL
\item   4 163,3 ~dg~ = ...~dag
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{470}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{15}{10}\) = \(\dfrac{150}{100}\)
\item   \(\dfrac{14}{100}\) = \(\dfrac{140}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   50,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 020}
\item   0,766  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 76,6}
\item   85  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 850}
\item   0,967  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,67}
\item   0,985  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 985}
\item   53,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 360}
\item   72,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 72 500}
\item   0,353  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 35,3}
\item   21  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 210}
\item   8,41  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 841}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   49,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,049 3}
\item   6 453 ~ : ~ 100 ~ = ~{\color{red} 64,53}
\item   537,3 ~ : ~ 10 ~ = ~{\color{red} 53,73}
\item   297,9 ~ : ~ 100 ~ = ~{\color{red} 2,979}
\item   338,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,338 6}
\item   873,4 ~ : ~ 100 ~ = ~{\color{red} 8,734}
\item   9 106 ~ : ~ 10 ~ = ~{\color{red} 910,6}
\item   33,52 ~ : ~ 100 ~ = ~{\color{red} 0,335 2}
\item   4 511 ~ : ~ 100 ~ = ~{\color{red} 45,11}
\item   60,7 ~ : ~ 100 ~ = ~{\color{red} 0,607}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,775 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~77,5
\item   0,899 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~89,9
\item   512 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~51 200
\item   8,22 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~822
\item   0,852 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~852
\item   0,185 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~18,5
\item   0,086 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~86
\item   3,66 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~36,6
\item   153 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~153 000
\item   0,067 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,67
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   746,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 74,67
}\item   403,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 40,32
}\item   6,467 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,646 7
}\item   1 479 ~ \(\times\)  0,1 ~ = ~{\color{red} 147,9
}\item   19,25 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,925
}\item   2 951 ~ \(\times\)  0,01 ~ = ~{\color{red} 29,51
}\item   8,269 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,082 69
}\item   896,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,896 8
}\item   831,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,315
}\item   3,534 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,353 4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,365 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,053 65
\item   5,722 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,057 22
\item   9 206 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,206
\item   8,777 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,087 77
\item   68,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,068 6
\item   8 914 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,914
\item   1,63 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 63
\item   9 872 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,872
\item   2 935 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,935
\item   4 098 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,098
\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 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 674 ~kg~ = {\color{red}  66 740 }~hg
\item   823,48 ~kL~ = {\color{red}  8 234 800 }~dL
\item   2 688,9 ~hg~ = {\color{red}  2 688 900 }~dg
\item   741,8 ~L~ = {\color{red}  74 180 }~cL
\item   200,68 ~kg~ = {\color{red}  20 068 }~dag
\item   6 952,4 ~dg~ = {\color{red}  695,24 }~g
\item   4 406,7 ~dL~ = {\color{red}  4,406 7 }~hL
\item   6 421,2 ~hg~ = {\color{red}  64 212 000 }~cg
\item   2 796,5 ~kL~ = {\color{red}  279 650 }~daL
\item   4 163,3 ~dg~ = {\color{red}  41,633 }~dag
\end{itemize}
\end{multicols}
\end{document}
