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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 312}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\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   \(\dfrac{40}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,206  ~ \(\times\)  ~ 1 000
\item   0,887  ~ \(\times\)  ~ 10
\item   3,13  ~ \(\times\)  ~ 10
\item   0,14  ~ \(\times\)  ~ 100
\item   88,5  ~ \(\times\)  ~ 1 000
\item   1,63  ~ \(\times\)  ~ 10
\item   8,27  ~ \(\times\)  ~ 100
\item   33,4  ~ \(\times\)  ~ 10
\item   0,194  ~ \(\times\)  ~ 10
\item   252  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   765,1  ~ : ~ 1 000
\item   516,4  ~ : ~ 100
\item   542,6  ~ : ~ 1 000
\item   3 263  ~ : ~ 10
\item   135,4  ~ : ~ 10
\item   758,1  ~ : ~ 10
\item   408,8  ~ : ~ 1 000
\item   8 039  ~ : ~ 10
\item   85,62  ~ : ~ 1 000
\item   18,84  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,864  ~ \(\times\)  ~ ... ~ = ~ 864
\item   0,1  ~ \(\times\)  ~ ... ~ = ~ 100
\item   920  ~ \(\times\)  ~ ... ~ = ~ 9 200
\item   884  ~ \(\times\)  ~ ... ~ = ~ 88 400
\item   0,5  ~ \(\times\)  ~ ... ~ = ~ 500
\item   25,1  ~ \(\times\)  ~ ... ~ = ~ 2 510
\item   30,4  ~ \(\times\)  ~ ... ~ = ~ 30 400
\item   251  ~ \(\times\)  ~ ... ~ = ~ 2 510
\item   33,3  ~ \(\times\)  ~ ... ~ = ~ 333
\item   0,021  ~ \(\times\)  ~ ... ~ = ~ 0,21
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,945  ~ \(\times\)  ~ 0,01
\item   2,328  ~ \(\times\)  ~ 0,001
\item   7 315  ~ \(\times\)  ~ 0,1
\item   94,62  ~ \(\times\)  ~ 0,001
\item   454,3  ~ \(\times\)  ~ 0,01
\item   4,671  ~ \(\times\)  ~ 0,001
\item   8,776  ~ \(\times\)  ~ 0,1
\item   7,45  ~ \(\times\)  ~ 0,1
\item   587,9  ~ \(\times\)  ~ 0,1
\item   22,41  ~ \(\times\)  ~ 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   97,59  ~ \(\times\)  ~ ... ~ = ~  0,975 9
\item   7,933  ~ \(\times\)  ~ ... ~ = ~  0,079 33
\item   5 783  ~ \(\times\)  ~ ... ~ = ~  578,3
\item   25,09  ~ \(\times\)  ~ ... ~ = ~  0,025 09
\item   591,6  ~ \(\times\)  ~ ... ~ = ~  0,591 6
\item   8 008  ~ \(\times\)  ~ ... ~ = ~  80,08
\item   65,07  ~ \(\times\)  ~ ... ~ = ~  0,650 7
\item   6 757  ~ \(\times\)  ~ ... ~ = ~  6,757
\item   9 411  ~ \(\times\)  ~ ... ~ = ~  9,411
\item   3,28  ~ \(\times\)  ~ ... ~ = ~  0,328
\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 ~hm~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   295,22 ~mg~ = ...~dag
\item   2 472,1 ~daL~ = ...~mL
\item   7 981,4 ~g~ = ...~dg
\item   3 447,2 ~dag~ = ...~dg
\item   142,05 ~kL~ = ...~mL
\item   1 416,8 ~dL~ = ...~mL
\item   483,15 ~dm~ = ...~km
\item   217,33 ~mL~ = ...~L
\item   3 953,8 ~kg~ = ...~g
\item   806,79 ~cg~ = ...~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   3 = \(\dfrac{30}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{1500}{100}\) = \(\dfrac{150}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{52}{10}\) = \(\dfrac{520}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{400}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,206  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 206}
\item   0,887  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,87}
\item   3,13  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 31,3}
\item   0,14  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14}
\item   88,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 88 500}
\item   1,63  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 16,3}
\item   8,27  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 827}
\item   33,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 334}
\item   0,194  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,94}
\item   252  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 520}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   765,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,765 1}
\item   516,4 ~ : ~ 100 ~ = ~{\color{red} 5,164}
\item   542,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,542 6}
\item   3 263 ~ : ~ 10 ~ = ~{\color{red} 326,3}
\item   135,4 ~ : ~ 10 ~ = ~{\color{red} 13,54}
\item   758,1 ~ : ~ 10 ~ = ~{\color{red} 75,81}
\item   408,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,408 8}
\item   8 039 ~ : ~ 10 ~ = ~{\color{red} 803,9}
\item   85,62 ~ : ~ 1 000 ~ = ~{\color{red} 0,085 62}
\item   18,84 ~ : ~ 100 ~ = ~{\color{red} 0,188 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,864 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~864
\item   0,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~100
\item   920 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 200
\item   884 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88 400
\item   0,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~500
\item   25,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 510
\item   30,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~30 400
\item   251 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 510
\item   33,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~333
\item   0,021 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,21
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,945 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,019 45
}\item   2,328 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 328
}\item   7 315 ~ \(\times\)  0,1 ~ = ~{\color{red} 731,5
}\item   94,62 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,094 62
}\item   454,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,543
}\item   4,671 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 671
}\item   8,776 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,877 6
}\item   7,45 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,745
}\item   587,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 58,79
}\item   22,41 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,022 41
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   97,59 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,975 9
\item   7,933 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,079 33
\item   5 783 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 578,3
\item   25,09 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,025 09
\item   591,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,591 6
\item   8 008 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 80,08
\item   65,07 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,650 7
\item   6 757 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,757
\item   9 411 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,411
\item   3,28 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,328
\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 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   295,22 ~mg~ = {\color{red}  0,029 522 }~dag
\item   2 472,1 ~daL~ = {\color{red}  24 721 000 }~mL
\item   7 981,4 ~g~ = {\color{red}  79 814 }~dg
\item   3 447,2 ~dag~ = {\color{red}  344 720 }~dg
\item   142,05 ~kL~ = {\color{red}  142 050 000 }~mL
\item   1 416,8 ~dL~ = {\color{red}  141 680 }~mL
\item   483,15 ~dm~ = {\color{red}  0,048 315 }~km
\item   217,33 ~mL~ = {\color{red}  0,217 33 }~L
\item   3 953,8 ~kg~ = {\color{red}  3 953 800 }~g
\item   806,79 ~cg~ = {\color{red}  8 067,9 }~mg
\end{itemize}
\end{multicols}
\end{document}
