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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 339}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{75}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   773  ~ \(\times\)  ~ 1 000
\item   0,39  ~ \(\times\)  ~ 10
\item   0,534  ~ \(\times\)  ~ 10
\item   0,094  ~ \(\times\)  ~ 100
\item   3,3  ~ \(\times\)  ~ 10
\item   0,09  ~ \(\times\)  ~ 100
\item   284  ~ \(\times\)  ~ 100
\item   8,14  ~ \(\times\)  ~ 1 000
\item   0,055  ~ \(\times\)  ~ 10
\item   0,187  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,59  ~ : ~ 1 000
\item   3,906  ~ : ~ 1 000
\item   29,53  ~ : ~ 100
\item   3 102  ~ : ~ 1 000
\item   335,5  ~ : ~ 100
\item   97,49  ~ : ~ 100
\item   565,8  ~ : ~ 10
\item   400,6  ~ : ~ 10
\item   6,077  ~ : ~ 10
\item   8,215  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 2
\item   15,5  ~ \(\times\)  ~ ... ~ = ~ 155
\item   3,94  ~ \(\times\)  ~ ... ~ = ~ 3 940
\item   0,087  ~ \(\times\)  ~ ... ~ = ~ 87
\item   0,101  ~ \(\times\)  ~ ... ~ = ~ 1,01
\item   6,71  ~ \(\times\)  ~ ... ~ = ~ 6 710
\item   0,324  ~ \(\times\)  ~ ... ~ = ~ 3,24
\item   0,073  ~ \(\times\)  ~ ... ~ = ~ 0,73
\item   0,359  ~ \(\times\)  ~ ... ~ = ~ 35,9
\item   0,143  ~ \(\times\)  ~ ... ~ = ~ 14,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   847,8  ~ \(\times\)  ~ 0,1
\item   15,91  ~ \(\times\)  ~ 0,001
\item   9,087  ~ \(\times\)  ~ 0,01
\item   9 301  ~ \(\times\)  ~ 0,01
\item   5 900  ~ \(\times\)  ~ 0,1
\item   897,6  ~ \(\times\)  ~ 0,001
\item   2,944  ~ \(\times\)  ~ 0,001
\item   17,36  ~ \(\times\)  ~ 0,1
\item   2 194  ~ \(\times\)  ~ 0,1
\item   9,661  ~ \(\times\)  ~ 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   458,7  ~ \(\times\)  ~ ... ~ = ~  45,87
\item   33,64  ~ \(\times\)  ~ ... ~ = ~  0,336 4
\item   365,2  ~ \(\times\)  ~ ... ~ = ~  36,52
\item   3,394  ~ \(\times\)  ~ ... ~ = ~  0,003 394
\item   32,89  ~ \(\times\)  ~ ... ~ = ~  0,032 89
\item   8 901  ~ \(\times\)  ~ ... ~ = ~  8,901
\item   785  ~ \(\times\)  ~ ... ~ = ~  7,85
\item   5 099  ~ \(\times\)  ~ ... ~ = ~  50,99
\item   929,2  ~ \(\times\)  ~ ... ~ = ~  9,292
\item   64,23  ~ \(\times\)  ~ ... ~ = ~  0,064 23
\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 ~dm~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   163,8 ~hg~ = ...~kg
\item   3 743,6 ~dag~ = ...~g
\item   1 253 ~m~ = ...~mm
\item   2 456 ~hL~ = ...~mL
\item   796,82 ~km~ = ...~mm
\item   545,85 ~mm~ = ...~km
\item   6 369,4 ~kg~ = ...~dg
\item   139,96 ~dam~ = ...~mm
\item   665,91 ~dg~ = ...~mg
\item   5 160,9 ~m~ = ...~dam
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{6800}{100}\) = \(\dfrac{680}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{75}{10}\) = \(\dfrac{750}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{910}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   773  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 773 000}
\item   0,39  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,9}
\item   0,534  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,34}
\item   0,094  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,4}
\item   3,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 33}
\item   0,09  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9}
\item   284  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 28 400}
\item   8,14  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 140}
\item   0,055  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,55}
\item   0,187  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 18,7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,59 ~ : ~ 1 000 ~ = ~{\color{red} 0,018 59}
\item   3,906 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 906}
\item   29,53 ~ : ~ 100 ~ = ~{\color{red} 0,295 3}
\item   3 102 ~ : ~ 1 000 ~ = ~{\color{red} 3,102}
\item   335,5 ~ : ~ 100 ~ = ~{\color{red} 3,355}
\item   97,49 ~ : ~ 100 ~ = ~{\color{red} 0,974 9}
\item   565,8 ~ : ~ 10 ~ = ~{\color{red} 56,58}
\item   400,6 ~ : ~ 10 ~ = ~{\color{red} 40,06}
\item   6,077 ~ : ~ 10 ~ = ~{\color{red} 0,607 7}
\item   8,215 ~ : ~ 10 ~ = ~{\color{red} 0,821 5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,002 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2
\item   15,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~155
\item   3,94 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 940
\item   0,087 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~87
\item   0,101 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,01
\item   6,71 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 710
\item   0,324 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,24
\item   0,073 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,73
\item   0,359 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~35,9
\item   0,143 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~14,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   847,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 84,78
}\item   15,91 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,015 91
}\item   9,087 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,090 87
}\item   9 301 ~ \(\times\)  0,01 ~ = ~{\color{red} 93,01
}\item   5 900 ~ \(\times\)  0,1 ~ = ~{\color{red} 590
}\item   897,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,897 6
}\item   2,944 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 944
}\item   17,36 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,736
}\item   2 194 ~ \(\times\)  0,1 ~ = ~{\color{red} 219,4
}\item   9,661 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,096 61
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   458,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 45,87
\item   33,64 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,336 4
\item   365,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 36,52
\item   3,394 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 394
\item   32,89 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,032 89
\item   8 901 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,901
\item   785 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,85
\item   5 099 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 50,99
\item   929,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,292
\item   64,23 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,064 23
\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 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   163,8 ~hg~ = {\color{red}  16,38 }~kg
\item   3 743,6 ~dag~ = {\color{red}  37 436 }~g
\item   1 253 ~m~ = {\color{red}  1 253 000 }~mm
\item   2 456 ~hL~ = {\color{red}  245 600 000 }~mL
\item   796,82 ~km~ = {\color{red}  796 820 000 }~mm
\item   545,85 ~mm~ = {\color{red}  0,000 545 85 }~km
\item   6 369,4 ~kg~ = {\color{red}  63 694 000 }~dg
\item   139,96 ~dam~ = {\color{red}  1 399 600 }~mm
\item   665,91 ~dg~ = {\color{red}  66 591 }~mg
\item   5 160,9 ~m~ = {\color{red}  516,09 }~dam
\end{itemize}
\end{multicols}
\end{document}
