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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 39}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,041  ~ \(\times\)  ~ 10
\item   6,7  ~ \(\times\)  ~ 1 000
\item   37,3  ~ \(\times\)  ~ 10
\item   310  ~ \(\times\)  ~ 100
\item   17  ~ \(\times\)  ~ 100
\item   0,365  ~ \(\times\)  ~ 10
\item   0,897  ~ \(\times\)  ~ 1 000
\item   6,03  ~ \(\times\)  ~ 100
\item   742  ~ \(\times\)  ~ 100
\item   4,5  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 354  ~ : ~ 1 000
\item   84,6  ~ : ~ 1 000
\item   7,981  ~ : ~ 100
\item   4,732  ~ : ~ 1 000
\item   5,852  ~ : ~ 10
\item   8,796  ~ : ~ 10
\item   29,27  ~ : ~ 1 000
\item   482,8  ~ : ~ 1 000
\item   1,725  ~ : ~ 1 000
\item   7 842  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43  ~ \(\times\)  ~ ... ~ = ~ 43 000
\item   0,755  ~ \(\times\)  ~ ... ~ = ~ 7,55
\item   0,092  ~ \(\times\)  ~ ... ~ = ~ 92
\item   0,613  ~ \(\times\)  ~ ... ~ = ~ 613
\item   0,014  ~ \(\times\)  ~ ... ~ = ~ 14
\item   235  ~ \(\times\)  ~ ... ~ = ~ 235 000
\item   46  ~ \(\times\)  ~ ... ~ = ~ 46 000
\item   91,9  ~ \(\times\)  ~ ... ~ = ~ 91 900
\item   25,6  ~ \(\times\)  ~ ... ~ = ~ 25 600
\item   0,01  ~ \(\times\)  ~ ... ~ = ~ 1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,23  ~ \(\times\)  ~ 0,001
\item   366,7  ~ \(\times\)  ~ 0,001
\item   243,5  ~ \(\times\)  ~ 0,1
\item   60,28  ~ \(\times\)  ~ 0,01
\item   3 030  ~ \(\times\)  ~ 0,1
\item   3 558  ~ \(\times\)  ~ 0,1
\item   890  ~ \(\times\)  ~ 0,001
\item   1 999  ~ \(\times\)  ~ 0,01
\item   9,191  ~ \(\times\)  ~ 0,01
\item   446,4  ~ \(\times\)  ~ 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   528,9  ~ \(\times\)  ~ ... ~ = ~  5,289
\item   8 807  ~ \(\times\)  ~ ... ~ = ~  880,7
\item   7 679  ~ \(\times\)  ~ ... ~ = ~  76,79
\item   544  ~ \(\times\)  ~ ... ~ = ~  54,4
\item   3,496  ~ \(\times\)  ~ ... ~ = ~  0,349 6
\item   827,1  ~ \(\times\)  ~ ... ~ = ~  8,271
\item   248,7  ~ \(\times\)  ~ ... ~ = ~  2,487
\item   34,12  ~ \(\times\)  ~ ... ~ = ~  0,341 2
\item   9,502  ~ \(\times\)  ~ ... ~ = ~  0,095 02
\item   1,014  ~ \(\times\)  ~ ... ~ = ~  0,101 4
\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 ~cm~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   858,62 ~g~ = ...~dag
\item   9 035,1 ~hm~ = ...~mm
\item   7 103,8 ~cg~ = ...~mg
\item   817,71 ~mm~ = ...~cm
\item   2 627,5 ~kL~ = ...~cL
\item   9 118,2 ~dag~ = ...~dg
\item   857 ~dg~ = ...~cg
\item   371,65 ~hL~ = ...~dL
\item   484,14 ~daL~ = ...~hL
\item   2 049,2 ~hm~ = ...~km
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{6000}{100}\) = \(\dfrac{600}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{390}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,041  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,41}
\item   6,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 700}
\item   37,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 373}
\item   310  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 31 000}
\item   17  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 700}
\item   0,365  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,65}
\item   0,897  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 897}
\item   6,03  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 603}
\item   742  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 74 200}
\item   4,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 500}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 354 ~ : ~ 1 000 ~ = ~{\color{red} 5,354}
\item   84,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,084 6}
\item   7,981 ~ : ~ 100 ~ = ~{\color{red} 0,079 81}
\item   4,732 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 732}
\item   5,852 ~ : ~ 10 ~ = ~{\color{red} 0,585 2}
\item   8,796 ~ : ~ 10 ~ = ~{\color{red} 0,879 6}
\item   29,27 ~ : ~ 1 000 ~ = ~{\color{red} 0,029 27}
\item   482,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,482 8}
\item   1,725 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 725}
\item   7 842 ~ : ~ 100 ~ = ~{\color{red} 78,42}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43 000
\item   0,755 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,55
\item   0,092 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~92
\item   0,613 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~613
\item   0,014 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14
\item   235 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~235 000
\item   46 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~46 000
\item   91,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~91 900
\item   25,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~25 600
\item   0,01 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,23 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,055 23
}\item   366,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,366 7
}\item   243,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 24,35
}\item   60,28 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,602 8
}\item   3 030 ~ \(\times\)  0,1 ~ = ~{\color{red} 303
}\item   3 558 ~ \(\times\)  0,1 ~ = ~{\color{red} 355,8
}\item   890 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,89
}\item   1 999 ~ \(\times\)  0,01 ~ = ~{\color{red} 19,99
}\item   9,191 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,091 91
}\item   446,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 44,64
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   528,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,289
\item   8 807 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 880,7
\item   7 679 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 76,79
\item   544 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 54,4
\item   3,496 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,349 6
\item   827,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,271
\item   248,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,487
\item   34,12 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,341 2
\item   9,502 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,095 02
\item   1,014 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,101 4
\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 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   858,62 ~g~ = {\color{red}  85,862 }~dag
\item   9 035,1 ~hm~ = {\color{red}  903 510 000 }~mm
\item   7 103,8 ~cg~ = {\color{red}  71 038 }~mg
\item   817,71 ~mm~ = {\color{red}  81,771 }~cm
\item   2 627,5 ~kL~ = {\color{red}  262 750 000 }~cL
\item   9 118,2 ~dag~ = {\color{red}  911 820 }~dg
\item   857 ~dg~ = {\color{red}  8 570 }~cg
\item   371,65 ~hL~ = {\color{red}  371 650 }~dL
\item   484,14 ~daL~ = {\color{red}  48,414 }~hL
\item   2 049,2 ~hm~ = {\color{red}  204,92 }~km
\end{itemize}
\end{multicols}
\end{document}
