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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 373}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,064  ~ \(\times\)  ~ 100
\item   0,417  ~ \(\times\)  ~ 1 000
\item   0,689  ~ \(\times\)  ~ 100
\item   480  ~ \(\times\)  ~ 1 000
\item   381  ~ \(\times\)  ~ 100
\item   806  ~ \(\times\)  ~ 10
\item   659  ~ \(\times\)  ~ 10
\item   66,4  ~ \(\times\)  ~ 10
\item   9,77  ~ \(\times\)  ~ 100
\item   663  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,67  ~ : ~ 10
\item   6,092  ~ : ~ 100
\item   44,21  ~ : ~ 10
\item   575,9  ~ : ~ 100
\item   21,11  ~ : ~ 100
\item   8 535  ~ : ~ 1 000
\item   897,6  ~ : ~ 1 000
\item   8 558  ~ : ~ 10
\item   942,1  ~ : ~ 10
\item   818,9  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,3  ~ \(\times\)  ~ ... ~ = ~ 1 530
\item   4,73  ~ \(\times\)  ~ ... ~ = ~ 47,3
\item   6,94  ~ \(\times\)  ~ ... ~ = ~ 694
\item   71,8  ~ \(\times\)  ~ ... ~ = ~ 718
\item   81,8  ~ \(\times\)  ~ ... ~ = ~ 81 800
\item   92  ~ \(\times\)  ~ ... ~ = ~ 920
\item   0,414  ~ \(\times\)  ~ ... ~ = ~ 41,4
\item   4,15  ~ \(\times\)  ~ ... ~ = ~ 4 150
\item   77,5  ~ \(\times\)  ~ ... ~ = ~ 77 500
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   246,7  ~ \(\times\)  ~ 0,001
\item   357,1  ~ \(\times\)  ~ 0,1
\item   6,414  ~ \(\times\)  ~ 0,01
\item   87,75  ~ \(\times\)  ~ 0,1
\item   0,652  ~ \(\times\)  ~ 0,1
\item   6,593  ~ \(\times\)  ~ 0,1
\item   3,241  ~ \(\times\)  ~ 0,01
\item   437,9  ~ \(\times\)  ~ 0,1
\item   9,57  ~ \(\times\)  ~ 0,1
\item   9 133  ~ \(\times\)  ~ 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   66,56  ~ \(\times\)  ~ ... ~ = ~  0,066 56
\item   9 360  ~ \(\times\)  ~ ... ~ = ~  93,6
\item   6,87  ~ \(\times\)  ~ ... ~ = ~  0,687
\item   24,49  ~ \(\times\)  ~ ... ~ = ~  0,244 9
\item   9,234  ~ \(\times\)  ~ ... ~ = ~  0,092 34
\item   5,588  ~ \(\times\)  ~ ... ~ = ~  0,005 588
\item   5 792  ~ \(\times\)  ~ ... ~ = ~  5,792
\item   18,83  ~ \(\times\)  ~ ... ~ = ~  0,188 3
\item   5,993  ~ \(\times\)  ~ ... ~ = ~  0,059 93
\item   65,3  ~ \(\times\)  ~ ... ~ = ~  6,53
\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 ~dam~ = ...~m
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 051,6 ~kg~ = ...~mg
\item   972,79 ~dm~ = ...~m
\item   225,5 ~cg~ = ...~dg
\item   118,09 ~mL~ = ...~cL
\item   8 333,8 ~dag~ = ...~g
\item   4 663 ~dm~ = ...~hm
\item   1 506,1 ~g~ = ...~hg
\item   702,59 ~dag~ = ...~kg
\item   1 113,9 ~dag~ = ...~cg
\item   8 557,2 ~mm~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{9500}{100}\) = \(\dfrac{950}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{420}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,064  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,4}
\item   0,417  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 417}
\item   0,689  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 68,9}
\item   480  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 480 000}
\item   381  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 38 100}
\item   806  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 060}
\item   659  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 590}
\item   66,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 664}
\item   9,77  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 977}
\item   663  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66 300}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,67 ~ : ~ 10 ~ = ~{\color{red} 4,167}
\item   6,092 ~ : ~ 100 ~ = ~{\color{red} 0,060 92}
\item   44,21 ~ : ~ 10 ~ = ~{\color{red} 4,421}
\item   575,9 ~ : ~ 100 ~ = ~{\color{red} 5,759}
\item   21,11 ~ : ~ 100 ~ = ~{\color{red} 0,211 1}
\item   8 535 ~ : ~ 1 000 ~ = ~{\color{red} 8,535}
\item   897,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,897 6}
\item   8 558 ~ : ~ 10 ~ = ~{\color{red} 855,8}
\item   942,1 ~ : ~ 10 ~ = ~{\color{red} 94,21}
\item   818,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,818 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 530
\item   4,73 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~47,3
\item   6,94 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~694
\item   71,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~718
\item   81,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~81 800
\item   92 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~920
\item   0,414 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~41,4
\item   4,15 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 150
\item   77,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~77 500
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   246,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,246 7
}\item   357,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 35,71
}\item   6,414 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,064 14
}\item   87,75 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,775
}\item   0,652 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,065 2
}\item   6,593 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,659 3
}\item   3,241 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,032 41
}\item   437,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 43,79
}\item   9,57 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,957
}\item   9 133 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,133
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,56 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,066 56
\item   9 360 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 93,6
\item   6,87 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,687
\item   24,49 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,244 9
\item   9,234 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,092 34
\item   5,588 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 588
\item   5 792 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,792
\item   18,83 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,188 3
\item   5,993 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,059 93
\item   65,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,53
\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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 051,6 ~kg~ = {\color{red}  4 051 600 000 }~mg
\item   972,79 ~dm~ = {\color{red}  97,279 }~m
\item   225,5 ~cg~ = {\color{red}  22,55 }~dg
\item   118,09 ~mL~ = {\color{red}  11,809 }~cL
\item   8 333,8 ~dag~ = {\color{red}  83 338 }~g
\item   4 663 ~dm~ = {\color{red}  4,663 }~hm
\item   1 506,1 ~g~ = {\color{red}  15,061 }~hg
\item   702,59 ~dag~ = {\color{red}  7,025 9 }~kg
\item   1 113,9 ~dag~ = {\color{red}  1 113 900 }~cg
\item   8 557,2 ~mm~ = {\color{red}  85,572 }~dm
\end{itemize}
\end{multicols}
\end{document}
