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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 94}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{66}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   878  ~ \(\times\)  ~ 1 000
\item   5,19  ~ \(\times\)  ~ 100
\item   0,045  ~ \(\times\)  ~ 100
\item   559  ~ \(\times\)  ~ 100
\item   0,022  ~ \(\times\)  ~ 100
\item   0,952  ~ \(\times\)  ~ 100
\item   82,5  ~ \(\times\)  ~ 1 000
\item   749  ~ \(\times\)  ~ 100
\item   48,6  ~ \(\times\)  ~ 100
\item   144  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,021  ~ : ~ 1 000
\item   4 642  ~ : ~ 100
\item   71,58  ~ : ~ 10
\item   9 045  ~ : ~ 100
\item   3 799  ~ : ~ 100
\item   560,7  ~ : ~ 100
\item   2 899  ~ : ~ 10
\item   781,9  ~ : ~ 100
\item   36,8  ~ : ~ 1 000
\item   8 297  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,075  ~ \(\times\)  ~ ... ~ = ~ 75
\item   297  ~ \(\times\)  ~ ... ~ = ~ 2 970
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 68
\item   65,9  ~ \(\times\)  ~ ... ~ = ~ 659
\item   83,7  ~ \(\times\)  ~ ... ~ = ~ 837
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 43
\item   64,6  ~ \(\times\)  ~ ... ~ = ~ 64 600
\item   23,3  ~ \(\times\)  ~ ... ~ = ~ 23 300
\item   0,244  ~ \(\times\)  ~ ... ~ = ~ 244
\item   0,017  ~ \(\times\)  ~ ... ~ = ~ 17
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   702,8  ~ \(\times\)  ~ 0,01
\item   6,115  ~ \(\times\)  ~ 0,1
\item   846,6  ~ \(\times\)  ~ 0,001
\item   5,325  ~ \(\times\)  ~ 0,1
\item   773,5  ~ \(\times\)  ~ 0,001
\item   55,18  ~ \(\times\)  ~ 0,01
\item   8 384  ~ \(\times\)  ~ 0,001
\item   54,05  ~ \(\times\)  ~ 0,1
\item   33,3  ~ \(\times\)  ~ 0,1
\item   331,8  ~ \(\times\)  ~ 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   5,176  ~ \(\times\)  ~ ... ~ = ~  0,051 76
\item   3 569  ~ \(\times\)  ~ ... ~ = ~  35,69
\item   6,519  ~ \(\times\)  ~ ... ~ = ~  0,651 9
\item   12,2  ~ \(\times\)  ~ ... ~ = ~  0,012 2
\item   25,54  ~ \(\times\)  ~ ... ~ = ~  2,554
\item   6 700  ~ \(\times\)  ~ ... ~ = ~  670
\item   1 781  ~ \(\times\)  ~ ... ~ = ~  178,1
\item   7 406  ~ \(\times\)  ~ ... ~ = ~  7,406
\item   75,1  ~ \(\times\)  ~ ... ~ = ~  7,51
\item   4,997  ~ \(\times\)  ~ ... ~ = ~  0,004 997
\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~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   637,27 ~dg~ = ...~kg
\item   985,35 ~hg~ = ...~g
\item   2 577,6 ~dag~ = ...~cg
\item   568,23 ~dam~ = ...~km
\item   243,16 ~cm~ = ...~hm
\item   5 308,7 ~km~ = ...~mm
\item   3 558,7 ~hL~ = ...~cL
\item   7 137,8 ~cm~ = ...~dm
\item   909,58 ~dL~ = ...~cL
\item   4 436,2 ~dam~ = ...~mm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{2600}{100}\) = \(\dfrac{260}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{490}{100}\)
\item   \(\dfrac{66}{100}\) = \(\dfrac{660}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   878  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 878 000}
\item   5,19  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 519}
\item   0,045  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,5}
\item   559  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 55 900}
\item   0,022  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,2}
\item   0,952  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 95,2}
\item   82,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 82 500}
\item   749  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 74 900}
\item   48,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 860}
\item   144  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 144 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,021 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 021}
\item   4 642 ~ : ~ 100 ~ = ~{\color{red} 46,42}
\item   71,58 ~ : ~ 10 ~ = ~{\color{red} 7,158}
\item   9 045 ~ : ~ 100 ~ = ~{\color{red} 90,45}
\item   3 799 ~ : ~ 100 ~ = ~{\color{red} 37,99}
\item   560,7 ~ : ~ 100 ~ = ~{\color{red} 5,607}
\item   2 899 ~ : ~ 10 ~ = ~{\color{red} 289,9}
\item   781,9 ~ : ~ 100 ~ = ~{\color{red} 7,819}
\item   36,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,036 8}
\item   8 297 ~ : ~ 1 000 ~ = ~{\color{red} 8,297}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,075 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~75
\item   297 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 970
\item   0,068 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~68
\item   65,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~659
\item   83,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~837
\item   0,043 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43
\item   64,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~64 600
\item   23,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~23 300
\item   0,244 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~244
\item   0,017 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~17
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   702,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,028
}\item   6,115 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,611 5
}\item   846,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,846 6
}\item   5,325 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,532 5
}\item   773,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,773 5
}\item   55,18 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,551 8
}\item   8 384 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,384
}\item   54,05 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,405
}\item   33,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,33
}\item   331,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 33,18
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,176 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,051 76
\item   3 569 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 35,69
\item   6,519 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,651 9
\item   12,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,012 2
\item   25,54 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,554
\item   6 700 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 670
\item   1 781 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 178,1
\item   7 406 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,406
\item   75,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,51
\item   4,997 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 997
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   637,27 ~dg~ = {\color{red}  0,063 727 }~kg
\item   985,35 ~hg~ = {\color{red}  98 535 }~g
\item   2 577,6 ~dag~ = {\color{red}  2 577 600 }~cg
\item   568,23 ~dam~ = {\color{red}  5,682 3 }~km
\item   243,16 ~cm~ = {\color{red}  0,024 316 }~hm
\item   5 308,7 ~km~ = {\color{red}  5 308 700 000 }~mm
\item   3 558,7 ~hL~ = {\color{red}  35 587 000 }~cL
\item   7 137,8 ~cm~ = {\color{red}  713,78 }~dm
\item   909,58 ~dL~ = {\color{red}  9 095,8 }~cL
\item   4 436,2 ~dam~ = {\color{red}  44 362 000 }~mm
\end{itemize}
\end{multicols}
\end{document}
