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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 346}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{25}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{82}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,51  ~ \(\times\)  ~ 1 000
\item   0,056  ~ \(\times\)  ~ 100
\item   48,9  ~ \(\times\)  ~ 1 000
\item   117  ~ \(\times\)  ~ 10
\item   0,044  ~ \(\times\)  ~ 10
\item   3,52  ~ \(\times\)  ~ 10
\item   1,6  ~ \(\times\)  ~ 100
\item   0,695  ~ \(\times\)  ~ 1 000
\item   0,095  ~ \(\times\)  ~ 100
\item   0,972  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   909,1  ~ : ~ 100
\item   17,42  ~ : ~ 1 000
\item   0,876  ~ : ~ 1 000
\item   5,392  ~ : ~ 100
\item   278,6  ~ : ~ 1 000
\item   5,595  ~ : ~ 1 000
\item   1,05  ~ : ~ 10
\item   835,9  ~ : ~ 100
\item   216  ~ : ~ 100
\item   9 448  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,076  ~ \(\times\)  ~ ... ~ = ~ 7,6
\item   43  ~ \(\times\)  ~ ... ~ = ~ 4 300
\item   63,2  ~ \(\times\)  ~ ... ~ = ~ 632
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 0,22
\item   87,9  ~ \(\times\)  ~ ... ~ = ~ 879
\item   86,8  ~ \(\times\)  ~ ... ~ = ~ 868
\item   237  ~ \(\times\)  ~ ... ~ = ~ 23 700
\item   3,04  ~ \(\times\)  ~ ... ~ = ~ 304
\item   0,648  ~ \(\times\)  ~ ... ~ = ~ 6,48
\item   0,571  ~ \(\times\)  ~ ... ~ = ~ 57,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,603  ~ \(\times\)  ~ 0,01
\item   927,3  ~ \(\times\)  ~ 0,001
\item   1 443  ~ \(\times\)  ~ 0,001
\item   25,4  ~ \(\times\)  ~ 0,001
\item   745,5  ~ \(\times\)  ~ 0,001
\item   6,138  ~ \(\times\)  ~ 0,1
\item   83,5  ~ \(\times\)  ~ 0,001
\item   21,86  ~ \(\times\)  ~ 0,1
\item   4,4  ~ \(\times\)  ~ 0,001
\item   1 264  ~ \(\times\)  ~ 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   3 636  ~ \(\times\)  ~ ... ~ = ~  3,636
\item   1,884  ~ \(\times\)  ~ ... ~ = ~  0,188 4
\item   4 578  ~ \(\times\)  ~ ... ~ = ~  457,8
\item   28,7  ~ \(\times\)  ~ ... ~ = ~  2,87
\item   6,808  ~ \(\times\)  ~ ... ~ = ~  0,068 08
\item   367,5  ~ \(\times\)  ~ ... ~ = ~  36,75
\item   6 075  ~ \(\times\)  ~ ... ~ = ~  607,5
\item   1 321  ~ \(\times\)  ~ ... ~ = ~  1,321
\item   85,8  ~ \(\times\)  ~ ... ~ = ~  0,858
\item   80,52  ~ \(\times\)  ~ ... ~ = ~  0,805 2
\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 ~hm~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   905,31 ~mm~ = ...~hm
\item   389,84 ~daL~ = ...~hL
\item   2 944,6 ~dL~ = ...~hL
\item   1 661,8 ~g~ = ...~hg
\item   709,39 ~cm~ = ...~mm
\item   612,99 ~cm~ = ...~dam
\item   4 238,3 ~L~ = ...~dL
\item   729,22 ~cL~ = ...~kL
\item   4 584,8 ~cL~ = ...~mL
\item   4 552,8 ~mL~ = ...~hL
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{8800}{100}\) = \(\dfrac{880}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{25}{10}\) = \(\dfrac{250}{100}\)
\item   \(\dfrac{82}{100}\) = \(\dfrac{820}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,51  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 510}
\item   0,056  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,6}
\item   48,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 48 900}
\item   117  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 170}
\item   0,044  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,44}
\item   3,52  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 35,2}
\item   1,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 160}
\item   0,695  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 695}
\item   0,095  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,5}
\item   0,972  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 97,2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   909,1 ~ : ~ 100 ~ = ~{\color{red} 9,091}
\item   17,42 ~ : ~ 1 000 ~ = ~{\color{red} 0,017 42}
\item   0,876 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 876}
\item   5,392 ~ : ~ 100 ~ = ~{\color{red} 0,053 92}
\item   278,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,278 6}
\item   5,595 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 595}
\item   1,05 ~ : ~ 10 ~ = ~{\color{red} 0,105}
\item   835,9 ~ : ~ 100 ~ = ~{\color{red} 8,359}
\item   216 ~ : ~ 100 ~ = ~{\color{red} 2,16}
\item   9 448 ~ : ~ 100 ~ = ~{\color{red} 94,48}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,076 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,6
\item   43 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 300
\item   63,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~632
\item   0,022 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,22
\item   87,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~879
\item   86,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~868
\item   237 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~23 700
\item   3,04 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~304
\item   0,648 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,48
\item   0,571 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~57,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,603 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,026 03
}\item   927,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,927 3
}\item   1 443 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,443
}\item   25,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,025 4
}\item   745,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,745 5
}\item   6,138 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,613 8
}\item   83,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,083 5
}\item   21,86 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,186
}\item   4,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 4
}\item   1 264 ~ \(\times\)  0,1 ~ = ~{\color{red} 126,4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 636 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,636
\item   1,884 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,188 4
\item   4 578 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 457,8
\item   28,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,87
\item   6,808 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,068 08
\item   367,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 36,75
\item   6 075 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 607,5
\item   1 321 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,321
\item   85,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,858
\item   80,52 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,805 2
\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 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   905,31 ~mm~ = {\color{red}  0,009 053 1 }~hm
\item   389,84 ~daL~ = {\color{red}  38,984 }~hL
\item   2 944,6 ~dL~ = {\color{red}  2,944 6 }~hL
\item   1 661,8 ~g~ = {\color{red}  16,618 }~hg
\item   709,39 ~cm~ = {\color{red}  7 093,9 }~mm
\item   612,99 ~cm~ = {\color{red}  0,612 99 }~dam
\item   4 238,3 ~L~ = {\color{red}  42 383 }~dL
\item   729,22 ~cL~ = {\color{red}  0,007 292 2 }~kL
\item   4 584,8 ~cL~ = {\color{red}  45 848 }~mL
\item   4 552,8 ~mL~ = {\color{red}  0,045 528 }~hL
\end{itemize}
\end{multicols}
\end{document}
