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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 254}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{38}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{11}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,074  ~ \(\times\)  ~ 1 000
\item   0,341  ~ \(\times\)  ~ 1 000
\item   60,2  ~ \(\times\)  ~ 100
\item   30  ~ \(\times\)  ~ 10
\item   89,1  ~ \(\times\)  ~ 1 000
\item   6,37  ~ \(\times\)  ~ 10
\item   0,036  ~ \(\times\)  ~ 10
\item   0,013  ~ \(\times\)  ~ 10
\item   416  ~ \(\times\)  ~ 1 000
\item   8,15  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   703,6  ~ : ~ 100
\item   8,991  ~ : ~ 10
\item   985,7  ~ : ~ 10
\item   5,866  ~ : ~ 100
\item   823  ~ : ~ 10
\item   636,8  ~ : ~ 100
\item   9,209  ~ : ~ 100
\item   29,33  ~ : ~ 1 000
\item   16,5  ~ : ~ 100
\item   229,1  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,019  ~ \(\times\)  ~ ... ~ = ~ 19
\item   15,9  ~ \(\times\)  ~ ... ~ = ~ 15 900
\item   9,07  ~ \(\times\)  ~ ... ~ = ~ 9 070
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 2
\item   343  ~ \(\times\)  ~ ... ~ = ~ 34 300
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 0,32
\item   0,015  ~ \(\times\)  ~ ... ~ = ~ 0,15
\item   947  ~ \(\times\)  ~ ... ~ = ~ 9 470
\item   0,9  ~ \(\times\)  ~ ... ~ = ~ 9
\item   590  ~ \(\times\)  ~ ... ~ = ~ 5 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,05  ~ \(\times\)  ~ 0,1
\item   82,47  ~ \(\times\)  ~ 0,01
\item   448,9  ~ \(\times\)  ~ 0,1
\item   33,79  ~ \(\times\)  ~ 0,01
\item   22,12  ~ \(\times\)  ~ 0,01
\item   7 977  ~ \(\times\)  ~ 0,1
\item   83,5  ~ \(\times\)  ~ 0,001
\item   85,2  ~ \(\times\)  ~ 0,01
\item   63,57  ~ \(\times\)  ~ 0,1
\item   52,89  ~ \(\times\)  ~ 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   768,6  ~ \(\times\)  ~ ... ~ = ~  76,86
\item   8,825  ~ \(\times\)  ~ ... ~ = ~  0,088 25
\item   20,27  ~ \(\times\)  ~ ... ~ = ~  2,027
\item   1 622  ~ \(\times\)  ~ ... ~ = ~  162,2
\item   651,9  ~ \(\times\)  ~ ... ~ = ~  6,519
\item   221,8  ~ \(\times\)  ~ ... ~ = ~  0,221 8
\item   871,1  ~ \(\times\)  ~ ... ~ = ~  8,711
\item   1 903  ~ \(\times\)  ~ ... ~ = ~  1,903
\item   8,736  ~ \(\times\)  ~ ... ~ = ~  0,873 6
\item   5,274  ~ \(\times\)  ~ ... ~ = ~  0,527 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 ~dm~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   123,51 ~kL~ = ...~mL
\item   9 600 ~cL~ = ...~kL
\item   537,89 ~mg~ = ...~cg
\item   9 492,9 ~cL~ = ...~L
\item   901,99 ~m~ = ...~cm
\item   550,76 ~mg~ = ...~hg
\item   673,94 ~mL~ = ...~hL
\item   356,49 ~mg~ = ...~dg
\item   7 537,1 ~cm~ = ...~km
\item   429,31 ~cg~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{38}{10}\) = \(\dfrac{380}{100}\)
\item   \(\dfrac{11}{100}\) = \(\dfrac{110}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,074  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 74}
\item   0,341  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 341}
\item   60,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 020}
\item   30  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 300}
\item   89,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 89 100}
\item   6,37  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 63,7}
\item   0,036  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,36}
\item   0,013  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,13}
\item   416  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 416 000}
\item   8,15  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 815}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   703,6 ~ : ~ 100 ~ = ~{\color{red} 7,036}
\item   8,991 ~ : ~ 10 ~ = ~{\color{red} 0,899 1}
\item   985,7 ~ : ~ 10 ~ = ~{\color{red} 98,57}
\item   5,866 ~ : ~ 100 ~ = ~{\color{red} 0,058 66}
\item   823 ~ : ~ 10 ~ = ~{\color{red} 82,3}
\item   636,8 ~ : ~ 100 ~ = ~{\color{red} 6,368}
\item   9,209 ~ : ~ 100 ~ = ~{\color{red} 0,092 09}
\item   29,33 ~ : ~ 1 000 ~ = ~{\color{red} 0,029 33}
\item   16,5 ~ : ~ 100 ~ = ~{\color{red} 0,165}
\item   229,1 ~ : ~ 10 ~ = ~{\color{red} 22,91}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,019 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~19
\item   15,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~15 900
\item   9,07 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 070
\item   0,002 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2
\item   343 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~34 300
\item   0,032 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,32
\item   0,015 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,15
\item   947 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 470
\item   0,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9
\item   590 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 900
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,05 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,405
}\item   82,47 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,824 7
}\item   448,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 44,89
}\item   33,79 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,337 9
}\item   22,12 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,221 2
}\item   7 977 ~ \(\times\)  0,1 ~ = ~{\color{red} 797,7
}\item   83,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,083 5
}\item   85,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,852
}\item   63,57 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,357
}\item   52,89 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,289
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   768,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 76,86
\item   8,825 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,088 25
\item   20,27 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,027
\item   1 622 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 162,2
\item   651,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,519
\item   221,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,221 8
\item   871,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,711
\item   1 903 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,903
\item   8,736 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,873 6
\item   5,274 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,527 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 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   123,51 ~kL~ = {\color{red}  123 510 000 }~mL
\item   9 600 ~cL~ = {\color{red}  0,096 }~kL
\item   537,89 ~mg~ = {\color{red}  53,789 }~cg
\item   9 492,9 ~cL~ = {\color{red}  94,929 }~L
\item   901,99 ~m~ = {\color{red}  90 199 }~cm
\item   550,76 ~mg~ = {\color{red}  0,005 507 6 }~hg
\item   673,94 ~mL~ = {\color{red}  0,006 739 4 }~hL
\item   356,49 ~mg~ = {\color{red}  3,564 9 }~dg
\item   7 537,1 ~cm~ = {\color{red}  0,075 371 }~km
\item   429,31 ~cg~ = {\color{red}  42,931 }~dg
\end{itemize}
\end{multicols}
\end{document}
