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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 375}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{33}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,019  ~ \(\times\)  ~ 100
\item   0,02  ~ \(\times\)  ~ 100
\item   0,041  ~ \(\times\)  ~ 1 000
\item   74,4  ~ \(\times\)  ~ 10
\item   419  ~ \(\times\)  ~ 10
\item   0,009  ~ \(\times\)  ~ 100
\item   3,15  ~ \(\times\)  ~ 10
\item   0,093  ~ \(\times\)  ~ 1 000
\item   235  ~ \(\times\)  ~ 1 000
\item   0,83  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   880,6  ~ : ~ 10
\item   6,515  ~ : ~ 1 000
\item   109,7  ~ : ~ 10
\item   6,779  ~ : ~ 10
\item   657  ~ : ~ 1 000
\item   47,29  ~ : ~ 100
\item   1 896  ~ : ~ 10
\item   1,414  ~ : ~ 10
\item   1 286  ~ : ~ 100
\item   82,69  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,159  ~ \(\times\)  ~ ... ~ = ~ 159
\item   90,3  ~ \(\times\)  ~ ... ~ = ~ 903
\item   2,54  ~ \(\times\)  ~ ... ~ = ~ 254
\item   0,88  ~ \(\times\)  ~ ... ~ = ~ 8,8
\item   9,69  ~ \(\times\)  ~ ... ~ = ~ 9 690
\item   55,6  ~ \(\times\)  ~ ... ~ = ~ 556
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 3,3
\item   543  ~ \(\times\)  ~ ... ~ = ~ 54 300
\item   77,4  ~ \(\times\)  ~ ... ~ = ~ 7 740
\item   0,08  ~ \(\times\)  ~ ... ~ = ~ 8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   906,7  ~ \(\times\)  ~ 0,1
\item   84,29  ~ \(\times\)  ~ 0,001
\item   400  ~ \(\times\)  ~ 0,01
\item   69,63  ~ \(\times\)  ~ 0,1
\item   41,96  ~ \(\times\)  ~ 0,001
\item   6 528  ~ \(\times\)  ~ 0,1
\item   9 072  ~ \(\times\)  ~ 0,01
\item   0,492  ~ \(\times\)  ~ 0,01
\item   14,65  ~ \(\times\)  ~ 0,001
\item   253,2  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 916  ~ \(\times\)  ~ ... ~ = ~  6,916
\item   44,16  ~ \(\times\)  ~ ... ~ = ~  0,044 16
\item   3,417  ~ \(\times\)  ~ ... ~ = ~  0,341 7
\item   5,003  ~ \(\times\)  ~ ... ~ = ~  0,005 003
\item   734  ~ \(\times\)  ~ ... ~ = ~  7,34
\item   7 624  ~ \(\times\)  ~ ... ~ = ~  7,624
\item   4 456  ~ \(\times\)  ~ ... ~ = ~  44,56
\item   1 631  ~ \(\times\)  ~ ... ~ = ~  1,631
\item   17,5  ~ \(\times\)  ~ ... ~ = ~  1,75
\item   4,049  ~ \(\times\)  ~ ... ~ = ~  0,404 9
\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 ~dam~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   433,08 ~mL~ = ...~dL
\item   945,91 ~mg~ = ...~hg
\item   442 ~dag~ = ...~dg
\item   910,03 ~kL~ = ...~hL
\item   7 558,5 ~dag~ = ...~kg
\item   875,19 ~cg~ = ...~dag
\item   903,74 ~m~ = ...~dm
\item   327,28 ~mg~ = ...~dg
\item   316,04 ~daL~ = ...~hL
\item   9 195 ~cL~ = ...~daL
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{33}{10}\) = \(\dfrac{330}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{440}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,019  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,9}
\item   0,02  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2}
\item   0,041  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 41}
\item   74,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 744}
\item   419  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 190}
\item   0,009  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,9}
\item   3,15  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 31,5}
\item   0,093  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 93}
\item   235  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 235 000}
\item   0,83  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   880,6 ~ : ~ 10 ~ = ~{\color{red} 88,06}
\item   6,515 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 515}
\item   109,7 ~ : ~ 10 ~ = ~{\color{red} 10,97}
\item   6,779 ~ : ~ 10 ~ = ~{\color{red} 0,677 9}
\item   657 ~ : ~ 1 000 ~ = ~{\color{red} 0,657}
\item   47,29 ~ : ~ 100 ~ = ~{\color{red} 0,472 9}
\item   1 896 ~ : ~ 10 ~ = ~{\color{red} 189,6}
\item   1,414 ~ : ~ 10 ~ = ~{\color{red} 0,141 4}
\item   1 286 ~ : ~ 100 ~ = ~{\color{red} 12,86}
\item   82,69 ~ : ~ 10 ~ = ~{\color{red} 8,269}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,159 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~159
\item   90,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~903
\item   2,54 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~254
\item   0,88 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,8
\item   9,69 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 690
\item   55,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~556
\item   0,033 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,3
\item   543 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~54 300
\item   77,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 740
\item   0,08 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   906,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 90,67
}\item   84,29 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,084 29
}\item   400 ~ \(\times\)  0,01 ~ = ~{\color{red} 4
}\item   69,63 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,963
}\item   41,96 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,041 96
}\item   6 528 ~ \(\times\)  0,1 ~ = ~{\color{red} 652,8
}\item   9 072 ~ \(\times\)  0,01 ~ = ~{\color{red} 90,72
}\item   0,492 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,004 92
}\item   14,65 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,014 65
}\item   253,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,532
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 916 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,916
\item   44,16 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,044 16
\item   3,417 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,341 7
\item   5,003 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 003
\item   734 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,34
\item   7 624 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,624
\item   4 456 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 44,56
\item   1 631 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,631
\item   17,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,75
\item   4,049 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,404 9
\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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   433,08 ~mL~ = {\color{red}  4,330 8 }~dL
\item   945,91 ~mg~ = {\color{red}  0,009 459 1 }~hg
\item   442 ~dag~ = {\color{red}  44 200 }~dg
\item   910,03 ~kL~ = {\color{red}  9 100,3 }~hL
\item   7 558,5 ~dag~ = {\color{red}  75,585 }~kg
\item   875,19 ~cg~ = {\color{red}  0,875 19 }~dag
\item   903,74 ~m~ = {\color{red}  9 037,4 }~dm
\item   327,28 ~mg~ = {\color{red}  3,272 8 }~dg
\item   316,04 ~daL~ = {\color{red}  31,604 }~hL
\item   9 195 ~cL~ = {\color{red}  9,195 }~daL
\end{itemize}
\end{multicols}
\end{document}
