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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 370}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{96}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   947  ~ \(\times\)  ~ 100
\item   0,064  ~ \(\times\)  ~ 10
\item   601  ~ \(\times\)  ~ 100
\item   0,6  ~ \(\times\)  ~ 1 000
\item   5,98  ~ \(\times\)  ~ 1 000
\item   57  ~ \(\times\)  ~ 100
\item   368  ~ \(\times\)  ~ 100
\item   3,99  ~ \(\times\)  ~ 1 000
\item   88,3  ~ \(\times\)  ~ 10
\item   0,028  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   60,14  ~ : ~ 10
\item   882,9  ~ : ~ 1 000
\item   956,6  ~ : ~ 10
\item   6,021  ~ : ~ 100
\item   1 980  ~ : ~ 100
\item   4,953  ~ : ~ 1 000
\item   893,7  ~ : ~ 10
\item   7,797  ~ : ~ 1 000
\item   4 509  ~ : ~ 100
\item   89,72  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   261  ~ \(\times\)  ~ ... ~ = ~ 26 100
\item   0,019  ~ \(\times\)  ~ ... ~ = ~ 19
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 0,28
\item   7,7  ~ \(\times\)  ~ ... ~ = ~ 770
\item   881  ~ \(\times\)  ~ ... ~ = ~ 88 100
\item   38,2  ~ \(\times\)  ~ ... ~ = ~ 3 820
\item   0,013  ~ \(\times\)  ~ ... ~ = ~ 1,3
\item   21,5  ~ \(\times\)  ~ ... ~ = ~ 215
\item   0,961  ~ \(\times\)  ~ ... ~ = ~ 96,1
\item   0,018  ~ \(\times\)  ~ ... ~ = ~ 1,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 101  ~ \(\times\)  ~ 0,1
\item   88,7  ~ \(\times\)  ~ 0,01
\item   3,241  ~ \(\times\)  ~ 0,01
\item   35,07  ~ \(\times\)  ~ 0,001
\item   7 319  ~ \(\times\)  ~ 0,01
\item   182,3  ~ \(\times\)  ~ 0,1
\item   5 672  ~ \(\times\)  ~ 0,1
\item   3 551  ~ \(\times\)  ~ 0,1
\item   2 997  ~ \(\times\)  ~ 0,01
\item   0,564  ~ \(\times\)  ~ 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   390  ~ \(\times\)  ~ ... ~ = ~  3,9
\item   304,9  ~ \(\times\)  ~ ... ~ = ~  30,49
\item   8,574  ~ \(\times\)  ~ ... ~ = ~  0,008 574
\item   3,098  ~ \(\times\)  ~ ... ~ = ~  0,003 098
\item   2,69  ~ \(\times\)  ~ ... ~ = ~  0,002 69
\item   4 808  ~ \(\times\)  ~ ... ~ = ~  48,08
\item   6,48  ~ \(\times\)  ~ ... ~ = ~  0,064 8
\item   5 337  ~ \(\times\)  ~ ... ~ = ~  5,337
\item   2,264  ~ \(\times\)  ~ ... ~ = ~  0,022 64
\item   82,61  ~ \(\times\)  ~ ... ~ = ~  0,082 61
\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~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   736,85 ~cL~ = ...~mL
\item   491,62 ~g~ = ...~dag
\item   4 435,2 ~L~ = ...~cL
\item   5 451,6 ~kL~ = ...~dL
\item   3 728 ~km~ = ...~hm
\item   527,48 ~mL~ = ...~hL
\item   302,61 ~dam~ = ...~km
\item   527,75 ~g~ = ...~hg
\item   1 839 ~L~ = ...~mL
\item   4 493,7 ~L~ = ...~dL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{8600}{100}\) = \(\dfrac{860}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{460}{100}\)
\item   \(\dfrac{96}{100}\) = \(\dfrac{960}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   947  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 94 700}
\item   0,064  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,64}
\item   601  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 60 100}
\item   0,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 600}
\item   5,98  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 980}
\item   57  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 700}
\item   368  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 36 800}
\item   3,99  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 990}
\item   88,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 883}
\item   0,028  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,28}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   60,14 ~ : ~ 10 ~ = ~{\color{red} 6,014}
\item   882,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,882 9}
\item   956,6 ~ : ~ 10 ~ = ~{\color{red} 95,66}
\item   6,021 ~ : ~ 100 ~ = ~{\color{red} 0,060 21}
\item   1 980 ~ : ~ 100 ~ = ~{\color{red} 19,8}
\item   4,953 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 953}
\item   893,7 ~ : ~ 10 ~ = ~{\color{red} 89,37}
\item   7,797 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 797}
\item   4 509 ~ : ~ 100 ~ = ~{\color{red} 45,09}
\item   89,72 ~ : ~ 1 000 ~ = ~{\color{red} 0,089 72}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   261 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~26 100
\item   0,019 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~19
\item   0,028 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,28
\item   7,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~770
\item   881 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88 100
\item   38,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 820
\item   0,013 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,3
\item   21,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~215
\item   0,961 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96,1
\item   0,018 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 101 ~ \(\times\)  0,1 ~ = ~{\color{red} 210,1
}\item   88,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,887
}\item   3,241 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,032 41
}\item   35,07 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,035 07
}\item   7 319 ~ \(\times\)  0,01 ~ = ~{\color{red} 73,19
}\item   182,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 18,23
}\item   5 672 ~ \(\times\)  0,1 ~ = ~{\color{red} 567,2
}\item   3 551 ~ \(\times\)  0,1 ~ = ~{\color{red} 355,1
}\item   2 997 ~ \(\times\)  0,01 ~ = ~{\color{red} 29,97
}\item   0,564 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,005 64
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   390 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,9
\item   304,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 30,49
\item   8,574 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 574
\item   3,098 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 098
\item   2,69 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 69
\item   4 808 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 48,08
\item   6,48 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,064 8
\item   5 337 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,337
\item   2,264 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,022 64
\item   82,61 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,082 61
\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~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   736,85 ~cL~ = {\color{red}  7 368,5 }~mL
\item   491,62 ~g~ = {\color{red}  49,162 }~dag
\item   4 435,2 ~L~ = {\color{red}  443 520 }~cL
\item   5 451,6 ~kL~ = {\color{red}  54 516 000 }~dL
\item   3 728 ~km~ = {\color{red}  37 280 }~hm
\item   527,48 ~mL~ = {\color{red}  0,005 274 8 }~hL
\item   302,61 ~dam~ = {\color{red}  3,026 1 }~km
\item   527,75 ~g~ = {\color{red}  5,277 5 }~hg
\item   1 839 ~L~ = {\color{red}  1 839 000 }~mL
\item   4 493,7 ~L~ = {\color{red}  44 937 }~dL
\end{itemize}
\end{multicols}
\end{document}
