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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 54}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{72}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{73}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   39,8  ~ \(\times\)  ~ 100
\item   0,035  ~ \(\times\)  ~ 1 000
\item   40  ~ \(\times\)  ~ 1 000
\item   213  ~ \(\times\)  ~ 100
\item   0,083  ~ \(\times\)  ~ 100
\item   621  ~ \(\times\)  ~ 1 000
\item   0,036  ~ \(\times\)  ~ 100
\item   0,962  ~ \(\times\)  ~ 100
\item   56,6  ~ \(\times\)  ~ 10
\item   6,7  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 273  ~ : ~ 100
\item   3,08  ~ : ~ 100
\item   10,7  ~ : ~ 1 000
\item   43,8  ~ : ~ 1 000
\item   2,336  ~ : ~ 10
\item   52,5  ~ : ~ 100
\item   633,4  ~ : ~ 100
\item   401,8  ~ : ~ 1 000
\item   0,363  ~ : ~ 1 000
\item   39,55  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,438  ~ \(\times\)  ~ ... ~ = ~ 43,8
\item   9,24  ~ \(\times\)  ~ ... ~ = ~ 9 240
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 2,8
\item   31,1  ~ \(\times\)  ~ ... ~ = ~ 3 110
\item   5,04  ~ \(\times\)  ~ ... ~ = ~ 50,4
\item   920  ~ \(\times\)  ~ ... ~ = ~ 920 000
\item   0,526  ~ \(\times\)  ~ ... ~ = ~ 5,26
\item   0,525  ~ \(\times\)  ~ ... ~ = ~ 5,25
\item   0,96  ~ \(\times\)  ~ ... ~ = ~ 960
\item   0,036  ~ \(\times\)  ~ ... ~ = ~ 3,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   53,27  ~ \(\times\)  ~ 0,1
\item   16,94  ~ \(\times\)  ~ 0,01
\item   6,668  ~ \(\times\)  ~ 0,01
\item   2,278  ~ \(\times\)  ~ 0,01
\item   5,295  ~ \(\times\)  ~ 0,01
\item   9 567  ~ \(\times\)  ~ 0,1
\item   88,9  ~ \(\times\)  ~ 0,01
\item   421,5  ~ \(\times\)  ~ 0,01
\item   57,22  ~ \(\times\)  ~ 0,001
\item   21,64  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 812  ~ \(\times\)  ~ ... ~ = ~  48,12
\item   164,9  ~ \(\times\)  ~ ... ~ = ~  0,164 9
\item   211,5  ~ \(\times\)  ~ ... ~ = ~  21,15
\item   41,2  ~ \(\times\)  ~ ... ~ = ~  4,12
\item   321,8  ~ \(\times\)  ~ ... ~ = ~  0,321 8
\item   55,53  ~ \(\times\)  ~ ... ~ = ~  0,555 3
\item   364,2  ~ \(\times\)  ~ ... ~ = ~  3,642
\item   4 358  ~ \(\times\)  ~ ... ~ = ~  4,358
\item   721  ~ \(\times\)  ~ ... ~ = ~  72,1
\item   31,24  ~ \(\times\)  ~ ... ~ = ~  0,312 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 ~cm~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   398,26 ~hm~ = ...~dm
\item   4 772,3 ~dm~ = ...~m
\item   1 335,2 ~kg~ = ...~dag
\item   8 614,8 ~kL~ = ...~daL
\item   8 331,6 ~hg~ = ...~dag
\item   5 525,9 ~mL~ = ...~cL
\item   4 744,7 ~hg~ = ...~kg
\item   2 622,3 ~dm~ = ...~km
\item   1 664,5 ~cm~ = ...~hm
\item   1 949,9 ~mm~ = ...~m
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{8200}{100}\) = \(\dfrac{820}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{72}{10}\) = \(\dfrac{720}{100}\)
\item   \(\dfrac{73}{100}\) = \(\dfrac{730}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   39,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 980}
\item   0,035  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 35}
\item   40  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 40 000}
\item   213  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 21 300}
\item   0,083  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,3}
\item   621  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 621 000}
\item   0,036  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,6}
\item   0,962  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 96,2}
\item   56,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 566}
\item   6,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 670}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 273 ~ : ~ 100 ~ = ~{\color{red} 72,73}
\item   3,08 ~ : ~ 100 ~ = ~{\color{red} 0,030 8}
\item   10,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,010 7}
\item   43,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,043 8}
\item   2,336 ~ : ~ 10 ~ = ~{\color{red} 0,233 6}
\item   52,5 ~ : ~ 100 ~ = ~{\color{red} 0,525}
\item   633,4 ~ : ~ 100 ~ = ~{\color{red} 6,334}
\item   401,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,401 8}
\item   0,363 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 363}
\item   39,55 ~ : ~ 100 ~ = ~{\color{red} 0,395 5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,438 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~43,8
\item   9,24 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 240
\item   0,028 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,8
\item   31,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 110
\item   5,04 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~50,4
\item   920 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~920 000
\item   0,526 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,26
\item   0,525 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,25
\item   0,96 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~960
\item   0,036 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   53,27 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,327
}\item   16,94 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,169 4
}\item   6,668 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,066 68
}\item   2,278 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,022 78
}\item   5,295 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,052 95
}\item   9 567 ~ \(\times\)  0,1 ~ = ~{\color{red} 956,7
}\item   88,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,889
}\item   421,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,215
}\item   57,22 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,057 22
}\item   21,64 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,021 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   4 812 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 48,12
\item   164,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,164 9
\item   211,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 21,15
\item   41,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,12
\item   321,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,321 8
\item   55,53 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,555 3
\item   364,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,642
\item   4 358 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,358
\item   721 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 72,1
\item   31,24 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,312 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 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   398,26 ~hm~ = {\color{red}  398 260 }~dm
\item   4 772,3 ~dm~ = {\color{red}  477,23 }~m
\item   1 335,2 ~kg~ = {\color{red}  133 520 }~dag
\item   8 614,8 ~kL~ = {\color{red}  861 480 }~daL
\item   8 331,6 ~hg~ = {\color{red}  83 316 }~dag
\item   5 525,9 ~mL~ = {\color{red}  552,59 }~cL
\item   4 744,7 ~hg~ = {\color{red}  474,47 }~kg
\item   2 622,3 ~dm~ = {\color{red}  0,262 23 }~km
\item   1 664,5 ~cm~ = {\color{red}  0,166 45 }~hm
\item   1 949,9 ~mm~ = {\color{red}  1,949 9 }~m
\end{itemize}
\end{multicols}
\end{document}
