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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 26}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{18}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{27}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,803  ~ \(\times\)  ~ 10
\item   0,076  ~ \(\times\)  ~ 1 000
\item   0,184  ~ \(\times\)  ~ 10
\item   0,774  ~ \(\times\)  ~ 1 000
\item   87,3  ~ \(\times\)  ~ 1 000
\item   885  ~ \(\times\)  ~ 1 000
\item   96,9  ~ \(\times\)  ~ 10
\item   14,1  ~ \(\times\)  ~ 1 000
\item   0,503  ~ \(\times\)  ~ 100
\item   0,026  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,98  ~ : ~ 1 000
\item   8 894  ~ : ~ 1 000
\item   819  ~ : ~ 100
\item   92,94  ~ : ~ 100
\item   7,038  ~ : ~ 1 000
\item   3 389  ~ : ~ 100
\item   3,334  ~ : ~ 100
\item   859,3  ~ : ~ 10
\item   1 729  ~ : ~ 10
\item   9 029  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42,5  ~ \(\times\)  ~ ... ~ = ~ 4 250
\item   619  ~ \(\times\)  ~ ... ~ = ~ 619 000
\item   343  ~ \(\times\)  ~ ... ~ = ~ 34 300
\item   811  ~ \(\times\)  ~ ... ~ = ~ 81 100
\item   0,732  ~ \(\times\)  ~ ... ~ = ~ 732
\item   85  ~ \(\times\)  ~ ... ~ = ~ 8 500
\item   10,7  ~ \(\times\)  ~ ... ~ = ~ 107
\item   1,45  ~ \(\times\)  ~ ... ~ = ~ 145
\item   0,091  ~ \(\times\)  ~ ... ~ = ~ 91
\item   0,723  ~ \(\times\)  ~ ... ~ = ~ 72,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,64  ~ \(\times\)  ~ 0,001
\item   6 491  ~ \(\times\)  ~ 0,1
\item   2 590  ~ \(\times\)  ~ 0,001
\item   1,928  ~ \(\times\)  ~ 0,1
\item   963,6  ~ \(\times\)  ~ 0,001
\item   659  ~ \(\times\)  ~ 0,01
\item   8,98  ~ \(\times\)  ~ 0,01
\item   2 786  ~ \(\times\)  ~ 0,01
\item   2 868  ~ \(\times\)  ~ 0,1
\item   642  ~ \(\times\)  ~ 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   7 036  ~ \(\times\)  ~ ... ~ = ~  70,36
\item   81,38  ~ \(\times\)  ~ ... ~ = ~  0,081 38
\item   9,061  ~ \(\times\)  ~ ... ~ = ~  0,906 1
\item   1 749  ~ \(\times\)  ~ ... ~ = ~  174,9
\item   730,4  ~ \(\times\)  ~ ... ~ = ~  7,304
\item   394  ~ \(\times\)  ~ ... ~ = ~  0,394
\item   8,295  ~ \(\times\)  ~ ... ~ = ~  0,082 95
\item   5 283  ~ \(\times\)  ~ ... ~ = ~  5,283
\item   118,2  ~ \(\times\)  ~ ... ~ = ~  0,118 2
\item   824  ~ \(\times\)  ~ ... ~ = ~  82,4
\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 ~dam~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   289,72 ~cg~ = ...~mg
\item   690,49 ~mg~ = ...~dg
\item   3 061,4 ~mm~ = ...~hm
\item   3 817,6 ~mg~ = ...~cg
\item   6 413,1 ~dag~ = ...~kg
\item   1 639,4 ~L~ = ...~cL
\item   509,69 ~kg~ = ...~mg
\item   926,05 ~mL~ = ...~L
\item   4 701,4 ~cm~ = ...~mm
\item   573,15 ~km~ = ...~mm
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{18}{10}\) = \(\dfrac{180}{100}\)
\item   \(\dfrac{27}{100}\) = \(\dfrac{270}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,803  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,03}
\item   0,076  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 76}
\item   0,184  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,84}
\item   0,774  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 774}
\item   87,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 87 300}
\item   885  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 885 000}
\item   96,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 969}
\item   14,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 14 100}
\item   0,503  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 50,3}
\item   0,026  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,26}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,98 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 98}
\item   8 894 ~ : ~ 1 000 ~ = ~{\color{red} 8,894}
\item   819 ~ : ~ 100 ~ = ~{\color{red} 8,19}
\item   92,94 ~ : ~ 100 ~ = ~{\color{red} 0,929 4}
\item   7,038 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 038}
\item   3 389 ~ : ~ 100 ~ = ~{\color{red} 33,89}
\item   3,334 ~ : ~ 100 ~ = ~{\color{red} 0,033 34}
\item   859,3 ~ : ~ 10 ~ = ~{\color{red} 85,93}
\item   1 729 ~ : ~ 10 ~ = ~{\color{red} 172,9}
\item   9 029 ~ : ~ 10 ~ = ~{\color{red} 902,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 250
\item   619 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~619 000
\item   343 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~34 300
\item   811 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~81 100
\item   0,732 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~732
\item   85 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 500
\item   10,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~107
\item   1,45 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~145
\item   0,091 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~91
\item   0,723 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~72,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,64 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 64
}\item   6 491 ~ \(\times\)  0,1 ~ = ~{\color{red} 649,1
}\item   2 590 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,59
}\item   1,928 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,192 8
}\item   963,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,963 6
}\item   659 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,59
}\item   8,98 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,089 8
}\item   2 786 ~ \(\times\)  0,01 ~ = ~{\color{red} 27,86
}\item   2 868 ~ \(\times\)  0,1 ~ = ~{\color{red} 286,8
}\item   642 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,642
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 036 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 70,36
\item   81,38 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,081 38
\item   9,061 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,906 1
\item   1 749 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 174,9
\item   730,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,304
\item   394 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,394
\item   8,295 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,082 95
\item   5 283 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,283
\item   118,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,118 2
\item   824 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 82,4
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   289,72 ~cg~ = {\color{red}  2 897,2 }~mg
\item   690,49 ~mg~ = {\color{red}  6,904 9 }~dg
\item   3 061,4 ~mm~ = {\color{red}  0,030 614 }~hm
\item   3 817,6 ~mg~ = {\color{red}  381,76 }~cg
\item   6 413,1 ~dag~ = {\color{red}  64,131 }~kg
\item   1 639,4 ~L~ = {\color{red}  163 940 }~cL
\item   509,69 ~kg~ = {\color{red}  509 690 000 }~mg
\item   926,05 ~mL~ = {\color{red}  0,926 05 }~L
\item   4 701,4 ~cm~ = {\color{red}  47 014 }~mm
\item   573,15 ~km~ = {\color{red}  573 150 000 }~mm
\end{itemize}
\end{multicols}
\end{document}
