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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 277}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,079  ~ \(\times\)  ~ 10
\item   0,644  ~ \(\times\)  ~ 100
\item   0,098  ~ \(\times\)  ~ 1 000
\item   0,06  ~ \(\times\)  ~ 10
\item   23,6  ~ \(\times\)  ~ 1 000
\item   9,86  ~ \(\times\)  ~ 10
\item   8,2  ~ \(\times\)  ~ 100
\item   501  ~ \(\times\)  ~ 10
\item   0,048  ~ \(\times\)  ~ 10
\item   0,048  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 403  ~ : ~ 100
\item   670,4  ~ : ~ 100
\item   6,615  ~ : ~ 10
\item   2,959  ~ : ~ 10
\item   2 196  ~ : ~ 100
\item   934,3  ~ : ~ 100
\item   3 221  ~ : ~ 10
\item   6 387  ~ : ~ 100
\item   262  ~ : ~ 10
\item   16,38  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,06  ~ \(\times\)  ~ ... ~ = ~ 206
\item   4,88  ~ \(\times\)  ~ ... ~ = ~ 488
\item   0,771  ~ \(\times\)  ~ ... ~ = ~ 7,71
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 0,43
\item   5,77  ~ \(\times\)  ~ ... ~ = ~ 577
\item   1,49  ~ \(\times\)  ~ ... ~ = ~ 1 490
\item   237  ~ \(\times\)  ~ ... ~ = ~ 2 370
\item   9,71  ~ \(\times\)  ~ ... ~ = ~ 971
\item   0,731  ~ \(\times\)  ~ ... ~ = ~ 73,1
\item   5,02  ~ \(\times\)  ~ ... ~ = ~ 502
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 562  ~ \(\times\)  ~ 0,1
\item   8,988  ~ \(\times\)  ~ 0,1
\item   75,69  ~ \(\times\)  ~ 0,1
\item   474,1  ~ \(\times\)  ~ 0,001
\item   7 811  ~ \(\times\)  ~ 0,001
\item   3 782  ~ \(\times\)  ~ 0,01
\item   6,058  ~ \(\times\)  ~ 0,01
\item   253,4  ~ \(\times\)  ~ 0,01
\item   38,39  ~ \(\times\)  ~ 0,1
\item   1,97  ~ \(\times\)  ~ 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   99,4  ~ \(\times\)  ~ ... ~ = ~  9,94
\item   72,55  ~ \(\times\)  ~ ... ~ = ~  0,725 5
\item   6 209  ~ \(\times\)  ~ ... ~ = ~  6,209
\item   9 416  ~ \(\times\)  ~ ... ~ = ~  9,416
\item   86,55  ~ \(\times\)  ~ ... ~ = ~  0,086 55
\item   1 908  ~ \(\times\)  ~ ... ~ = ~  190,8
\item   1 855  ~ \(\times\)  ~ ... ~ = ~  1,855
\item   935,3  ~ \(\times\)  ~ ... ~ = ~  0,935 3
\item   5 003  ~ \(\times\)  ~ ... ~ = ~  500,3
\item   8,468  ~ \(\times\)  ~ ... ~ = ~  0,846 8
\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 ~m~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   137,95 ~kL~ = ...~L
\item   3 359 ~m~ = ...~dam
\item   146,3 ~hg~ = ...~g
\item   727,71 ~mg~ = ...~dg
\item   5 055,7 ~cg~ = ...~mg
\item   6 971 ~kg~ = ...~mg
\item   8 914,7 ~L~ = ...~cL
\item   4 911,4 ~hL~ = ...~cL
\item   683,04 ~mg~ = ...~cg
\item   7 365,5 ~dg~ = ...~hg
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{3800}{100}\) = \(\dfrac{380}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{320}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,079  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,79}
\item   0,644  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 64,4}
\item   0,098  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 98}
\item   0,06  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,6}
\item   23,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 23 600}
\item   9,86  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 98,6}
\item   8,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 820}
\item   501  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 010}
\item   0,048  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,48}
\item   0,048  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 48}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 403 ~ : ~ 100 ~ = ~{\color{red} 34,03}
\item   670,4 ~ : ~ 100 ~ = ~{\color{red} 6,704}
\item   6,615 ~ : ~ 10 ~ = ~{\color{red} 0,661 5}
\item   2,959 ~ : ~ 10 ~ = ~{\color{red} 0,295 9}
\item   2 196 ~ : ~ 100 ~ = ~{\color{red} 21,96}
\item   934,3 ~ : ~ 100 ~ = ~{\color{red} 9,343}
\item   3 221 ~ : ~ 10 ~ = ~{\color{red} 322,1}
\item   6 387 ~ : ~ 100 ~ = ~{\color{red} 63,87}
\item   262 ~ : ~ 10 ~ = ~{\color{red} 26,2}
\item   16,38 ~ : ~ 10 ~ = ~{\color{red} 1,638}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,06 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~206
\item   4,88 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~488
\item   0,771 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,71
\item   0,043 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,43
\item   5,77 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~577
\item   1,49 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 490
\item   237 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 370
\item   9,71 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~971
\item   0,731 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~73,1
\item   5,02 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~502
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 562 ~ \(\times\)  0,1 ~ = ~{\color{red} 256,2
}\item   8,988 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,898 8
}\item   75,69 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,569
}\item   474,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,474 1
}\item   7 811 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,811
}\item   3 782 ~ \(\times\)  0,01 ~ = ~{\color{red} 37,82
}\item   6,058 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,060 58
}\item   253,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,534
}\item   38,39 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,839
}\item   1,97 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 97
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   99,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,94
\item   72,55 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,725 5
\item   6 209 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,209
\item   9 416 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,416
\item   86,55 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,086 55
\item   1 908 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 190,8
\item   1 855 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,855
\item   935,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,935 3
\item   5 003 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 500,3
\item   8,468 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,846 8
\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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   137,95 ~kL~ = {\color{red}  137 950 }~L
\item   3 359 ~m~ = {\color{red}  335,9 }~dam
\item   146,3 ~hg~ = {\color{red}  14 630 }~g
\item   727,71 ~mg~ = {\color{red}  7,277 1 }~dg
\item   5 055,7 ~cg~ = {\color{red}  50 557 }~mg
\item   6 971 ~kg~ = {\color{red}  6 971 000 000 }~mg
\item   8 914,7 ~L~ = {\color{red}  891 470 }~cL
\item   4 911,4 ~hL~ = {\color{red}  49 114 000 }~cL
\item   683,04 ~mg~ = {\color{red}  68,304 }~cg
\item   7 365,5 ~dg~ = {\color{red}  7,365 5 }~hg
\end{itemize}
\end{multicols}
\end{document}
