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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 394}

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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   \(\dfrac{5500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{20}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,45  ~ \(\times\)  ~ 10
\item   0,193  ~ \(\times\)  ~ 1 000
\item   0,22  ~ \(\times\)  ~ 100
\item   626  ~ \(\times\)  ~ 100
\item   0,075  ~ \(\times\)  ~ 100
\item   215  ~ \(\times\)  ~ 10
\item   0,099  ~ \(\times\)  ~ 10
\item   64,6  ~ \(\times\)  ~ 100
\item   9,73  ~ \(\times\)  ~ 1 000
\item   604  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,276  ~ : ~ 100
\item   0,137  ~ : ~ 100
\item   14,38  ~ : ~ 100
\item   75,25  ~ : ~ 10
\item   4,812  ~ : ~ 100
\item   16,06  ~ : ~ 10
\item   56,59  ~ : ~ 100
\item   8 673  ~ : ~ 1 000
\item   8 934  ~ : ~ 100
\item   56,17  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,214  ~ \(\times\)  ~ ... ~ = ~ 214
\item   4,46  ~ \(\times\)  ~ ... ~ = ~ 44,6
\item   0,73  ~ \(\times\)  ~ ... ~ = ~ 730
\item   39,8  ~ \(\times\)  ~ ... ~ = ~ 3 980
\item   710  ~ \(\times\)  ~ ... ~ = ~ 7 100
\item   0,913  ~ \(\times\)  ~ ... ~ = ~ 9,13
\item   1,87  ~ \(\times\)  ~ ... ~ = ~ 1 870
\item   7,61  ~ \(\times\)  ~ ... ~ = ~ 761
\item   54,7  ~ \(\times\)  ~ ... ~ = ~ 54 700
\item   22,7  ~ \(\times\)  ~ ... ~ = ~ 22 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   44,15  ~ \(\times\)  ~ 0,1
\item   7,342  ~ \(\times\)  ~ 0,001
\item   4 952  ~ \(\times\)  ~ 0,001
\item   7 554  ~ \(\times\)  ~ 0,001
\item   70,18  ~ \(\times\)  ~ 0,1
\item   45,5  ~ \(\times\)  ~ 0,001
\item   77,17  ~ \(\times\)  ~ 0,001
\item   4,274  ~ \(\times\)  ~ 0,001
\item   229  ~ \(\times\)  ~ 0,001
\item   901  ~ \(\times\)  ~ 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   3,407  ~ \(\times\)  ~ ... ~ = ~  0,034 07
\item   4 933  ~ \(\times\)  ~ ... ~ = ~  493,3
\item   4 929  ~ \(\times\)  ~ ... ~ = ~  4,929
\item   92,56  ~ \(\times\)  ~ ... ~ = ~  0,092 56
\item   7 892  ~ \(\times\)  ~ ... ~ = ~  7,892
\item   6,566  ~ \(\times\)  ~ ... ~ = ~  0,006 566
\item   543,5  ~ \(\times\)  ~ ... ~ = ~  0,543 5
\item   3 055  ~ \(\times\)  ~ ... ~ = ~  305,5
\item   7 236  ~ \(\times\)  ~ ... ~ = ~  723,6
\item   24,55  ~ \(\times\)  ~ ... ~ = ~  0,245 5
\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 ~km~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   509,4 ~daL~ = ...~mL
\item   4 817,1 ~dm~ = ...~m
\item   434,63 ~kg~ = ...~g
\item   8 201,3 ~dag~ = ...~dg
\item   8 808,1 ~dag~ = ...~kg
\item   3 737,6 ~hg~ = ...~cg
\item   8 611,6 ~cm~ = ...~mm
\item   502,22 ~hg~ = ...~mg
\item   1 830,1 ~L~ = ...~dL
\item   9 320,3 ~kL~ = ...~L
\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   \(\dfrac{5500}{100}\) = \(\dfrac{550}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{740}{100}\)
\item   \(\dfrac{20}{100}\) = \(\dfrac{200}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,45  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 34,5}
\item   0,193  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 193}
\item   0,22  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 22}
\item   626  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 62 600}
\item   0,075  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,5}
\item   215  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 150}
\item   0,099  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,99}
\item   64,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 460}
\item   9,73  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 730}
\item   604  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 040}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,276 ~ : ~ 100 ~ = ~{\color{red} 0,042 76}
\item   0,137 ~ : ~ 100 ~ = ~{\color{red} 0,001 37}
\item   14,38 ~ : ~ 100 ~ = ~{\color{red} 0,143 8}
\item   75,25 ~ : ~ 10 ~ = ~{\color{red} 7,525}
\item   4,812 ~ : ~ 100 ~ = ~{\color{red} 0,048 12}
\item   16,06 ~ : ~ 10 ~ = ~{\color{red} 1,606}
\item   56,59 ~ : ~ 100 ~ = ~{\color{red} 0,565 9}
\item   8 673 ~ : ~ 1 000 ~ = ~{\color{red} 8,673}
\item   8 934 ~ : ~ 100 ~ = ~{\color{red} 89,34}
\item   56,17 ~ : ~ 10 ~ = ~{\color{red} 5,617}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,214 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~214
\item   4,46 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~44,6
\item   0,73 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~730
\item   39,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 980
\item   710 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 100
\item   0,913 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,13
\item   1,87 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 870
\item   7,61 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~761
\item   54,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~54 700
\item   22,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~22 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   44,15 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,415
}\item   7,342 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 342
}\item   4 952 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,952
}\item   7 554 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,554
}\item   70,18 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,018
}\item   45,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,045 5
}\item   77,17 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,077 17
}\item   4,274 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 274
}\item   229 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,229
}\item   901 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,901
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,407 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,034 07
\item   4 933 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 493,3
\item   4 929 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,929
\item   92,56 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,092 56
\item   7 892 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,892
\item   6,566 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 566
\item   543,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,543 5
\item   3 055 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 305,5
\item   7 236 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 723,6
\item   24,55 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,245 5
\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 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   509,4 ~daL~ = {\color{red}  5 094 000 }~mL
\item   4 817,1 ~dm~ = {\color{red}  481,71 }~m
\item   434,63 ~kg~ = {\color{red}  434 630 }~g
\item   8 201,3 ~dag~ = {\color{red}  820 130 }~dg
\item   8 808,1 ~dag~ = {\color{red}  88,081 }~kg
\item   3 737,6 ~hg~ = {\color{red}  37 376 000 }~cg
\item   8 611,6 ~cm~ = {\color{red}  86 116 }~mm
\item   502,22 ~hg~ = {\color{red}  50 222 000 }~mg
\item   1 830,1 ~L~ = {\color{red}  18 301 }~dL
\item   9 320,3 ~kL~ = {\color{red}  9 320 300 }~L
\end{itemize}
\end{multicols}
\end{document}
