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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 249}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{80}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{31}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,017  ~ \(\times\)  ~ 1 000
\item   426  ~ \(\times\)  ~ 100
\item   572  ~ \(\times\)  ~ 1 000
\item   68,5  ~ \(\times\)  ~ 100
\item   81,6  ~ \(\times\)  ~ 10
\item   5,03  ~ \(\times\)  ~ 100
\item   5,71  ~ \(\times\)  ~ 10
\item   0,215  ~ \(\times\)  ~ 100
\item   930  ~ \(\times\)  ~ 100
\item   5,79  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 698  ~ : ~ 10
\item   121,3  ~ : ~ 100
\item   380  ~ : ~ 100
\item   69,65  ~ : ~ 10
\item   5 948  ~ : ~ 100
\item   383,4  ~ : ~ 100
\item   51,31  ~ : ~ 10
\item   4,509  ~ : ~ 10
\item   9,002  ~ : ~ 10
\item   617  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,19  ~ \(\times\)  ~ ... ~ = ~ 2 190
\item   0,242  ~ \(\times\)  ~ ... ~ = ~ 242
\item   0,038  ~ \(\times\)  ~ ... ~ = ~ 3,8
\item   0,816  ~ \(\times\)  ~ ... ~ = ~ 8,16
\item   0,248  ~ \(\times\)  ~ ... ~ = ~ 24,8
\item   302  ~ \(\times\)  ~ ... ~ = ~ 30 200
\item   65,4  ~ \(\times\)  ~ ... ~ = ~ 65 400
\item   53,1  ~ \(\times\)  ~ ... ~ = ~ 531
\item   7,97  ~ \(\times\)  ~ ... ~ = ~ 797
\item   606  ~ \(\times\)  ~ ... ~ = ~ 606 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 735  ~ \(\times\)  ~ 0,01
\item   2,472  ~ \(\times\)  ~ 0,001
\item   2 340  ~ \(\times\)  ~ 0,1
\item   2 614  ~ \(\times\)  ~ 0,001
\item   422,5  ~ \(\times\)  ~ 0,001
\item   33,67  ~ \(\times\)  ~ 0,1
\item   5,149  ~ \(\times\)  ~ 0,01
\item   5,077  ~ \(\times\)  ~ 0,001
\item   97,76  ~ \(\times\)  ~ 0,001
\item   9 213  ~ \(\times\)  ~ 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   8,475  ~ \(\times\)  ~ ... ~ = ~  0,008 475
\item   84,27  ~ \(\times\)  ~ ... ~ = ~  8,427
\item   23,79  ~ \(\times\)  ~ ... ~ = ~  2,379
\item   34,22  ~ \(\times\)  ~ ... ~ = ~  0,034 22
\item   18,09  ~ \(\times\)  ~ ... ~ = ~  1,809
\item   42,24  ~ \(\times\)  ~ ... ~ = ~  4,224
\item   5 097  ~ \(\times\)  ~ ... ~ = ~  5,097
\item   2,032  ~ \(\times\)  ~ ... ~ = ~  0,020 32
\item   14,74  ~ \(\times\)  ~ ... ~ = ~  0,014 74
\item   90,34  ~ \(\times\)  ~ ... ~ = ~  0,090 34
\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~ = ...~km
\item   1 ~m~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 625,5 ~L~ = ...~mL
\item   4 221,4 ~dm~ = ...~cm
\item   463,94 ~kL~ = ...~cL
\item   420,8 ~m~ = ...~km
\item   632,12 ~daL~ = ...~dL
\item   966,22 ~cL~ = ...~dL
\item   4 913,1 ~dg~ = ...~dag
\item   4 707,1 ~dam~ = ...~mm
\item   1 328,4 ~kL~ = ...~dL
\item   3 284,4 ~dag~ = ...~cg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{8700}{100}\) = \(\dfrac{870}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{80}{10}\) = \(\dfrac{800}{100}\)
\item   \(\dfrac{31}{100}\) = \(\dfrac{310}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,017  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 17}
\item   426  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 42 600}
\item   572  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 572 000}
\item   68,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 850}
\item   81,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 816}
\item   5,03  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 503}
\item   5,71  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 57,1}
\item   0,215  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 21,5}
\item   930  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 93 000}
\item   5,79  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 790}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 698 ~ : ~ 10 ~ = ~{\color{red} 769,8}
\item   121,3 ~ : ~ 100 ~ = ~{\color{red} 1,213}
\item   380 ~ : ~ 100 ~ = ~{\color{red} 3,8}
\item   69,65 ~ : ~ 10 ~ = ~{\color{red} 6,965}
\item   5 948 ~ : ~ 100 ~ = ~{\color{red} 59,48}
\item   383,4 ~ : ~ 100 ~ = ~{\color{red} 3,834}
\item   51,31 ~ : ~ 10 ~ = ~{\color{red} 5,131}
\item   4,509 ~ : ~ 10 ~ = ~{\color{red} 0,450 9}
\item   9,002 ~ : ~ 10 ~ = ~{\color{red} 0,900 2}
\item   617 ~ : ~ 100 ~ = ~{\color{red} 6,17}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,19 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 190
\item   0,242 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~242
\item   0,038 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,8
\item   0,816 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,16
\item   0,248 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~24,8
\item   302 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30 200
\item   65,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~65 400
\item   53,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~531
\item   7,97 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~797
\item   606 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~606 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 735 ~ \(\times\)  0,01 ~ = ~{\color{red} 77,35
}\item   2,472 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 472
}\item   2 340 ~ \(\times\)  0,1 ~ = ~{\color{red} 234
}\item   2 614 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,614
}\item   422,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,422 5
}\item   33,67 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,367
}\item   5,149 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,051 49
}\item   5,077 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 077
}\item   97,76 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,097 76
}\item   9 213 ~ \(\times\)  0,01 ~ = ~{\color{red} 92,13
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,475 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 475
\item   84,27 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,427
\item   23,79 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,379
\item   34,22 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,034 22
\item   18,09 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,809
\item   42,24 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,224
\item   5 097 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,097
\item   2,032 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,020 32
\item   14,74 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,014 74
\item   90,34 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,090 34
\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~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 625,5 ~L~ = {\color{red}  4 625 500 }~mL
\item   4 221,4 ~dm~ = {\color{red}  42 214 }~cm
\item   463,94 ~kL~ = {\color{red}  46 394 000 }~cL
\item   420,8 ~m~ = {\color{red}  0,420 8 }~km
\item   632,12 ~daL~ = {\color{red}  63 212 }~dL
\item   966,22 ~cL~ = {\color{red}  96,622 }~dL
\item   4 913,1 ~dg~ = {\color{red}  49,131 }~dag
\item   4 707,1 ~dam~ = {\color{red}  47 071 000 }~mm
\item   1 328,4 ~kL~ = {\color{red}  13 284 000 }~dL
\item   3 284,4 ~dag~ = {\color{red}  3 284 400 }~cg
\end{itemize}
\end{multicols}
\end{document}
