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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 182}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{51}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,25  ~ \(\times\)  ~ 10
\item   8,12  ~ \(\times\)  ~ 10
\item   0,065  ~ \(\times\)  ~ 100
\item   7,18  ~ \(\times\)  ~ 10
\item   10,4  ~ \(\times\)  ~ 100
\item   786  ~ \(\times\)  ~ 1 000
\item   718  ~ \(\times\)  ~ 10
\item   59,3  ~ \(\times\)  ~ 1 000
\item   0,024  ~ \(\times\)  ~ 1 000
\item   859  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,946  ~ : ~ 1 000
\item   22,24  ~ : ~ 1 000
\item   831,4  ~ : ~ 100
\item   6,322  ~ : ~ 10
\item   3,449  ~ : ~ 10
\item   6,409  ~ : ~ 10
\item   7,247  ~ : ~ 1 000
\item   78,11  ~ : ~ 100
\item   422,9  ~ : ~ 10
\item   6 567  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,154  ~ \(\times\)  ~ ... ~ = ~ 15,4
\item   21,4  ~ \(\times\)  ~ ... ~ = ~ 214
\item   0,037  ~ \(\times\)  ~ ... ~ = ~ 0,37
\item   0,31  ~ \(\times\)  ~ ... ~ = ~ 310
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 0,68
\item   567  ~ \(\times\)  ~ ... ~ = ~ 5 670
\item   64  ~ \(\times\)  ~ ... ~ = ~ 6 400
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 0,58
\item   0,083  ~ \(\times\)  ~ ... ~ = ~ 0,83
\item   76,4  ~ \(\times\)  ~ ... ~ = ~ 7 640
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   22,72  ~ \(\times\)  ~ 0,001
\item   8,105  ~ \(\times\)  ~ 0,1
\item   6,226  ~ \(\times\)  ~ 0,001
\item   0,504  ~ \(\times\)  ~ 0,1
\item   423,1  ~ \(\times\)  ~ 0,01
\item   30,5  ~ \(\times\)  ~ 0,001
\item   3,658  ~ \(\times\)  ~ 0,1
\item   6 776  ~ \(\times\)  ~ 0,1
\item   13,67  ~ \(\times\)  ~ 0,001
\item   3 643  ~ \(\times\)  ~ 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   8 748  ~ \(\times\)  ~ ... ~ = ~  87,48
\item   11,78  ~ \(\times\)  ~ ... ~ = ~  0,117 8
\item   138  ~ \(\times\)  ~ ... ~ = ~  0,138
\item   98,18  ~ \(\times\)  ~ ... ~ = ~  9,818
\item   89,96  ~ \(\times\)  ~ ... ~ = ~  8,996
\item   424,2  ~ \(\times\)  ~ ... ~ = ~  4,242
\item   342,3  ~ \(\times\)  ~ ... ~ = ~  3,423
\item   1 299  ~ \(\times\)  ~ ... ~ = ~  1,299
\item   151,6  ~ \(\times\)  ~ ... ~ = ~  15,16
\item   925  ~ \(\times\)  ~ ... ~ = ~  92,5
\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 ~dam~ = ...~m
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   693,46 ~daL~ = ...~mL
\item   604,07 ~kg~ = ...~dg
\item   3 346,9 ~mL~ = ...~hL
\item   6 644 ~dam~ = ...~dm
\item   5 585 ~kL~ = ...~dL
\item   2 006,1 ~dag~ = ...~dg
\item   480,47 ~cL~ = ...~L
\item   8 692,4 ~mm~ = ...~dam
\item   1 132,4 ~dg~ = ...~mg
\item   395,68 ~cL~ = ...~dL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{4000}{100}\) = \(\dfrac{400}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{51}{10}\) = \(\dfrac{510}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{550}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,25  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 92,5}
\item   8,12  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 81,2}
\item   0,065  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,5}
\item   7,18  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 71,8}
\item   10,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 040}
\item   786  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 786 000}
\item   718  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 180}
\item   59,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 59 300}
\item   0,024  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 24}
\item   859  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 859 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,946 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 946}
\item   22,24 ~ : ~ 1 000 ~ = ~{\color{red} 0,022 24}
\item   831,4 ~ : ~ 100 ~ = ~{\color{red} 8,314}
\item   6,322 ~ : ~ 10 ~ = ~{\color{red} 0,632 2}
\item   3,449 ~ : ~ 10 ~ = ~{\color{red} 0,344 9}
\item   6,409 ~ : ~ 10 ~ = ~{\color{red} 0,640 9}
\item   7,247 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 247}
\item   78,11 ~ : ~ 100 ~ = ~{\color{red} 0,781 1}
\item   422,9 ~ : ~ 10 ~ = ~{\color{red} 42,29}
\item   6 567 ~ : ~ 100 ~ = ~{\color{red} 65,67}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,154 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~15,4
\item   21,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~214
\item   0,037 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,37
\item   0,31 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~310
\item   0,068 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,68
\item   567 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 670
\item   64 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 400
\item   0,058 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,58
\item   0,083 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,83
\item   76,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 640
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   22,72 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,022 72
}\item   8,105 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,810 5
}\item   6,226 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 226
}\item   0,504 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,050 4
}\item   423,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,231
}\item   30,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 5
}\item   3,658 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,365 8
}\item   6 776 ~ \(\times\)  0,1 ~ = ~{\color{red} 677,6
}\item   13,67 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,013 67
}\item   3 643 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,643
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 748 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 87,48
\item   11,78 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,117 8
\item   138 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,138
\item   98,18 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,818
\item   89,96 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,996
\item   424,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,242
\item   342,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,423
\item   1 299 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,299
\item   151,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 15,16
\item   925 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 92,5
\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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   693,46 ~daL~ = {\color{red}  6 934 600 }~mL
\item   604,07 ~kg~ = {\color{red}  6 040 700 }~dg
\item   3 346,9 ~mL~ = {\color{red}  0,033 469 }~hL
\item   6 644 ~dam~ = {\color{red}  664 400 }~dm
\item   5 585 ~kL~ = {\color{red}  55 850 000 }~dL
\item   2 006,1 ~dag~ = {\color{red}  200 610 }~dg
\item   480,47 ~cL~ = {\color{red}  4,804 7 }~L
\item   8 692,4 ~mm~ = {\color{red}  0,869 24 }~dam
\item   1 132,4 ~dg~ = {\color{red}  113 240 }~mg
\item   395,68 ~cL~ = {\color{red}  39,568 }~dL
\end{itemize}
\end{multicols}
\end{document}
