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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 69}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{88}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   0,034  ~ \(\times\)  ~ 100
\item   0,484  ~ \(\times\)  ~ 1 000
\item   0,046  ~ \(\times\)  ~ 100
\item   0,058  ~ \(\times\)  ~ 100
\item   0,154  ~ \(\times\)  ~ 100
\item   0,074  ~ \(\times\)  ~ 100
\item   15,9  ~ \(\times\)  ~ 10
\item   32,6  ~ \(\times\)  ~ 1 000
\item   0,095  ~ \(\times\)  ~ 10
\item   114  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,71  ~ : ~ 1 000
\item   6 197  ~ : ~ 10
\item   163,7  ~ : ~ 10
\item   247,8  ~ : ~ 10
\item   458,1  ~ : ~ 100
\item   14,2  ~ : ~ 1 000
\item   4,418  ~ : ~ 10
\item   4 280  ~ : ~ 1 000
\item   21,19  ~ : ~ 100
\item   456,4  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,509  ~ \(\times\)  ~ ... ~ = ~ 5,09
\item   0,029  ~ \(\times\)  ~ ... ~ = ~ 0,29
\item   0,961  ~ \(\times\)  ~ ... ~ = ~ 9,61
\item   6,79  ~ \(\times\)  ~ ... ~ = ~ 679
\item   0,505  ~ \(\times\)  ~ ... ~ = ~ 50,5
\item   0,069  ~ \(\times\)  ~ ... ~ = ~ 0,69
\item   5,54  ~ \(\times\)  ~ ... ~ = ~ 5 540
\item   0,083  ~ \(\times\)  ~ ... ~ = ~ 83
\item   398  ~ \(\times\)  ~ ... ~ = ~ 3 980
\item   0,819  ~ \(\times\)  ~ ... ~ = ~ 819
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   722,4  ~ \(\times\)  ~ 0,1
\item   6,064  ~ \(\times\)  ~ 0,1
\item   0,545  ~ \(\times\)  ~ 0,01
\item   41,24  ~ \(\times\)  ~ 0,01
\item   2 587  ~ \(\times\)  ~ 0,01
\item   1 986  ~ \(\times\)  ~ 0,01
\item   745,7  ~ \(\times\)  ~ 0,001
\item   91,04  ~ \(\times\)  ~ 0,1
\item   2,142  ~ \(\times\)  ~ 0,1
\item   9 208  ~ \(\times\)  ~ 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   1,3  ~ \(\times\)  ~ ... ~ = ~  0,13
\item   8,931  ~ \(\times\)  ~ ... ~ = ~  0,008 931
\item   88,68  ~ \(\times\)  ~ ... ~ = ~  8,868
\item   6,34  ~ \(\times\)  ~ ... ~ = ~  0,006 34
\item   4,259  ~ \(\times\)  ~ ... ~ = ~  0,425 9
\item   93,9  ~ \(\times\)  ~ ... ~ = ~  9,39
\item   4 826  ~ \(\times\)  ~ ... ~ = ~  4,826
\item   131,2  ~ \(\times\)  ~ ... ~ = ~  1,312
\item   3 189  ~ \(\times\)  ~ ... ~ = ~  31,89
\item   34,89  ~ \(\times\)  ~ ... ~ = ~  0,034 89
\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~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   717,48 ~hg~ = ...~mg
\item   645,63 ~daL~ = ...~cL
\item   281,81 ~L~ = ...~daL
\item   2 367,9 ~mm~ = ...~m
\item   1 804,2 ~daL~ = ...~mL
\item   5 616,2 ~daL~ = ...~dL
\item   827,03 ~L~ = ...~mL
\item   5 589,7 ~mm~ = ...~cm
\item   123,13 ~dL~ = ...~cL
\item   594,32 ~dm~ = ...~hm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{320}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{88}{10}\) = \(\dfrac{880}{100}\)
\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   0,034  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,4}
\item   0,484  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 484}
\item   0,046  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,6}
\item   0,058  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,8}
\item   0,154  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 15,4}
\item   0,074  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,4}
\item   15,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 159}
\item   32,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32 600}
\item   0,095  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,95}
\item   114  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 11 400}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,71 ~ : ~ 1 000 ~ = ~{\color{red} 0,011 71}
\item   6 197 ~ : ~ 10 ~ = ~{\color{red} 619,7}
\item   163,7 ~ : ~ 10 ~ = ~{\color{red} 16,37}
\item   247,8 ~ : ~ 10 ~ = ~{\color{red} 24,78}
\item   458,1 ~ : ~ 100 ~ = ~{\color{red} 4,581}
\item   14,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,014 2}
\item   4,418 ~ : ~ 10 ~ = ~{\color{red} 0,441 8}
\item   4 280 ~ : ~ 1 000 ~ = ~{\color{red} 4,28}
\item   21,19 ~ : ~ 100 ~ = ~{\color{red} 0,211 9}
\item   456,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,456 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,509 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,09
\item   0,029 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,29
\item   0,961 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,61
\item   6,79 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~679
\item   0,505 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~50,5
\item   0,069 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,69
\item   5,54 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 540
\item   0,083 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~83
\item   398 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 980
\item   0,819 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~819
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   722,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 72,24
}\item   6,064 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,606 4
}\item   0,545 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,005 45
}\item   41,24 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,412 4
}\item   2 587 ~ \(\times\)  0,01 ~ = ~{\color{red} 25,87
}\item   1 986 ~ \(\times\)  0,01 ~ = ~{\color{red} 19,86
}\item   745,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,745 7
}\item   91,04 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,104
}\item   2,142 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,214 2
}\item   9 208 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,208
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,13
\item   8,931 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 931
\item   88,68 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,868
\item   6,34 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 34
\item   4,259 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,425 9
\item   93,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,39
\item   4 826 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,826
\item   131,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,312
\item   3 189 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 31,89
\item   34,89 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,034 89
\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}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\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   717,48 ~hg~ = {\color{red}  71 748 000 }~mg
\item   645,63 ~daL~ = {\color{red}  645 630 }~cL
\item   281,81 ~L~ = {\color{red}  28,181 }~daL
\item   2 367,9 ~mm~ = {\color{red}  2,367 9 }~m
\item   1 804,2 ~daL~ = {\color{red}  18 042 000 }~mL
\item   5 616,2 ~daL~ = {\color{red}  561 620 }~dL
\item   827,03 ~L~ = {\color{red}  827 030 }~mL
\item   5 589,7 ~mm~ = {\color{red}  558,97 }~cm
\item   123,13 ~dL~ = {\color{red}  1 231,3 }~cL
\item   594,32 ~dm~ = {\color{red}  0,594 32 }~hm
\end{itemize}
\end{multicols}
\end{document}
