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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 285}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{43}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,364  ~ \(\times\)  ~ 100
\item   0,59  ~ \(\times\)  ~ 100
\item   86  ~ \(\times\)  ~ 1 000
\item   73,3  ~ \(\times\)  ~ 100
\item   423  ~ \(\times\)  ~ 10
\item   0,038  ~ \(\times\)  ~ 100
\item   77,8  ~ \(\times\)  ~ 10
\item   809  ~ \(\times\)  ~ 100
\item   0,011  ~ \(\times\)  ~ 100
\item   0,185  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,709  ~ : ~ 100
\item   918,8  ~ : ~ 1 000
\item   76,64  ~ : ~ 100
\item   735,2  ~ : ~ 100
\item   575,5  ~ : ~ 100
\item   136,3  ~ : ~ 100
\item   353,8  ~ : ~ 10
\item   3 758  ~ : ~ 100
\item   168,6  ~ : ~ 100
\item   9 531  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,45  ~ \(\times\)  ~ ... ~ = ~ 450
\item   370  ~ \(\times\)  ~ ... ~ = ~ 3 700
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 0,64
\item   8,73  ~ \(\times\)  ~ ... ~ = ~ 87,3
\item   0,82  ~ \(\times\)  ~ ... ~ = ~ 820
\item   0,42  ~ \(\times\)  ~ ... ~ = ~ 420
\item   0,066  ~ \(\times\)  ~ ... ~ = ~ 6,6
\item   629  ~ \(\times\)  ~ ... ~ = ~ 62 900
\item   341  ~ \(\times\)  ~ ... ~ = ~ 341 000
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 0,02
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   94,83  ~ \(\times\)  ~ 0,1
\item   335,3  ~ \(\times\)  ~ 0,01
\item   678,5  ~ \(\times\)  ~ 0,1
\item   51,62  ~ \(\times\)  ~ 0,001
\item   7 197  ~ \(\times\)  ~ 0,001
\item   1,533  ~ \(\times\)  ~ 0,01
\item   33,17  ~ \(\times\)  ~ 0,1
\item   957,5  ~ \(\times\)  ~ 0,001
\item   83,6  ~ \(\times\)  ~ 0,01
\item   1,921  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   903,7  ~ \(\times\)  ~ ... ~ = ~  90,37
\item   7,201  ~ \(\times\)  ~ ... ~ = ~  0,720 1
\item   28,5  ~ \(\times\)  ~ ... ~ = ~  2,85
\item   81  ~ \(\times\)  ~ ... ~ = ~  0,081
\item   314,3  ~ \(\times\)  ~ ... ~ = ~  0,314 3
\item   944,6  ~ \(\times\)  ~ ... ~ = ~  9,446
\item   869  ~ \(\times\)  ~ ... ~ = ~  8,69
\item   638,9  ~ \(\times\)  ~ ... ~ = ~  63,89
\item   9,778  ~ \(\times\)  ~ ... ~ = ~  0,977 8
\item   20,2  ~ \(\times\)  ~ ... ~ = ~  0,020 2
\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 ~hm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   402,93 ~daL~ = ...~dL
\item   9 655,9 ~g~ = ...~kg
\item   825,84 ~mg~ = ...~dag
\item   400,98 ~cm~ = ...~hm
\item   139,42 ~km~ = ...~m
\item   676,98 ~dag~ = ...~hg
\item   7 172,7 ~daL~ = ...~cL
\item   8 170,7 ~dam~ = ...~mm
\item   4 895,7 ~kg~ = ...~dg
\item   539,47 ~cm~ = ...~mm
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{8300}{100}\) = \(\dfrac{830}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{22}{10}\) = \(\dfrac{220}{100}\)
\item   \(\dfrac{43}{100}\) = \(\dfrac{430}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,364  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 36,4}
\item   0,59  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 59}
\item   86  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 86 000}
\item   73,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 330}
\item   423  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 230}
\item   0,038  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,8}
\item   77,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 778}
\item   809  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80 900}
\item   0,011  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,1}
\item   0,185  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,85}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,709 ~ : ~ 100 ~ = ~{\color{red} 0,017 09}
\item   918,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,918 8}
\item   76,64 ~ : ~ 100 ~ = ~{\color{red} 0,766 4}
\item   735,2 ~ : ~ 100 ~ = ~{\color{red} 7,352}
\item   575,5 ~ : ~ 100 ~ = ~{\color{red} 5,755}
\item   136,3 ~ : ~ 100 ~ = ~{\color{red} 1,363}
\item   353,8 ~ : ~ 10 ~ = ~{\color{red} 35,38}
\item   3 758 ~ : ~ 100 ~ = ~{\color{red} 37,58}
\item   168,6 ~ : ~ 100 ~ = ~{\color{red} 1,686}
\item   9 531 ~ : ~ 100 ~ = ~{\color{red} 95,31}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,45 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~450
\item   370 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 700
\item   0,064 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,64
\item   8,73 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~87,3
\item   0,82 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~820
\item   0,42 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~420
\item   0,066 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,6
\item   629 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~62 900
\item   341 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~341 000
\item   0,002 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,02
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   94,83 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,483
}\item   335,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,353
}\item   678,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 67,85
}\item   51,62 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,051 62
}\item   7 197 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,197
}\item   1,533 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,015 33
}\item   33,17 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,317
}\item   957,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,957 5
}\item   83,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,836
}\item   1,921 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,192 1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   903,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 90,37
\item   7,201 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,720 1
\item   28,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,85
\item   81 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,081
\item   314,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,314 3
\item   944,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,446
\item   869 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,69
\item   638,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 63,89
\item   9,778 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,977 8
\item   20,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,020 2
\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 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   402,93 ~daL~ = {\color{red}  40 293 }~dL
\item   9 655,9 ~g~ = {\color{red}  9,655 9 }~kg
\item   825,84 ~mg~ = {\color{red}  0,082 584 }~dag
\item   400,98 ~cm~ = {\color{red}  0,040 098 }~hm
\item   139,42 ~km~ = {\color{red}  139 420 }~m
\item   676,98 ~dag~ = {\color{red}  67,698 }~hg
\item   7 172,7 ~daL~ = {\color{red}  7 172 700 }~cL
\item   8 170,7 ~dam~ = {\color{red}  81 707 000 }~mm
\item   4 895,7 ~kg~ = {\color{red}  48 957 000 }~dg
\item   539,47 ~cm~ = {\color{red}  5 394,7 }~mm
\end{itemize}
\end{multicols}
\end{document}
