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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 276}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{45}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{46}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,013  ~ \(\times\)  ~ 10
\item   0,883  ~ \(\times\)  ~ 100
\item   2,1  ~ \(\times\)  ~ 100
\item   404  ~ \(\times\)  ~ 10
\item   7,36  ~ \(\times\)  ~ 10
\item   0,03  ~ \(\times\)  ~ 1 000
\item   883  ~ \(\times\)  ~ 10
\item   0,229  ~ \(\times\)  ~ 1 000
\item   0,45  ~ \(\times\)  ~ 100
\item   1,84  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,65  ~ : ~ 10
\item   1,293  ~ : ~ 1 000
\item   40  ~ : ~ 10
\item   67,12  ~ : ~ 1 000
\item   1,21  ~ : ~ 10
\item   8,491  ~ : ~ 1 000
\item   429,2  ~ : ~ 100
\item   85,2  ~ : ~ 1 000
\item   1,987  ~ : ~ 10
\item   7,714  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,597  ~ \(\times\)  ~ ... ~ = ~ 597
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 6,8
\item   888  ~ \(\times\)  ~ ... ~ = ~ 88 800
\item   15,9  ~ \(\times\)  ~ ... ~ = ~ 159
\item   0,469  ~ \(\times\)  ~ ... ~ = ~ 46,9
\item   700  ~ \(\times\)  ~ ... ~ = ~ 7 000
\item   4,34  ~ \(\times\)  ~ ... ~ = ~ 43,4
\item   0,477  ~ \(\times\)  ~ ... ~ = ~ 477
\item   0,029  ~ \(\times\)  ~ ... ~ = ~ 2,9
\item   18,5  ~ \(\times\)  ~ ... ~ = ~ 185
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   340,8  ~ \(\times\)  ~ 0,1
\item   9,619  ~ \(\times\)  ~ 0,01
\item   3 812  ~ \(\times\)  ~ 0,01
\item   8,602  ~ \(\times\)  ~ 0,001
\item   4 034  ~ \(\times\)  ~ 0,001
\item   7 623  ~ \(\times\)  ~ 0,1
\item   725,9  ~ \(\times\)  ~ 0,001
\item   5,859  ~ \(\times\)  ~ 0,001
\item   2 557  ~ \(\times\)  ~ 0,01
\item   11,71  ~ \(\times\)  ~ 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   2 544  ~ \(\times\)  ~ ... ~ = ~  25,44
\item   6 395  ~ \(\times\)  ~ ... ~ = ~  6,395
\item   64,48  ~ \(\times\)  ~ ... ~ = ~  0,064 48
\item   2,868  ~ \(\times\)  ~ ... ~ = ~  0,286 8
\item   3 958  ~ \(\times\)  ~ ... ~ = ~  395,8
\item   765,7  ~ \(\times\)  ~ ... ~ = ~  0,765 7
\item   8 675  ~ \(\times\)  ~ ... ~ = ~  86,75
\item   322,3  ~ \(\times\)  ~ ... ~ = ~  0,322 3
\item   9 806  ~ \(\times\)  ~ ... ~ = ~  98,06
\item   681,5  ~ \(\times\)  ~ ... ~ = ~  68,15
\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~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 022,6 ~L~ = ...~kL
\item   907,9 ~cg~ = ...~dag
\item   3 570,6 ~dg~ = ...~cg
\item   4 681,7 ~dam~ = ...~dm
\item   7 282,3 ~hg~ = ...~mg
\item   608,45 ~hm~ = ...~cm
\item   428,13 ~m~ = ...~km
\item   2 251,4 ~mg~ = ...~dg
\item   166,7 ~dg~ = ...~dag
\item   244,79 ~cL~ = ...~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   6 = \(\dfrac{60}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{360}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{45}{10}\) = \(\dfrac{450}{100}\)
\item   \(\dfrac{46}{100}\) = \(\dfrac{460}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,013  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,13}
\item   0,883  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 88,3}
\item   2,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 210}
\item   404  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 040}
\item   7,36  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 73,6}
\item   0,03  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 30}
\item   883  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 830}
\item   0,229  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 229}
\item   0,45  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 45}
\item   1,84  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 840}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,65 ~ : ~ 10 ~ = ~{\color{red} 7,965}
\item   1,293 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 293}
\item   40 ~ : ~ 10 ~ = ~{\color{red} 4}
\item   67,12 ~ : ~ 1 000 ~ = ~{\color{red} 0,067 12}
\item   1,21 ~ : ~ 10 ~ = ~{\color{red} 0,121}
\item   8,491 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 491}
\item   429,2 ~ : ~ 100 ~ = ~{\color{red} 4,292}
\item   85,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,085 2}
\item   1,987 ~ : ~ 10 ~ = ~{\color{red} 0,198 7}
\item   7,714 ~ : ~ 10 ~ = ~{\color{red} 0,771 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,597 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~597
\item   0,068 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,8
\item   888 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88 800
\item   15,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~159
\item   0,469 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~46,9
\item   700 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 000
\item   4,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~43,4
\item   0,477 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~477
\item   0,029 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,9
\item   18,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~185
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   340,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 34,08
}\item   9,619 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,096 19
}\item   3 812 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,12
}\item   8,602 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 602
}\item   4 034 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,034
}\item   7 623 ~ \(\times\)  0,1 ~ = ~{\color{red} 762,3
}\item   725,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,725 9
}\item   5,859 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 859
}\item   2 557 ~ \(\times\)  0,01 ~ = ~{\color{red} 25,57
}\item   11,71 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,117 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   2 544 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 25,44
\item   6 395 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,395
\item   64,48 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,064 48
\item   2,868 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,286 8
\item   3 958 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 395,8
\item   765,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,765 7
\item   8 675 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 86,75
\item   322,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,322 3
\item   9 806 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 98,06
\item   681,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 68,15
\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}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 022,6 ~L~ = {\color{red}  8,022 6 }~kL
\item   907,9 ~cg~ = {\color{red}  0,907 9 }~dag
\item   3 570,6 ~dg~ = {\color{red}  35 706 }~cg
\item   4 681,7 ~dam~ = {\color{red}  468 170 }~dm
\item   7 282,3 ~hg~ = {\color{red}  728 230 000 }~mg
\item   608,45 ~hm~ = {\color{red}  6 084 500 }~cm
\item   428,13 ~m~ = {\color{red}  0,428 13 }~km
\item   2 251,4 ~mg~ = {\color{red}  22,514 }~dg
\item   166,7 ~dg~ = {\color{red}  1,667 }~dag
\item   244,79 ~cL~ = {\color{red}  2,447 9 }~L
\end{itemize}
\end{multicols}
\end{document}
