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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 270}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{85}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   95,7  ~ \(\times\)  ~ 10
\item   0,875  ~ \(\times\)  ~ 1 000
\item   3,08  ~ \(\times\)  ~ 1 000
\item   0,088  ~ \(\times\)  ~ 100
\item   0,982  ~ \(\times\)  ~ 100
\item   0,094  ~ \(\times\)  ~ 10
\item   0,071  ~ \(\times\)  ~ 100
\item   0,078  ~ \(\times\)  ~ 10
\item   0,29  ~ \(\times\)  ~ 1 000
\item   0,001  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   83,6  ~ : ~ 100
\item   525,8  ~ : ~ 1 000
\item   82,47  ~ : ~ 10
\item   602,8  ~ : ~ 100
\item   1,465  ~ : ~ 100
\item   5 220  ~ : ~ 1 000
\item   6 228  ~ : ~ 100
\item   9,343  ~ : ~ 100
\item   8 509  ~ : ~ 10
\item   28,78  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,042  ~ \(\times\)  ~ ... ~ = ~ 42
\item   6,14  ~ \(\times\)  ~ ... ~ = ~ 614
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 8,4
\item   0,04  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   92,8  ~ \(\times\)  ~ ... ~ = ~ 92 800
\item   410  ~ \(\times\)  ~ ... ~ = ~ 41 000
\item   771  ~ \(\times\)  ~ ... ~ = ~ 771 000
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 60
\item   3,92  ~ \(\times\)  ~ ... ~ = ~ 392
\item   0,038  ~ \(\times\)  ~ ... ~ = ~ 38
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,779  ~ \(\times\)  ~ 0,01
\item   3,592  ~ \(\times\)  ~ 0,001
\item   26,99  ~ \(\times\)  ~ 0,1
\item   3 161  ~ \(\times\)  ~ 0,001
\item   0,985  ~ \(\times\)  ~ 0,01
\item   7,013  ~ \(\times\)  ~ 0,001
\item   0,344  ~ \(\times\)  ~ 0,1
\item   46,23  ~ \(\times\)  ~ 0,001
\item   797,3  ~ \(\times\)  ~ 0,1
\item   4,064  ~ \(\times\)  ~ 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   7,836  ~ \(\times\)  ~ ... ~ = ~  0,007 836
\item   5,077  ~ \(\times\)  ~ ... ~ = ~  0,005 077
\item   75,52  ~ \(\times\)  ~ ... ~ = ~  0,755 2
\item   71,4  ~ \(\times\)  ~ ... ~ = ~  0,071 4
\item   7,863  ~ \(\times\)  ~ ... ~ = ~  0,007 863
\item   110,2  ~ \(\times\)  ~ ... ~ = ~  1,102
\item   3,646  ~ \(\times\)  ~ ... ~ = ~  0,003 646
\item   4 948  ~ \(\times\)  ~ ... ~ = ~  49,48
\item   97,35  ~ \(\times\)  ~ ... ~ = ~  9,735
\item   1 237  ~ \(\times\)  ~ ... ~ = ~  123,7
\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~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   769,89 ~mm~ = ...~hm
\item   178,16 ~hm~ = ...~dm
\item   7 284,5 ~dg~ = ...~kg
\item   531,48 ~m~ = ...~dm
\item   397,94 ~L~ = ...~hL
\item   167,53 ~cL~ = ...~kL
\item   650,42 ~hL~ = ...~cL
\item   1 673,6 ~g~ = ...~cg
\item   928,78 ~g~ = ...~hg
\item   1 559,6 ~mL~ = ...~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   3 = \(\dfrac{30}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{2100}{100}\) = \(\dfrac{210}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{130}{100}\)
\item   \(\dfrac{85}{100}\) = \(\dfrac{850}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   95,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 957}
\item   0,875  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 875}
\item   3,08  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 080}
\item   0,088  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,8}
\item   0,982  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 98,2}
\item   0,094  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,94}
\item   0,071  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,1}
\item   0,078  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,78}
\item   0,29  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 290}
\item   0,001  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   83,6 ~ : ~ 100 ~ = ~{\color{red} 0,836}
\item   525,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,525 8}
\item   82,47 ~ : ~ 10 ~ = ~{\color{red} 8,247}
\item   602,8 ~ : ~ 100 ~ = ~{\color{red} 6,028}
\item   1,465 ~ : ~ 100 ~ = ~{\color{red} 0,014 65}
\item   5 220 ~ : ~ 1 000 ~ = ~{\color{red} 5,22}
\item   6 228 ~ : ~ 100 ~ = ~{\color{red} 62,28}
\item   9,343 ~ : ~ 100 ~ = ~{\color{red} 0,093 43}
\item   8 509 ~ : ~ 10 ~ = ~{\color{red} 850,9}
\item   28,78 ~ : ~ 100 ~ = ~{\color{red} 0,287 8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,042 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~42
\item   6,14 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~614
\item   0,084 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,4
\item   0,04 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,4
\item   92,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~92 800
\item   410 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~41 000
\item   771 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~771 000
\item   0,06 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~60
\item   3,92 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~392
\item   0,038 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~38
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,779 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,007 79
}\item   3,592 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 592
}\item   26,99 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,699
}\item   3 161 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,161
}\item   0,985 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,009 85
}\item   7,013 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 013
}\item   0,344 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,034 4
}\item   46,23 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,046 23
}\item   797,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 79,73
}\item   4,064 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,040 64
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,836 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 836
\item   5,077 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 077
\item   75,52 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,755 2
\item   71,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,071 4
\item   7,863 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 863
\item   110,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,102
\item   3,646 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 646
\item   4 948 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 49,48
\item   97,35 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,735
\item   1 237 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 123,7
\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~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   769,89 ~mm~ = {\color{red}  0,007 698 9 }~hm
\item   178,16 ~hm~ = {\color{red}  178 160 }~dm
\item   7 284,5 ~dg~ = {\color{red}  0,728 45 }~kg
\item   531,48 ~m~ = {\color{red}  5 314,8 }~dm
\item   397,94 ~L~ = {\color{red}  3,979 4 }~hL
\item   167,53 ~cL~ = {\color{red}  0,001 675 3 }~kL
\item   650,42 ~hL~ = {\color{red}  6 504 200 }~cL
\item   1 673,6 ~g~ = {\color{red}  167 360 }~cg
\item   928,78 ~g~ = {\color{red}  9,287 8 }~hg
\item   1 559,6 ~mL~ = {\color{red}  15,596 }~dL
\end{itemize}
\end{multicols}
\end{document}
