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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 159}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{42}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{77}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87  ~ \(\times\)  ~ 1 000
\item   207  ~ \(\times\)  ~ 1 000
\item   0,508  ~ \(\times\)  ~ 10
\item   0,288  ~ \(\times\)  ~ 10
\item   0,496  ~ \(\times\)  ~ 1 000
\item   3,09  ~ \(\times\)  ~ 1 000
\item   2,65  ~ \(\times\)  ~ 10
\item   0,004  ~ \(\times\)  ~ 10
\item   0,418  ~ \(\times\)  ~ 100
\item   659  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   31,15  ~ : ~ 100
\item   901,8  ~ : ~ 10
\item   838  ~ : ~ 10
\item   88,47  ~ : ~ 100
\item   9 835  ~ : ~ 10
\item   150,3  ~ : ~ 100
\item   894,6  ~ : ~ 1 000
\item   8 322  ~ : ~ 1 000
\item   5 812  ~ : ~ 100
\item   3,328  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,964  ~ \(\times\)  ~ ... ~ = ~ 9,64
\item   0,078  ~ \(\times\)  ~ ... ~ = ~ 0,78
\item   0,22  ~ \(\times\)  ~ ... ~ = ~ 220
\item   226  ~ \(\times\)  ~ ... ~ = ~ 22 600
\item   0,887  ~ \(\times\)  ~ ... ~ = ~ 88,7
\item   2,55  ~ \(\times\)  ~ ... ~ = ~ 255
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 9,7
\item   2,66  ~ \(\times\)  ~ ... ~ = ~ 26,6
\item   563  ~ \(\times\)  ~ ... ~ = ~ 563 000
\item   7,18  ~ \(\times\)  ~ ... ~ = ~ 7 180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 786  ~ \(\times\)  ~ 0,1
\item   9 613  ~ \(\times\)  ~ 0,1
\item   9,32  ~ \(\times\)  ~ 0,001
\item   93,51  ~ \(\times\)  ~ 0,01
\item   341,6  ~ \(\times\)  ~ 0,001
\item   282,2  ~ \(\times\)  ~ 0,001
\item   69,35  ~ \(\times\)  ~ 0,001
\item   7,888  ~ \(\times\)  ~ 0,1
\item   66,7  ~ \(\times\)  ~ 0,1
\item   5,346  ~ \(\times\)  ~ 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   20,24  ~ \(\times\)  ~ ... ~ = ~  0,020 24
\item   15,87  ~ \(\times\)  ~ ... ~ = ~  1,587
\item   726,3  ~ \(\times\)  ~ ... ~ = ~  7,263
\item   77,2  ~ \(\times\)  ~ ... ~ = ~  7,72
\item   8 785  ~ \(\times\)  ~ ... ~ = ~  87,85
\item   6,097  ~ \(\times\)  ~ ... ~ = ~  0,609 7
\item   853,9  ~ \(\times\)  ~ ... ~ = ~  0,853 9
\item   6,124  ~ \(\times\)  ~ ... ~ = ~  0,612 4
\item   65,6  ~ \(\times\)  ~ ... ~ = ~  0,656
\item   4 493  ~ \(\times\)  ~ ... ~ = ~  44,93
\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~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   999,93 ~kL~ = ...~dL
\item   892,84 ~dm~ = ...~dam
\item   176,01 ~cL~ = ...~L
\item   892,21 ~g~ = ...~kg
\item   149,91 ~cg~ = ...~dg
\item   820,2 ~mL~ = ...~cL
\item   790,93 ~kg~ = ...~hg
\item   361,23 ~hg~ = ...~dg
\item   6 317,2 ~cg~ = ...~hg
\item   695,13 ~g~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{970}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{42}{10}\) = \(\dfrac{420}{100}\)
\item   \(\dfrac{77}{100}\) = \(\dfrac{770}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 87 000}
\item   207  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 207 000}
\item   0,508  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,08}
\item   0,288  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,88}
\item   0,496  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 496}
\item   3,09  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 090}
\item   2,65  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 26,5}
\item   0,004  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,04}
\item   0,418  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 41,8}
\item   659  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 590}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   31,15 ~ : ~ 100 ~ = ~{\color{red} 0,311 5}
\item   901,8 ~ : ~ 10 ~ = ~{\color{red} 90,18}
\item   838 ~ : ~ 10 ~ = ~{\color{red} 83,8}
\item   88,47 ~ : ~ 100 ~ = ~{\color{red} 0,884 7}
\item   9 835 ~ : ~ 10 ~ = ~{\color{red} 983,5}
\item   150,3 ~ : ~ 100 ~ = ~{\color{red} 1,503}
\item   894,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,894 6}
\item   8 322 ~ : ~ 1 000 ~ = ~{\color{red} 8,322}
\item   5 812 ~ : ~ 100 ~ = ~{\color{red} 58,12}
\item   3,328 ~ : ~ 100 ~ = ~{\color{red} 0,033 28}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,964 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,64
\item   0,078 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,78
\item   0,22 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~220
\item   226 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22 600
\item   0,887 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88,7
\item   2,55 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~255
\item   0,097 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,7
\item   2,66 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~26,6
\item   563 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~563 000
\item   7,18 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 786 ~ \(\times\)  0,1 ~ = ~{\color{red} 678,6
}\item   9 613 ~ \(\times\)  0,1 ~ = ~{\color{red} 961,3
}\item   9,32 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 32
}\item   93,51 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,935 1
}\item   341,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,341 6
}\item   282,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,282 2
}\item   69,35 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,069 35
}\item   7,888 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,788 8
}\item   66,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,67
}\item   5,346 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,534 6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,24 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,020 24
\item   15,87 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,587
\item   726,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,263
\item   77,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,72
\item   8 785 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 87,85
\item   6,097 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,609 7
\item   853,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,853 9
\item   6,124 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,612 4
\item   65,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,656
\item   4 493 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 44,93
\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~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   999,93 ~kL~ = {\color{red}  9 999 300 }~dL
\item   892,84 ~dm~ = {\color{red}  8,928 4 }~dam
\item   176,01 ~cL~ = {\color{red}  1,760 1 }~L
\item   892,21 ~g~ = {\color{red}  0,892 21 }~kg
\item   149,91 ~cg~ = {\color{red}  14,991 }~dg
\item   820,2 ~mL~ = {\color{red}  82,02 }~cL
\item   790,93 ~kg~ = {\color{red}  7 909,3 }~hg
\item   361,23 ~hg~ = {\color{red}  361 230 }~dg
\item   6 317,2 ~cg~ = {\color{red}  0,631 72 }~hg
\item   695,13 ~g~ = {\color{red}  6 951,3 }~dg
\end{itemize}
\end{multicols}
\end{document}
