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Vinil7 [7]
3 years ago
5

okay so I don't really understand how to change a decimal to a fraction and the teacher never really explained it to us and she

went really fast and like I hate showing my work because I'll always mess up

Mathematics
1 answer:
Fofino [41]3 years ago
5 0

\bf 0.2121\overline{21}\qquad \qquad \qquad x=0.2121\overline{21}\\\\ -------------------------------\\\\ \stackrel{\textit{moving the 21 to the left}}{\stackrel{100\cdot x}{100\cdot 0.2121\overline{21}}}\implies  21.2121\overline{21}\implies  \begin{array}{llll} 21&+&0.2121\overline{21}\\ 21&+&x \end{array} \\\\\\ therefore\qquad \qquad 100x  = 21+x\implies 99x=21 \\\\\\ x=\cfrac{21}{99}\implies x=\stackrel{simplified}{\cfrac{7}{33}}

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