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zmey [24]
3 years ago
13

Rewrite as a simplified fraction 1.6 <-- repeating=?

Mathematics
1 answer:
Norma-Jean [14]3 years ago
6 0
1.6666...=1.\overline{6}=1.(6)\\\\x=1.6666...\ \ \ |multiply\ both\ sides\ by\ 10\\10x=16.6666...\\\\10x-x=16.6666...-1.6666...\\9x=15\ \ \ \ |divide\ both\ sides\ by\ 9\\\\x=\frac{15}{9}\\\\\boxed{x=1\frac{6}{9}}\\\\simplify\\\\x=1\frac{6:3}{9:3}=\boxed{1\frac{2}{3}}
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