Trong các đẳng thức sau đây, đẳng thức nào sai?
\(0,\left(37\right)+0,\left(62\right)=1.\)\(0,\left(33\right).3=1.\)\(0,\left(31\right)=0,3\left(13\right).\)\(0,\left(3\right)+0,\left(4\right)=1.\)Hướng dẫn giải:Ta có:
+) \(0,\left(37\right)+0,\left(62\right)=0,\left(01\right).37+0,\left(01\right).62=0,\left(01\right).99=\dfrac{1}{99}.99=1\).
+) \(0,\left(33\right).3=0,\left(01\right).33.3=\dfrac{1}{99}.99=1.\)
+) \(0,\left(31\right)=0,\left(01\right).31=\dfrac{1}{99}.31=\dfrac{31}{99};\)
\(0,3\left(13\right)=0,3+0,0\left(13\right)=\dfrac{3}{10}+\dfrac{1}{10}.0,\left(13\right)=\dfrac{3}{10}+\dfrac{1}{10}.0,\left(01\right).13=\dfrac{3}{10}+\dfrac{1}{10}.\dfrac{1}{99}.13=\dfrac{31}{99}.\)
\(\Rightarrow0,\left(31\right)=0,3\left(13\right).\)
+) \(0,\left(3\right)+0,\left(4\right)=0,\left(1\right).3+0,\left(1\right).4=\dfrac{1}{9}.3+\dfrac{1}{9}.4=\dfrac{7}{9}\ne1.\)
