Question

Can you show me how to do Thisss.

Answer 1

$x=0.\overline{3}\\ 10x=3.\overline{3}\\ 10x-x=3.\overline{3}-0.\overline{3}\\ 9x=3\\ x=\dfrac{3}{9}=\dfrac{1}{3}\\\\ x=-0.\overline{2}\\ 10x=-2.\overline{2}\\ 10x-x=-2.\overline{2}-(-0.\overline{2})\\ 9x=-2.\overline{2}+0.\overline{2}\\ 9x=-2\\ x=-\dfrac{2}{9}\\\\ x=1.\overline{7}\\ 10x=17.\overline{7}\\ 10x-x=17.\overline{7}-1.\overline{7}\\ 9x=16\\ x=\dfrac{16}{9}=1\dfrac{7}{9}$

$x=-2.\overline{6}\\ 10x=-26.\overline{6}\\ 10x-x=-26.\overline{6}-(-2.\overline{6})\\ 9x=-26.\overline{6}+2.\overline{6}\\ 9x=-24\\ x=-\dfrac{24}{9}=-2\dfrac{2}{3}\\\\ x=0.4\overline{6}\\ 10x=4.\overline{6}\\ 100x=46.\overline{6}\\ 100x-10x=46.\overline{6}-4.\overline{6}\\ 90x=42\\ x=\dfrac{42}{90}=\dfrac{7}{15}$

$x=-1.8\overline{3}\\ 10x=-18.\overline{3}\\ 100x=-183.\overline{3}\\ 100x-10x=-183.\overline{3}-(-18.\overline{3})\\ 90x=-183.\overline{3}+18.\overline{3}\\ 90x=-165\\ x=-\dfrac{165}{90}=-1\dfrac{5}{6}$