Question

3) A expressão 1,2 +0,2222.... -0,9999...

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Answer 1

$x=0,222... \times10\\10x=2,222....$

$\underline{\begin{cases}10x=2,\cancel{222....}\\x=0,\cancel{222...}\end{cases}}$

$9x=2\\x=\dfrac{2}{9}$

$0,999... =1$

$1,2+0,222... -0,999... =\dfrac{6}{5}+\dfrac{2}{9}-1$

$\dfrac{54+10-45}{45}\\\dfrac{19}{45}$

$\boxed{\boxed{\mathsf{1,2+0,222... -0,999.. =\dfrac{19}{45}}}}$