Question

SE 2,63333333= a/b, então quanto será a-b?

Answer 1

$\bigg(\dfrac{a}{b}\bigg)=2.6\bar{3}\ \therefore\ 10\bigg(\dfrac{a}{b}\bigg)=26.\bar{3}\ \therefore\ 100\bigg(\dfrac{a}{b}\bigg)=263.\bar{3}$$a-b=79-30\ \therefore\ \boxed{a-b=49}$

$100\bigg(\dfrac{a}{b}\bigg)-10\bigg(\dfrac{a}{b}\bigg)=263.\bar{3}-26.\bar{3}\ \therefore\ 90\bigg(\dfrac{a}{b}\bigg)=237\ \therefore$

$\bigg(\dfrac{a}{b}\bigg)=\dfrac{237}{90}\ \therefore\ \boxed{\bigg(\dfrac{a}{b}\bigg)=\dfrac{79}{30}}\ \to\ \boxed{a=79}\ \text{e}\ \boxed{b=30}$

$a-b=79-30\ \therefore\ \boxed{a-b=49}$