## anonymous 4 years ago solve the equation.

1. anonymous

$6\overline{.2}= p/q$

2. anonymous

solve for p and q.

3. anonymous

$6\tfrac{2}{9}=\frac{6\times 9+2}{9}$

4. Hero

satellite, where's the general approach?

5. anonymous

In an example in my book it tells me to multiply the equation by 10 and then a bunch of other work.

6. anonymous

$x=\overline{.2}$ $10x=2.\overline{.2}$ $9x=2.\overline{.2}-\overline{.2}=2$ $9x=2\implies x=\frac{2}{9}$

7. anonymous

So is P=2 and Q=9?

8. anonymous

no you have to add 6

9. anonymous

$6\tfrac{2}{9}=\frac{6\times 9+2}{9}=\frac{56}{9}$

10. anonymous

it is easier just to remember that $\overline{.1}=\frac{1}{9}$ $\overline{.2}=\frac{2}{9}$ $\overline{.3}=\frac{3}{9}=\frac{1}{3}$ $\overline{.4}=\frac{4}{9}$ $\overline{.5}=\frac{5}{9}$ etc

11. anonymous

so 56/9 is final answer and oh that helps a lot i can never remember those.

12. anonymous

And for my other problems of homework i have the exact same problem except it is 6.25 and then 6.251