3rd Grade Math Help! I need help with this one problem!?

Question

I need help with this problem, but could you really explain it to me, and not just give me an answer? I want to understand it!

Change the decimal into a fraction.

.666... (continued)

How do you do this?

Answer 1

I'm going to give you two different answers.  One is pure arithmetic, which is all that I would have understood in the 3rd grade, and the second uses equations which I would not have understood in the third grade.  

1) Every completely repetitive decimal is a fraction with the numerator between 0 and 8, and the denominator equal to 9.  So:

0/9 = .00000000000000000

1/9 = .11111111111111111

2/9 = .22222222222222222

3/9 = .33333333333333333

4/9 = .44444444444444444

5/9 = .55555555555555555

6/9 = .66666666666666666   <<<<<

7/9 = .77777777777777777

8/9 = .88888888888888888

Side Note:  14/9 = 1.555555555555  but in this case the one is not equal to five, otherwise I'd have to enter every integer numerator possible over a denominator of 9.

In your problem .6666666666666666 = 6/9 = [(2 x 3) / (3 x 3)] = 2/3

Final Answer 2/3   <<<<<

--------------------------------------...

2)  I'll do this  by algebra below, but you probably haven't had that.

Anyway, if

       x = .666666666666666666      then

10x = 6.66666666666666666

So 10x - x = 6  (subtracting the top equation from the bottom).

10x - x = 9x = 6

9x = 6       so x = 6/9 = 2/3   <<<<<

Answer 2

Gerry was right up till the end when he said "1/3"

He should have said 2/3.

6/9

To break 6/9 down to a more simplified version

6/3 =2

9/3 =3

put the 2 back over the 3

2/3 (Because 6/9 = 2/3)

Answer 3

Let x = .66666666....

10x = 6.66666666....

10x - x = 6

9x = 6

x = 6/9 = 2/3

I'm not sure this is 3rd grade level

Answer 4

asumming 0.666... =x

multiple with 10

we have

6.666... = 10x

and diference will be

6 = 9x

so x= 6/9 or 2/3

generally every decimal in form of

0.NNN...  will change to fraction N/9