#2**+10 **

If you mean 0.26666666.... with the 6's recurring, then do the following:

Let x = 0.266666....

Mutiply x by 100:

100x = 26.666666.....

Multiply x by 10:

10x = 2.666666.....

Subtract 10x from 100x:

100x - 10x = 26.66666.... - 2.66666..... so

90x = 24

Divide by 90

x = 24/90

or x = 4/15

.

On the other hand, if you mean 0.266266266... then

Let x = 0.266266266...

Multiply by 1000

1000x = 266.266266266....

Subtract x from 1000x

1000x - x = 266.266266266... - 0.266266266...

999x = 266

x = 266/999

.

Alan
May 13, 2015

#2**+10 **

Best Answer

If you mean 0.26666666.... with the 6's recurring, then do the following:

Let x = 0.266666....

Mutiply x by 100:

100x = 26.666666.....

Multiply x by 10:

10x = 2.666666.....

Subtract 10x from 100x:

100x - 10x = 26.66666.... - 2.66666..... so

90x = 24

Divide by 90

x = 24/90

or x = 4/15

.

On the other hand, if you mean 0.266266266... then

Let x = 0.266266266...

Multiply by 1000

1000x = 266.266266266....

Subtract x from 1000x

1000x - x = 266.266266266... - 0.266266266...

999x = 266

x = 266/999

.

Alan
May 13, 2015