How do I express 0.6969... in the form of p/q where p and q are integers?

How do I express 0.dot6dot90..6.9 in the form of p/qpq where p and q are integers?

Your help is greatly appreciated!

3 Answers
Jul 22, 2018

I'm assuming it is 0.69 recurring

Explanation:

Let x=0.6969...

So 100x=69.6969...

Subtract the first from the second and all the decimal numbers will disappear to leave

99x=69

Divide by 99

x=69/99

Divide by 3

x=23/33

Jul 22, 2018

0.dot6dot9=23/33

Explanation:

Let 0.dot6dot9=0.6969696969....................=x

Then 100x=69.6969696969..............................

Subtracting former from latter we get

99x=69

Hence, x=69/99=23/33

i.e. 0.dot6dot9=23/33

Explanation:

Let

x=0.69696969............\ \quad (1)

100x=69.69696969............\ \quad (2)

subtracting (1) from (2) as follows

100x-x=(69.696969...)-(0.696969....)

99x=69

x=69/99

x=23/33