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

##
How do I express #0.dot6dot9# in the form of #p/q# where **p** and **q** are integers?

Your help is greatly appreciated!

How do I express **p** and **q** are integers?

Your help is greatly appreciated!

##### 3 Answers

I'm assuming it is 0.69 recurring

#### Explanation:

Let

So

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

Divide by 99

Divide by 3

#### Explanation:

Let

Then

Subtracting former from latter we get

Hence,

i.e.

#### Explanation:

Let

subtracting (1) from (2) as follows