Question

How can I covert this 0.688= to a fraction

Answer 1

You have to convert the following number into a fraction:

$0.6\bar{8}\bar{8}$

This is a periodic decimal number, which explicitely is 0.68888888....

In order to convert this number to a fraction you proceed as follow:

$0.6\bar{8}=\frac{68-0}{99}=\frac{68}{99}$

You put 0.68 and not 0.688 because to do the convertion you need only the first periodic number (that is, only the first 8). The key is to put in the numerator the complete number as whole number, that is, 68. To this number you subtract the whole part of the decimal number, this whole part is 0 because of the 0.688. Then, in the numerator you have 68 - 0. In the denominator you write a number composed only by 9's. The number of 9 numbers is determined by the number of digits of the first number in the numerator. That is two 9 numbers