Final answer:
The repeating decimal 0.131313... can be expressed as the ratio 13/99 by using an algebraic method where the repeating pattern of the decimal is isolated and then subtracted to find the ratio.
Step-by-step explanation:
To express the repeating decimal 0.131313... as the ratio of two integers, we can use a simple algebraic method. Let's define the repeating decimal as x:
x = 0.131313...
Multiplying both sides of the equation by 100, since the repeat is two digits long, gives us:
100x = 13.131313...
Now we subtract the original x from this to get the following:
100x - x = 13.131313... - 0.131313...
99x = 13
Dividing both sides by 99 gives us:
x = 13 / 99
Therefore, the repeating decimal 0.131313... is represented as the ratio 13/99 which is in the form of two integers.