jmc

Question

If 0.1331 is written as a fraction ab with a and b being positive integers with a greatest common divisor of 1, what is a+b?

Accepted Answer

Let x = 0.1331, so 10000x = 1331.1331. As a result, 9999x = 1331, so x = 13319999. We can factor out 11 out of both the numerator and denominator, so x = 121909. Thus a+b=121+909 = 1030.