If the question referred to **.36**, without repetition, it would be **36/100**.

However, since it repeats, it is referring to **36/99**.

[If there are n repeating digits, write the part that repeats over n nines. In this case, there are 2 repeating digits, so we write them over 2 nines.]

That can be simplified to **4/11**.

You would then multiply **4/11 * 11/2**.

The 11s will cancel, leaving you with **4/2**, which is just **2**.

This equation might seem difficult to solve without a calculator, but a neat trick for dividing 1 by 11 and finding the decimal equivalents of the fractions is that the decimal equivalent of a fraction with the denominator of 11 is a repeating 2-digit decimal of the numerator multiplied by 9. Here's an example:

5/11 = 0.454545... (5*9 = 45)

So, for 0.363636, we know that 36/9 is 4, and that the fraction in play here is 4/11. Now, the original question of 0.363636 * 11/2 is much easier, because we can use two fractions instead of a decimal. We just need to multiply them:

4/11 * 11/2 = 4*11 / 11*2

4*11 / 11*2 = 44/22

44/22 = 4/2

4/2 = 2

Therefore, 0.36363636 (or 4/11) multiplied by 11/2 is equal to 2.