Alright, so we have 1.3/0.0338. Since it's easier (in my opinion) to work with whole numbers, we can multiply the fraction by 10000/10000 to get 13000/338. With a bit of guess and check, we can see that 338*30=338*3*10 1 2 (what I carry is at the top) 338 x3 ____ 1114
Multiplying that by 10, I get 11140, which isn't enough. Trying 338*40, which is 338*4*10, we can add 338 to 338*3 to get 338*4 to get
2 1114 +338 ____ 1462
Multiplying that by 10, we get 14620, which is more than 13000 - something we don't want. Repeating this for 338*35 (which is 338*3.5*10, and 3.5 is 3*338+338/2)=11830 and which isn't enough, we then move on to something between 35 and 40 (the number doesn't matter), say 39. 338*39=338*3.9*10, and 338*3.9 is 338*3+338*9/10, and 338*39 results to 13182, which is more than 13000 , but only by a tiny bit, so we can try 38 using the same method, getting 12844, which is smaller, so we know it's between 38 and 39. Finding the difference between 13000 and 12844, we get 13000-12844=156 and the answer is therefore 38+156/338
