There are two techniques that you can use:
1) Learn how to work with zeros. Best way - always use 10^power instead of zeros
300x9000 = 3*10ˆ2 x 9*10ˆ3=3x9*10ˆ(2+3)=27*10ˆ5
Handwritten it looks not that complicated. If you get used to writing all the numbers that way, you will never lose zeros and all multiplications/divisions will be replaced with + or -.
In your case, it will look like 63 * 10ˆ5 / 72 * 10ˆ2
2) If you need the precise calculation - you can use the basic division technique, calculating 630 / 72 * 10ˆ2 = 875
3) If you don't need it precise - Learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems
In your case, it will be roughly 6/7 * 10ˆ3 = 85.7 * 10ˆ3 or 857. Since I know that it was the rough calculation and the real number should be bigger, I would round the final result to 870