Multiplying by Powers of 5

There are times in life when you just get lucky. It turns out that one of those lucky little moments occurs each and every time you need to multiply one number by another number that happens to be a power of 5. For example, let's say you need to find 36 x 5 (which, of course, fits the bill since 5 is the first power of 5). The trick is to recognize the fact that 5 = 10 / 2. Why is that helpful? Because it means that we can find 36 x 5 by instead finding 36 x 10 (which is easy) and then dividing the result by 2. In this case, 36 x 10 = 360, and 360 / 2 = 180. Impressively speedy, right?

But we're not done! What if we instead need to solve the problem 36 x 25? Well, this trick is all about multiplying by powers of 5…and 25 = 5^2 is certainly that. So how does it work in this case? The trick here is to recognize that 25 = 100 / 4. And in general, the trick with powers of 5 is to recognize that they are always some multiple of 10 divided by an integer. This tells us that 36 x 25 = 36 x 100 / 4. Since we can quickly figure out that 36 x 100 = 3,600, it's easy to find that 36 x 25 = 3,600 / 4 = 900.