Estimate multiplying multi digit numbers

What I would like to do in this video is get some practice estimating the product of multi-digit numbers, and there's just no better way of getting practice than just trying it ourselves.

So, right over here, it says estimate 29 times 3198. Why don't you pause this video and try to estimate this? Of course, you can do this by multiplying this out on paper or using a calculator, but this is a useful skill. Try to do it in your head; see if you can estimate what this is going to be.

Well, before even looking at these answers, I would say this is going to be approximately equal to... Let's see, 29 is awfully close to 30, and then I could multiply that times... I could either multiply that times 3200, which is awfully close to 3198, or if I want an even more rough approximation, I could say that's roughly equal to 30 times 3,000.

So, if I did 30 times 3,000, 3 times 3 is equal to 9, and then I have one, two, three, four zeros. One, two, three, four zeros! And actually, my approximation, it turns out, is here right over here: 90,000.

Now, if I wanted a slightly better approximation, I could have said this is approximately equal to 30 times 3200. This you could also do in your head. You could say, well, what is 3 times 32? Well, that is going to be 96, and then you have one, two, three zeros. One, two, three zeros! So this would be a slightly better approximation, and if this is what you got, the closest answer here is still going to be equal to 90,000.

Let's do another example. So here we are asked to estimate 137 times 18. So pause this video again and see if you can come up with an estimate; try to do it in your head.

Well, there's once again many ways of trying to tackle it. The way I would tackle it, I would say, well, that's pretty close to 140 times 20, and then this would be equal to 14 times 2 is 28, and then we have two zeros here, so that would be roughly 2800. But when I look over here, there is no 2800, and so maybe the closest one right over here is 2,000.

So that could be an approximation. Another way... it looks actually the way that they did it is they even did a coarser approximation. They rounded this to the nearest hundred, and so they said this is approximately equal to 100 times... and they rounded this to the nearest 10: 100 times 20, which is even easier to do in your head, which is equal to 2000, which is this choice that they got right over here.