Intro to multiplying decimals

Let's see if we can multiply 9 times 0.6. Or another way to write it, we want to calculate 9 times 0.6. I'll write it like this-- 0.6. We want to figure out what this is equal to. And I encourage you to pause the video and try to figure it out on your own. And I'll give you a little bit of a hint. 0.6 is the same thing as 6 divided by 10. We know that if we start with 6, which we could write as 6.0, and if you were to divide it by 10, dividing by 10 is equivalent to moving the decimal place one place to the left. So 6 divided by 10 is 0.6. We are moving the decimal one place to the left. So I'm assuming you given a go at it. But what I'm going to do is use this that we already know to rewrite what we're trying to multiply. So 9 times 0.6 is the same thing is 9 times-- 0.6 is 6 divided by 10. And this expression right over here, we could either do the 6 divided by 10 first, in which case we would get 0.6, and this would turn into this problem. Or we could do the 9 times 6 first. And so let's do 9 times 6, which we know how to calculate, and then divide by 10, which we also know how to do. That. all about just moving the decimal place. So we could write 9 times 6. 9 times 6, we already know, is 54. I'll do that in orange-- is going to be 54. So this right over here is 54. And now to get to this expression, we have to divide by 10. We have to divide by 10. And what happens when we divide something by 10? And we've seen this in previous videos, why this is the case. This is all about what decimal notation means. Each place represents 10 times as much as the place to its right, or each place represents 1/10 of the place to the left. So 54 divided by 10, this is going to be-- you could start with 54. And I'll put a 0 here after the decimal. And when you divide by 10, that's equivalent of shifting the decimal one to the left. This is going to be equal to 5.4. And that should make sense to you. 5 times 10 is 50. 0.4 times 10 is 4. So it makes sense that 54 divided by 10-- I shouldn't say equal. I'd write 54 divided by 10 is equal to 5.4. So this right over here is equal to 5.4, and that's what this is. This is equal to 5.4. Notice, 9 times 6 is 54. 9 times 0.6 is 5.4. Now you might see a little pattern here. Between these two numbers, I had exactly one number to the right of the decimal. When I take its product, let's say I ignored the decimal. I just said 9 times 6, I would've gotten 54. But then I have to divide by 10 in order to take account of the decimal, take account of the fact this wasn't a 6. This was a 6/10. And so I have one number to the right of the decimal here. And I want to you to think about that whether that's a general principle. Can we just count the total numbers of digits to the right of the decimals and then our product is going to have the same number of digits to right of the decimal? I'll let you to think about that.