Multiplying decimals using estimation

- [Instructor] So let's see if we can come up ways to compute what 2.8 times 4.73 is. So pause this video, and try to work it out. And, actually, I'll give you a hint. Try to figure out, just using the digits, not even paying attention to the decimals, the digits that the product would have, and then use estimation to think about where to place the decimal in your product so you get a reasonable answer. All right, now, let's do this together. So let's just imagine that we were multiplying these numbers without decimals. So that would be a situation where we would have 473 times 28, and so we could try to compute that. And, so, we could think about let's multiply everything times the eight, so three times eight is 24, seven times eight is 56, plus two is 58. And then four times eight is 32, plus five is 37. And then we could multiply everything times the two. I'll cross those out so I don't get confused. Three times two is going to be six, so we have to be very careful, we are now in the tens place, so we want a zero here, so three times two tens is going to be six tens. Seven times two is 14. Four times two is eight, plus one is nine. We add everything together, and we get four plus zero is four, eight plus six is 14, and then one plus seven plus four is 12, and then we get one plus three is four, plus nine is equal to 13. So we know that the final answer has the digits one, three, two, four, four in that order. One, three, two, four, four. So now we have to think about where would we put a decimal for this to be a reasonable answer? And here's where estimation is useful. We know that 2.8 times 4.73 is going to be roughly equal to what? Well, 2.8 is pretty close to three, so I'll estimate 2.8 as being three. And 4.73 is, if I had to estimate, I would say, "Hey, it'd be pretty close to five." So this should be pretty close to three times five, so it should be close to 15. So if I were to put the decimal there, that's way more than 15, so that doesn't seem reasonable. Even if I were to put the decimal there, 1,324.4 is still way more than 15. If I were to put the decimal there, still way more than 15. If I were to put the decimal there, hey, that actually feels about right. 13 and 244 thousandths is, is approaching 15, it's in the ballpark. And it's actually the closest, 'cause if we were to put the decimal there, then we go to 1.3244, so a lot less than 15. So if we want this to be roughly equal to 15, we definitely would wanna put the decimal right over there. That is the most reasonable computation we can do, 'cause we know the digits are going to be one, three, two, four, four, and this helps us put the decimal. In the future, we're gonna come up with ways of doing it that where you don't necessarily have to estimate, but I encourage you, the estimation is always key. If you ever in your life forget some type of method or process for multiplying decimals, it's the estimation that allows you to understand whether you're coming up with a reasonable answer. This is really important, 'cause the decimal, there's a, I remember reading a news story a couple years ago where someone put in a stock trade where they got the decimal wrong. And because of that, they essentially sold 10 times as many shares as they were supposed to, and so they lost hundreds of millions of dollars. So, anyway, decimals are important.