Estimating with multiplying decimals and whole numbers

- [Instructor] We are asked to estimate what is 2.7 times 4 roughly equal to? Pause this video and see if you can answer that. Alright, so we can think of 2.7 times 4 as being roughly equal to, or some people might say, as approximately equal to. Well let's see, 2.7, that's two ones and seven tenths. So we could think about well what's the nearest whole number to 2.7? And so 2.7 is pretty close to 3, it's in fact closer to 3 than it is to 2. So we could say that this is roughly equal to three times four. And then three times four is, of course, equal to 12. And you can see that these other answers actually seem quite unreasonable. 1.2, if I take something and I multiply times four, I shouldn't get an answer that is less than my original something. And then to go from, and then to take something that's roughly equal to three times four to get to 120, that doesn't make sense, and definitely doesn't make sense to get to 1,200. Let's do another example. So here we said what is roughly equal to 78 times 19.88. So pause this video and try to answer that. Alright, well this is really the same idea. We wanna think about, well what are numbers that these numbers are close to that are easy to multiply with. So for example, 78, that is pretty close to 80 and then 19.88, or 19 and 88 hundredths, that's pretty close to 20. It's closer to 20 than it is to 19 and even if it was closer to 19, just to estimate I probably would still go to 20 because it's easier to multiply with 20. So this is going to be pretty close to 20. So all of this is going to be roughly equal to 80 times 20. And you might already recognize that this is going to be 8 times 2 times 10 times 10 and I could write it that way, no reason for me to skip steps. But you would normally do this in your head. So 80 is the same thing as 8 times 10, we do that in that purple color so that you can see it. So this is the same thing as 8 times 10 times two times ten which we could then write this is going to be 8 times 2 which is 16, so the 8 and the 2, you get 16 times 10 times 10 is times 100 so this should be 1,600. 1,600 which is this choice right over here. And it's always good to just do reality check to make sure it's reasonable. It wouldn't make any sense if I take a number close to 80 and I multiply it by some number that's close to 20 and get a smaller number than 80. It also, if you have a number that's close to 80, to get 160 you'd only have to multiply it by roughly 2. But here we're multiplying by roughly 20. And then to go to 80, or roughly 80, to 16,000, well then you wouldn't have to multiply by something that's close to 20, you'd have to multiply by something that's close to 200. So I like our answer.