Estimating with decimal multiplication

We are asked to estimate what is 2.7 times 4 roughly equal to. Pause this video and see if you can answer that.

All right, so we could think of 2.7 times 4 as being roughly equal to, or some people might say as approximately equal to. Let's see, 2.7, that's two ones and seven tenths. 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 3 times 4. And then 3 times 4 is, of course, equal to 12.

You can see that these other answers actually seem quite unreasonable. 1.2, if I take something and I multiply it times 4, I shouldn't get an answer that is less than my original something. And then to take something that's roughly equal to three times four to get to 120, that doesn't make sense. It definitely doesn't make sense to get to 1200.

Let's do another example. So here, we say we said what is roughly equal to 78 times 19.88. So pause this video and try to answer that.

All right, well, this is really the same idea. We want to think about 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 80 times 20. You might already recognize that this is going to be 8 times 2 times 10 times 10. And I could write it that way, actually 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. Let me do that in that purple color so you can see it.

So this is the same thing as 8 times 10 times 2 times 10, 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 sixteen hundred. Sixteen hundred, which is this choice right over here.

It's always good to just do a 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 sometimes 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 two.

But here we're multiplying by roughly 20, and then to go from 82, 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 something that's close to 200. So I like our answer.