Estimating decimal subtraction (thousandths)

0:00- [Instructor] In this video, we're gonna get some practice estimating the difference of numbers with decimals in them. So for example, if I wanted you to estimate what 16.39 minus 5.847 is, what do you think this is approximately equal to? This little squiggly equals sign means we're estimating.

0:21It's not... It doesn't have to be exact. Pause this video and think about that. Well, there's a lot of ways that you might want to do this. The way that I think about it is, well, okay, both of these numbers are a lot larger than one. So maybe I round to the ones place and then I can do the subtraction in my head.

0:40So for example, 16.39, this right over here. Let me draw a little number line here. And we know that it is between 16 and 17, 16.39. It's a little bit less than halfway. So it's maybe right over here. And from that, you can see that it is rounding to the one's place.

1:02It's closer to 16 than it is to 17. So we could say this is approximately 16 right over here. And then we could do the same thing for 5.847. We know that that is between five and six on the number line. I could put arrows here if I want, just to make clear that these things keep going.

1:28This would be halfway. 5.847 is much closer to this end right over here. It's going to be right over there. (laughs) I took a little weird turn there. But if we're rounding it to the nearest one, to the nearest whole number, we can see that it's much closer to six.

1:45So we're gonna round up to six. So we could say this is approximately equal to six. And so this is going to be roughly equal to or approximately equal to 16 minus six. So this is approximately equal to 16. I keep switching colors in the wrong way. 16 minus six, which is, of course, going to be equal to 10.

2:15So it's not gonna be exactly 10, but roughly 10. Now let's do another example where the numbers are a lot smaller. So let's say we wanna figure out what does 0.781 minus 0.326 approximately equal? Pause this video and try to think about that. Well, here it wouldn't make sense rounding to the nearest whole number because this is going to round to zero.

2:39So let's think if we just had the whole number. So let's think about it a little bit differently. Why don't we round to the nearest 10th, to the nearest 10th? So let's put a number line here. And well, let me think about this first one. This first number over here, 0.781.

2:58It is larger than 0.7 and it is less than 0.8. And if this were halfway, where does this sit on the number line? Well, 0.781. 0.781 is going to be much closer to this end right over here. So you could see if you round to the nearest 10th, you're going to round up to 0.8.

3:27So this is approximately 0.8. And then we could do something similar with this number. Once again, we're rounding to the nearest 10th. This is greater than 0.3, and it's less than 0.4. This is less than halfway, 0.326. So it's going to be someplace around there.

3:52If we're rounding to the nearest 10th, we're clearly closer to 0.3 than we are to 0.4. So we'll round down to 0.3. So this is going to be approximately equal to 0.8 minus 0.3, which we can do in our heads. This is going to be 0.5. So the whole point of this is estimating when we're subtracting decimals.

4:22Now one of the really useful things about this is when you might use it every day in life if you don't have to figure out the exact number, but you just want an estimate it. But it's also good once you learn to actually calculate how to subtract decimals to double check your answer.

4:36Does it sound reasonable after you've done all of the mathematics.