Estimating decimal subtraction (thousandths) | Grade 5 (TX TEKS) | Khan Academy

In this video, we're going to 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 5.84 is, what do you think this is approximately equal to? This little squiggly equal sign means we're estimating; it doesn't have to be exact. Pause this video and think about that.

Well, there are a lot of ways that you might want to do this. The way I think about it is, well, okay, both of these numbers are a lot larger than one, so maybe I round to the one's place, and then I can do the subtraction in my head. So, 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 is a little bit less than halfway, so it's maybe right over here. From that, you can see that it is, for rounding to the ones place, it's closer to 16 than it is to 17. So we could say this is approximately 16 right over here.

Then we could do the same thing for 5.84. We know that that is between 5 and 6 on the number line. I could put arrows here if I want just to make clear that these things keep going. This would be halfway; 5.84 is much closer to this end right over here. It's going to be right over there. 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 6, so we're going to round up to 6.

So we could say this is approximately equal to 6, and so this is going to be roughly equal to or approximately equal to 16 minus 6, which is of course going to be equal to 10. So it's not going to be exactly 10 but roughly 10. Now, let's do another example where the numbers are a lot smaller.

So, let's say we want to 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. So let's think if we said whole number, so let's think about it a little bit differently. Why don't we round to the nearest tenth? To the nearest tenth.

So, let's put a number line here. And, well, let me think about this first one. This first number over here, 0.781, 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 is going to be much closer to this end right over here. So you could see if you round to the nearest tenth, you're going to round up to 0.8. So this is approximately 0.8.

Then we could do something similar with this number. Once again, we're rounding to the nearest tenth. This is greater than 0.3 and it's less than 0.4. This is less than half; 0.326, so it's going to be someplace around there. If we're rounding to the nearest tenth, we would, 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. Now, one of the really useful things about this is what you might use every day in life if you don't have to figure out the exact number but you just want to estimate it.

But it's also good once you learn to actually calculate how to subtract decimals to double-check your answer. Does it sound reasonable after you've done all of the mathematics?