Adding decimals with thousandths

- [Instructor] So, what we have here are two questions where they're asking us to add decimals. So, pause this video and have a go at this before we do this together. All right, so, let's tackle this first question up here. And what I like to do is line up these numbers based on place value. So, I could rewrite this as 0.45 plus, now let's line up the ones place. So, that's a zero in either case. And we're essentially going to line up the decimal as well. Line up the tenths place, so this is zero. And then, the hundredths place. And then the thousandths place. So, this is another way to write the same thing. And now what I want to go is to the smallest place value. So, let's go to the thousandths place. And you might say, "Hey, "this top number doesn't have a thousandths digit." Well, you could just put a zero there. And so, we could first think about adding zero thousandths to three thousandths. Well, that's going to be three thousandths, a three in the thousandths place. Then, I could go over to the hundredths place, five hundredths plus one hundredth is six hundredths. Then I can go to the tenths place. Four tenths plus zero tenths, or no tenths, is going to be four tenths, of course. And then, I don't have any ones. The decimal will just show up right there to the left of the tenths place. And then I have zero ones plus zero ones. Well, that's just still going to be zero. So, there you have it. This is going to be 0.463. Now let's do this example right over here. Same idea. Let me line them up based on place value. So, 0.745 plus, lemme write that a little bit neater, plus 0.285. Always double check. Make sure you're lined up with the right place values. A lot of times you'll see people do things like 0.745 plus maybe 0.285. If you did something like this, you're going to make a mistake. So, make sure that you line up based on place value. And the easiest way is often to line up the decimal. But once you do that, we go through the same idea where we start in the thousandths place. So, we have five thousandths plus five thousandths, that's 10 thousandths. Or well, you can't put a 10 in the thousandths place. 10 thousandths is the same thing as one hundredth. So, one way to think about it is this is zero thousandths and one hundredth. We regrouped. Some people might say, "Hey, five plus five is 10, right, "zero carry the one." But what's really going on here is you're saying five thousandths plus five thousandths is 10 thousandths. 10 thousandths is one hundredth and zero thousandths is another way to think about it. So now, we go to the hundredths place. One hundredth plus four hundredths plus eight hundredths. One plus four plus eight is 13 hundredths. 13 hundredths is the same thing as three hundredths and one tenth. We regrouped that one tenth or that 10 hundredths as one 10th. And then, we go to the tenths place and we have one plus seven plus two. That's 10 tenths. Well, 10 tenths is a whole. So, we could regroup 10 tenths as one whole. So, what we would do is we would say, okay, that is the same thing as zero tenths and one whole. And then last but not least, we can add the one whole plus a bunch of zero wholes, or zero ones, and we're gonna be left with just a one and we're done. This is going to be equal to 1.030.