Adding decimals with thousandths | Adding decimals | Grade 5 (TX TEKS) | Khan Academy

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. 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 one's place, so that's a zero.

In this case, we're essentially going to line up the decimal as well. Line up the Ten's place, so this is zero, and then the hundreds place, and then the thousand's place. This is another way to write the same thing.

Now what I want to do is go to the smallest place value. So let's go to the thousand's place, and you might say, "Hey, this top number doesn't have a thousand's digit." Well, you could just put a zero there.

So we could first think about adding 0,000 to 3,000. Well, that's going to be 3 thousand; a three in the thousand's place. Then I could go over to the hundreds place: 5 hundredths plus 1 hundredth is 6 hundredths.

Then I can go to the 10's Place: 4 tenths plus 0 tenths, or no tenths, is going to be 4 tenths. Of course, I don't have any ones, so the decimal will just show up right there to the left of the 10's place.

And then, 0 ones plus 0 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: 0.745 plus... let me 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 0.4, 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. 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 thousand's place.

So we have 5 thousand plus 5 thousand; that's 10 thousand. Or, well, you can't put a 10 in the thousand's place. 10 thousand is the same thing as 1 hundredth. So one way to think about it is this is 0, and 1 hundredth.

We regrouped. Some people might say, "Hey, 5 + 5 is 10, right? The zero carry the one." But what's really going on here is you're saying 5 thousand plus 5 thousand is 10 thousand. 10 thousand is 1 hundredth and 0 thousand is another way to think about it.

So now we go to the hundred's place: 1 hundred plus 4 hundred plus 8 hundredths. 1 plus 4 plus 8 is 13 hundredths. 13 hundredths is the same thing as 3 hundredths and 1 tenth. We regrouped that 1 tenth or that 10 hundredths as 1 one.

Then we go to the 10's place and we have 1 plus 7 plus 2; that's 10 tenths. Well, 10 tenths is a whole. So we could regroup 10/10 as 1 whole.

What we would do is we would say, "Okay, that is the same thing as 0 tens and 1 whole." And last but not least, we can add the 1 whole plus a bunch of zero holes or zero ones, and we're going to be left with just a 1.

And we're done! This is going to be equal to 1.03.