Subtracting decimals: standard algorithm
We need to calculate 9.005 minus 3.6, or we could view it as 9 and 5 thousandths minus 3 and 6 tenths. Whenever you do a subtracting decimals problem, the most important thing, and this is true when you're adding decimals as well, is you have to line up the decimals. So this is 9.005 minus 3.6. So we've lined up the decimals, and now we're ready to subtract. Now we can subtract. So we start up here. We have 5 minus nothing. You can imagine this 3.6, or this 3 and 6 tenths, we could add two zeroes right here, and it would be the same thing as 3 and 600 thousandths, which is the same thing as 6 tenths. And when you look at it that way, you'd say, OK, 5 minus 0 is nothing, and you just write a 5 right there. Or you could have said, if there's nothing there, it would have been 5 minus nothing is 5. Then you have 0 minus 0, which is just 0. And then you have a 0 minus 6. And you can't subtract 6 from 0. So we need to get something into this space right here, and what we essentially are going to do is regroup. We're going to take one 1 from the 9, so let's do that. So let's take one 1 from the 9, so it becomes an 8. And we need to do something with that one 1. We're going to put it in the tenths place. Now remember, one whole is equal to 10 tenths. This is the tenths place. So then this will become 10. Sometimes it's taught that you're borrowing the 1, but you're really taking it, and you're actually taking 10 from the place to your left. So one whole is 10 tenths, we're in the tenths place. So you have 10 minus 6. Let me switch colors. 10 minus 6 is 4. You have your decimal right there, and then you have 8 minus 3 is 5. So 9.005 minus 3.6 is 5.405.