Everyone, welcome back. So in this problem, we have these two blocks. We're told some information about the side lengths of block a, which are 0.5 meters, 0.875, and 2.25. And we are directly told what the volume of block b is. We don't have to do any calculations there. We're asked to find what the total combined volume of the blocks is, expressed with the correct number of significant figures. That's really important. Alright? Let's go ahead and get started here.
So, if you want to find the total volume, I'm going to just call this Vtotal, you can think about this as, well, I've got these two blocks. The total volume of them both combined is really just going to be the volume of block a plus the volume of block b. We already know what the volume of block b is. We just have to figure out what it is for a. And because it's a block, I'm just going to assume that it's a cube, then the volume of a cube is just going to be length times width times height. Right? That's what volume is equal to. So in other words, I can actually write this as one total equation just by doing length times width times height plus the volume of block b.
Now I'm just going to go ahead and replace some of these things with some numbers here. So this is going to be 0.50 times 0.875 times 2.250, and that's going to be plus the volume, which is 2.6. So how do I actually do this? Remember, significant figures are going to be important, especially when you're dealing with calculations involving operations. And if you look here, I actually have a mixture of operations. I've got multiplication here over in this parenthesis, and then I've got addition. So I'm going to stick to rule 3, right, which is that I'm going to have to use PEMDAS, and then I'm going to have to sort of save all the values in the intermediate steps, and I'll do all the rounding at the end. So the first thing I'm going to have to do here is I'm going to have to figure out what is this first intermediate step where I'm only just doing multiplication.
Well, for multiplication, we're going to follow rule 2. Right? When we're doing multiplication, we're looking at the significant figures. Here, there are two significant figures. Here, there's three, and then here, there are four. If I just plug this into my calculator, what I'm going to get is I'm going to get 0.984375. So remember, I'm not going to round yet. I'm going to save all of these numbers. But what I'm going to do is I'm going to indicate where my last significant figure is. I'm going to put a little mark here. So the last one that's significant is the 8 because this is the second significant figure. This is the least number of significant figures that I have.
Alright? So without rounding anything, now what I'm going to do is I'm going to take 0.984375, and I'm going to add this to 2.6. So now what happens is, now you're actually just doing addition and subtraction. So now for this final answer here, we're going to have to stick to the rule where we're going to look at the decimal places, and we're going to have to stick to the least number of decimal places. Alright? So what happens here is, here we have one decimal place. I'm going to put 1 DP here, and this is going to be the second decimal place. That's the last significant figure for that number over here. So when you add these things together, what you're going to get is 3.584375. But now we have to round it. So right? So we're going to round this final answer to the first decimal place, and what you're going to get here is 3.6 meters cubed. Right? So this is the correct answer.
So notice how, again, we don't want to round in the intermediate steps because by rounding, you're basically sacrificing some accuracy, and then your answer actually could be off by quite a bit if you just keep on rounding in the immediate steps. Alright. So it's always good to keep all your digits and then round at the end according to that rule. That's it for this one, folks. Let me know if you have any questions.