# Video: Understanding the Relationship between Units and Their Prefixes

Which of the following is the number of watts in a terawatt (TW)? [A] 10³ W [B] 10⁶ W [C] 10⁹ W [D] 10¹⁰ W [E] 10¹² W

03:13

### Video Transcript

Which of the following is the number of watts in a terawatt, shortened TW? A) 10 to the power of three watts. B) 10 to the power of six watts. C) 10 to the power of nine watts. D) 10 to the power of 10 watts. E) 10 to the power of 12 watts.

Okay, so in this question, what we need to do is to recall the conversion between watts and terawatts. But before we do, let’s recall that a watt is the base unit of power. And it’s abbreviated as a capital W and a terawatt, which is abbreviated capital TW, is some multiple of a watt. Specifically, the prefix tera is used in terawatt. And this prefix has a very specific meaning. Now, in the SI system, there are lots of different prefixes that can be used to label multiples or fractions of units. So if in this case our unit is the watt, then we can make a list of some of these prefixes in this particular case used with the watt.

So here’s what we mean by this. We can start with one of the prefixes known as the kilo. And when used with a watt, we can say that one kilo watt, which is abbreviated one kW, is equivalent to 1000 watts because the prefix kilo means 1000. And of course, we can write 1000 as 10 to the power of three. At this point, we can see that option A in our question is claiming that 10 to the power of three watts is equivalent to one terawatt. But as we’ve just seen, 10 to the power of three watts is equivalent to one kilo watt and therefore option A is not the answer that we’re looking for.

Moving on then, the next prefix up, that’s equivalent to one million watts, is known as a megawatt, abbreviated MW. And, of course, one million watts is the same thing as 10 to the power of six watts, which means that we see that 10 to the power of six watts is equivalent to a megawatt not a terawatt. And therefore Option B is not the answer that we’re looking for. Moving on then, the next prefix up is one, gigawatt abbreviated one GW, and is equivalent to 10 to the nine watts or one billion watts at which point we can see a couple of things.

Firstly, option C is not the answer to our question because 10 to the nine watts is a gigawatt not a terawatt. And secondly, as we go down our list of prefixes, we see that each prefix is equivalent to 1000 times the previous prefix. In other words, we can see that one megawatt, which is 10 to the six watts, is the same thing as 1000 multiplied by a kilowatt. And one gigawatt is 1000 lots of a megawatt. Essentially, what we’re doing is we’re increasing this power by three every time we go down the list because multiplying by 10 to the power of three is the same thing as multiplying by 1000. And therefore, at this point, we can probably guess that there isn’t a commonly used SI prefix that’s equivalent to 10 to the power of 10 watts. But let’s hold off on that for now.

Let’s continue compiling a list of prefixes. The next one on our list is going to be one terawatt. The terawatt abbreviated as TW is equivalent to 10 to the power of 12 watts. And we can see that 10 to the power of 12 watts is indeed a possible solution to our question. Therefore, at this point, we can definitely rule our option D and say that the answer to a question is that the number of watts in a terawatt is equal to 10 to the power of 12.