Video: Using Unit Prefixes to Represent Very Small Numbers

Which of the following is equal to one nanowatt when multiplied by one watt? [A] 10⁹ [B] 10⁻⁸ [C] 10⁻⁹ [D] 10⁶ [E] 10⁻⁶.

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Video Transcript

Which of the following is equal to one nanowatt when multiplied by one watt? A) 10 to the power of nine, B) 10 to the power of negative eight, C) 10 to the power of negative nine, D) 10 to the power of six, E) 10 to the power of negative six.

Okay, so this question is worded in a bit of a confusing way. Essentially, what it’s asking us is which one of these options — so let’s say one of these options will be filled out in this blank here — is equal to one nanowatt, which we can write as one lower case n capital W, when multiplied by one watt. In other words, we have to stick one of the options A to E in this blank here, and when we multiply that option by one watt, we get one nanowatt.

So, let’s start by recalling that the watt is a unit of power, and nano is a prefix. Specifically, it’s one of the SI prefixes used to represent either a large multiple or a small fraction of the unit that we’re using, in this case the watt. More specifically, we can recall that one nanowatt, abbreviated nW, is equal to 10 to the power of negative nine watts.

And therefore, looking at the options A to E that we’ve been given, we can see that if we stick 10 to the power of negative nine into our blank here, then what we’d get is 10 to the power of negative nine multiplied by one watt is equal to one nanowatt. Which we’ve already seen is equivalent to 10 to the power of negative nine watts. And 10 to the power of negative nine multiplied by one is indeed equivalent to 10 to the power of negative nine. Therefore, we’ve got the exact same thing on the left-hand side and on the right-hand side. In other words then, the answer that we’re looking for is option C. 10 to the power of negative nine multiplied by one watt is equivalent to one nanowatt.

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