Video Transcript
A device measured a force of 6.3 nanonewtons. How many newtons are there in this measurement? 6.3 times 10 to the negative six newtons, 6.3 times 10 to the negative nine newtons, 6.3 times 10 to the negative 10 newtons, 6.3 times 10 to the negative 15 newtons.
This question is asking us to take the result of a measurement with units of nanonewtons and reexpress it in units of newtons without changing its value.
Now, the word “nanonewtons” consists of “newtons,” which is the base unit, and a prefix nano-. Now, we recall that unit prefixes represent powers of 10. In particular, the prefix nano- represents 10 to the negative nine. To represent this, we write nano- equals 10 to the negative nine. And what this equality means is that we can always replace the prefix nano- with the number 10 to the negative nine without changing the overall value of our quantity.
Unfortunately, there is no way to derive the correspondence between prefixes and powers of 10. Instead, these are some of the few facts in physics that we just need to memorize in order to recall and use later. Anyway, because nano- stands for 10 to the negative nine, we can write that nanonewtons are equal to 10 to the negative nine newtons, where again by this equality we mean that we can replace nanonewtons with 10 to the negative nine newtons without changing our value.
From the question, we know our initial value is 6.3 nanonewtons. So, if we replace nanonewtons with 10 to the negative nine newtons, we get 6.3 times 10 to the negative nine newtons. And this is answer choice (B). 6.3 nanonewtons is 6.3 times 10 to the negative nine newtons.
