Determine the absolute and relative uncertainty to the following multiplication and division problem. 1.12(±0.01) x 0.546 (±0.01) / 3.12(±0.02) x 1.12 (0.03)

So just as above, we have to figure out what the absolute and relative uncertainties will be for this problem that has the operations of multiplication and division. So what we're going to do here first is we're going to determine what our answer would be when we just take into account the measurements themselves. So here, when we multiply the two top numbers and divide them by the bottom numbers that are also multiplying one another, we get 0.175. We wonit worry about the number of final digits for this measurement until we get to our absolute uncertainty and we use the real rule. At this point, because we have operations of multiplication and division, remember we first determine our percent relative uncertainty. So we're going to take the measurements of each. Well, we're going to take the uncertainties of each and divide them by their measurements times 100. So here for this first one is going to give me 0.892 857%, which we can round to 0.89%. Then we're going to have 0.01 divided by the measurement of 0.546 times 100 gives me 1.8315%. So that's going to round down to 1.83%. We have 0.02 divided by 3.12 times 100, which is going to give me 0.64-1026%, which we round to 0.64%. And then finally, we have 0.03 divided by 1.12 times 100 gives me 2.67857%, which we round down to just 2.7%. All right, now we have to figure out what our overall percent relative uncertainty will be. So we're going to say here write that over here. So our percent relative uncertainty equals each of these measurements added together. Plus 0.89% squared plus 1.83% squared plus 0.64 percent squared. So right now that gives me square root of 11.7317%. So at the end, that gives me 3.42516%. So we'll keep it at 3.4% for right now. All right. Now, remember this represents our percent relative uncertainty. Our relative uncertainty would just be that percentage divided by 100. That would be our relative uncertainty. Then if I take that relative uncertainty and multiply it by my measurement that I got earlier, that'll be my absolute uncertainty. So that comes out to 0.00595. So that's 0.006. Because our absolute uncertainty here has 3 decimal places, that means that my final measurement will have 3 decimal places as well. So we'd say here, 0.175 plus or minus 0.006 equals our absolute uncertainty. And then, 0.175 plus or minus 0.03 gives us our measurement with the relative uncertainty. So, hopefully, you guys were able to follow along. Just applying the steps that we did up above, we're able to ascertain that the answer for absolute and relative uncertainty are these two answers here.