Here are example states. A TA can grade 4 assignments per hour. If each assignment has 12 questions, how many questions can the TA grade in 130 minutes? Alright. So, if we're going to approach a question like this, let's look at our steps. If present, start with the given amount that is not a conversion factor. So remember, our given amount is when we have a single unit by itself that isn't tied to another. We're going to say within this question, our 130 minutes is our given amount. Identify the end amount you want to isolate for your unknown. So, we're going to say here this is our given amount, we have to figure out what our end amount will be. So, our end amount is over here. They're asking us how many questions. So, questions will be our end amount.

Step 2, write down all the conversion factors. So, all our conversion factors, let's see. We have 4 assignments per hour. Remember, 'per' is the word that connects different units together. So, one is 4 assignments every per hour, so that's 4 assignments for every 1 hour. They tell me also each assignment has 12 questions. So, that means one assignment is 12 questions. Okay. So, 12 questions. Now, this last part, find the connection between the given amount and the conversion factors in order to isolate the end amount. So, let's look at the given amount. The given amount has minutes within it, but neither of the conversion factors has minutes involved. What we do have is hours. That tells me there's a conversion factor that's even before either one of these two.

So, our first conversion factor actually involves us first changing minutes into hours. So, we have minutes here on the bottom, hours here on top. 1 hour is 60 minutes. Minutes cancel out this way. And the reason we're doing that is because now that we have hours, we can connect it to the hours here within this conversion factor. So, that'll be my second conversion factor, bringing in the 1 hour for every 4 assignments. Now that we have hours lined up, they cancel out. Now we have assignments, and we need to get the questions. Here is our last conversion factor. Now it has assignments and questions within it, but we need assignments to cancel out. So, assignments need to be here on the bottom, right? And then we need questions, questions go here on top. And it is one assignment is 12 questions. Remember, one of the first things we said is that conversion factors, we can flip them. They can be presented in two different ways. Here, we had to flip the initial conversion factor so that assignments could cancel one another out. They have to be on opposite levels to do that. So, in conversion factor 3, what I'll have left at the end is questions.

So what we do now is we're going to multiply 130 times 4 times 12 divided by 60. So when we do all of that, we're gonna get here a 130 well, actually, no. Not a 130. We're gonna get here, as our final answer, 104 questions. So, we have 104 questions as our end amount, but remember we need to worry about significant figures. 130 has 2 significant figures, 4 has 1 significant figure, 12 has 2 significant figures, 60 has 1 significant figure. So, we need to go and have only 1 significant figure as our final answer. So, we'd say roughly about 100 questions is what the TA could do within 130 minutes, which is a lot of questions. Alright. So now that we've done this example where we've set up the basic principles behind dimensional analysis, let's continue onward and do some practice questions.