In 2011, the total amount of energy produced as electricity around the world was 20900 terawatt-hours. 21 percent of this amount came from renewable resources. What is the amount of energy produced as electricity around the world from renewable resources in 2011? Give your answer in terawatt-hours.
Okay, so there’s a lot to unpack here. Firstly, we’ve been told that, in 2011, the total amount of energy produced as electricity, which we will call 𝐸 subscript tot, was equal to 20900 terawatt-hours. Now, this unit here, terawatt-hours, is a rather interesting one.
Firstly, the prefix tera just means 10 to the power of 12. But then, we’ve got the unit of watt multiplied by the unit of hours. Now, watt is a unit of power, not of energy. And an hour is a unit of time, which we’ll call 𝑡. But if we recall the relationship between power, energy, and time, this relationship is that power is equal to the energy transferred per unit time. And therefore, if we rearrange the equation by multiplying both sides by the time 𝑡, then on the right-hand side, we can see that we’ve got a 𝑡 in the numerator and denominator. Those can cancel. And what we’re left with is that power multiplied by time on the left-hand side or time multiplied by power is equal to the energy transferred in that time.
But then, this means that if we multiply a unit of power by a unit of time, then we will get some unit of energy. And therefore, the watt hour is indeed a unit of energy. And hence, a terawatt-hour is also a unit of energy. It’s just 10 to the 12 lots of a watt hour. So this means that even though the watt itself is not a unit of energy and that hour itself is not a unit of energy, the watt hour and therefore the terawatt-hour is indeed a unit of energy. Which means it’s perfectly reasonable for the question to give us the total energy produced in 2011 in the unit of terawatt-hours and also for it to ask us to give our answer in terawatt-hours. Anyway, so this is the amount of energy produced in total in 2011.
In the question, we’ve been told that 21 percent of this total energy came from renewable resources. And so we can say that 21 percent of the total energy produced in 2011 is equal to the energy produced by renewable resources. We’ll call this 𝐸 subscript r. And we’ve actually been asked to find this quantity 𝐸 subscript r, the amount of energy produced in 2011 from renewable resources. So to do this, what we need to do is to find 21 percent of all of the energy produced in 2011. The way we can go about doing this is to remember that 21 percent is the same thing as 21 out of 100 because the word percent simply means per cent or per 100. And so 21 percent means 21 per 100 or 21 out of 100.
In other words, if we were to take our total energy, which was 20900 terawatt-hours, and then split it into 100 bits, then 21 of those bits would’ve been produced from renewable resources. And hence, we can say that the energy produced from renewable resources is equal to 20900 terawatt-hours multiplied by 21 over 100. And then, when we simplify the right-hand side of this equation, we find that the energy produced from renewable resources is 4389 terawatt-hours. However, this is not the final answer to our question because if we look carefully, the two quantities that we’ve used in order to calculate this energy produced from renewable resources is firstly the total energy produced in 2011. And secondly, the fact that 21 percent of this energy was produced from renewable resources.
Now, the quantity 20900 is given to three significant figures. Here’s the first significant figure. Here’s the second. And here’s the third. And then, past the significant figure, it looks like we’ve rounded these values. So 𝐸 subscript tot is given to three significant figures. However, the quantity 21 percent is only given to two significant figures. And as we can recall, we should always give our answer to the lowest number of significant figures that the quantities used to calculate this answer were given to.
So in this case, we had a quantity given to three significant figures and another one given to two significant figures. Two is the lowest number of significant figures. So we’ll have to give our answer to two significant figures as well. So here’s the first significant figure. And here’s the second. We’re going to have to round off at this point. But in order to work out what happens to our three, we’re gonna have to look at the next digit. Now, this digit is an eight. Eight is greater than or equal to five. And therefore, the three is going to round up.
This means that, to two significant figures, we can say that the amount of energy produced all over the world in 2011 from renewable resources was 4400 terawatt-hours.