Orders of Magnitude Estimation Problem

[Physiona]

Hello, I'm sort of stuck with this order of magnitude question I have came across.
Q: The annual global production of jet fuel in 2010 was approximately 783 million litres.
An aeroplane consumes 0.03 litres of jet fuel per passenger for every kilometre it flies.
Estimate the number of passengers could be transported from the U.K to Australia every year. (A distance of 15223 Km)
I know that I have to round each value to the power of 10, but the estimation of passengers confused me. I'm not sure what to do.

 

[Greg Bernhardt]

Show us as far as you can get and then we can help guide you.

 

[Charles Link]

You don't need to know how many passengers are on each plane, because the info you have gives the jet fuel consumed per passenger per kilometer. The biggest question here is, does the plane need to fly back on a return flight? If so, how much fuel does it use? For the purpose at hand, you could probably assign the number zero to this. $\\$ Additional item: In the future, please use the homework template for homework questions.

 

[Physiona]

You don't need to know how many passengers are on each plane, because the info you have gives the jet fuel consumed per passenger per kilometer. The biggest question here is, does the plane need to fly back on a return flight? If so, how much fuel does it use? For the purpose at hand, you could probably assign the number zero to this. $\\$ Additional item: In the future, please use the homework template for homework questions.

Thank you for the reply. No the plane doesn't need to fly back, as it doesn't appoint that in the question. So far, I have calculated the orders of magnitude which I have to round to. According to my teacher, I rounded 783 million to 100,000,000 million and I rounded 0.03 to 0.01, and 15,223 to 10,000. Then I did 0.01 X 10,000 which equals to 100Km. I know 0.01 L is for 1 passenger for every KM, but I'm stuck on the bit where I have to estimate how many passengers it can carry. I understand the logical method but the tricky part is applying it to the estimation.
Thank you.
(I would assign the template, but it's locked and I cannot copy it here as its filtered through my email as my teacher has sent it directly, sorry)

 

[BvU]

This rounding off prescription is weird. How many litres for one passenger to fly from UK to AU ?

 

[Charles Link]

You should be able to write an equation where $x$ is the number of passengers, and $x$ multiplied by a couple of things is equal to the available fuel. Once you have that equation, you can solve it for $x$.

 

[Physiona]

This rounding off prescription is weird. How many litres for one passenger to fly from UK to AU ?

It's given in the question. That's all the actual question provides. The plane will consume 0.03L per passenger for every kilometre it flies. But when I used orders of magnitude, it apparently rounds to 0.01L

 

[Physiona]

You should be able to write an equation where $x$ is the number of passengers, and $x$ multiplied by a couple of things is equal to the available fuel. Once you have that equation, you can solve it for $x$.

Thank you for your reply. But how do I link the order of magnitude to that? As I have to use it.

 

[Charles Link]

Thank you for your reply. But how do I link the order of magnitude to that? As I have to use it.

I would wait until you get the final answer to them turn it into an order of magnitude calculation. If you start rounding up one factor of 3 and then round down another, if those approximations go in opposite directions, pretty soon you can be off by a factor of 10, which is an order of magnitude off. Even the number $.03$ that they give you is already rounded off somewhat. A number like 783 you can round off to 800, but there is no need to initially round it off to 1000.

 

[Physiona]

I would wait until you get the final answer to them turn it into an order of magnitude calculation. If you start rounding up one factor of 3 and then round down another, if those approximations go in opposite directions, pretty soon you can be off by a factor of 10, which is an order of magnitude off. Even the number $.03$ that they give you is already rounded off somewhat. A number like 783 you can round off to 800, but there is no need to initially round it off to 1000.

Oh okay, so I don't have to use the orders of magnitude to round the values to the powers of 10, right, and I round my final answer to an order of magnitude? (If that's what you are trying to say) I'll do it, and I'll show you my working out . Thank you.

 

[BvU]

This rounding off prescription is weird. How many litres for one passenger to fly from UK to AU ?

It's given in the question. That's all the actual question provides.

What is? The prescription, or the .03 l/km ?

The plane will consume 0.03L per passenger for every kilometre it flies. But when I used orders of magnitude, it apparently rounds to 0.01L

No. One kilometre fuel is given -- in one decimal accuracy.
So 15523 km use up 450 litres -- 500 if you insist on crude rounding off.