Fermi Questions Marathon

[hmcginny]

So the US is E13 square meters in area, there are maybe E6 maple trees in the US, if we're counting just the area they take up on the ground, each one has a round trunk maybe half a meter in radius so ~1.5 m^2 so E6/E13 is E-7.

What percentage of the earth's mass consists of humans?

And cngu23 you didn't take into count exponential growth for the population question. Earth's population grows a little over 1% every year, so it will double every 70 years. 1 trillion is 1000 billion and 1000/6.7 is around 150. the closest power of 2 to 150 is 128 which is 2^7 so the population will double 7 times, meaning 490 years, however the doubling time is a little less than 70 years because the growth rate is slightly over 1%, so the answer is E2.

[cngu23]

So the US is E13 square meters in area, there are maybe E6 maple trees in the US, if we're counting just the area they take up on the ground, each one has a round trunk maybe half a meter in radius so ~1.5 m^2 so E6/E13 is E-7.

What percentage of the earth's mass consists of humans?

And cngu23 you didn't take into count exponential growth for the population question. Earth's population grows a little over 1% every year, so it will double every 70 years. 1 trillion is 1000 billion and 1000/6.7 is around 150. the closest power of 2 to 150 is 128 which is 2^7 so the population will double 7 times, meaning 490 years, however the doubling time is a little less than 70 years because the growth rate is slightly over 1%, so the answer is E2.

True. I could have used the growth rate formula but I didn't have enough time. Fermi questions are based more on quick yet accurate estimations. Also, I don't think that fermi questions should require anything more than multiplying many unit conversions.

Mass of earth 6E24 kilograms
Human population 7E9
Let's say the average human weights 80 Kilograms? 8E1

Mass of all humans will be 7E9 x 8E1 = 56E10 ~ 6E11

So I divide the mass of the earth by the mass of all humans 6E11 / 6E24

So all the humans weight 1/10E13 the mass of the Earth.


Question: How many sodium atoms fit on the word "question"?

[hmcginny]

So an average atom has a radius of 3E-10 m or 3E-8 m. the word question is around 2 cm long by 1 cm high but has no depth (its light). so you could fit E12 atoms on the word question (E-2/E-8)^2. of course the word question doesn't fill the space but even if its only half that its still the same order of magnitude.

growth rate formula made sense to me just because it only took maybe 30 seconds longer to use and got me closer to the actual number. i'm not sure how long the test will actually be, but with two people splitting it I can't imagine you will have to do more than a question a minute at competition.

How many big macs have been sold at McDonald's?

[Bogoradwee]

so.... Big Macs came out in the 70's... right? so I'm gonna just say 1975... I remember hearing that mcdonald's has served over 9 billion people, and they're more popular now than ever. The company started in... mid-fifties? so, since 1955 it's been 56 years, since 1975 they've probably had something like 80% of their total sales, so 7.2 billion sales total, I'm gonna guess 1B<x<5B so my answer is 9.

How many times more powerful are computer processors now than they were when Windows 98 came out?

{click for answer} (Click to Show Hidden Text)

{8}

Edit: idk where I got some of those numbers for big macs. I think my final answer is off

[cngu23]

How many times more powerful are computer processors now than they were when Windows 98 came out?

{click for answer} (Click to Show Hidden Text)

{8}

Edit: idk where I got some of those numbers for big macs. I think my final answer is off

Am I missing something or can you explain the math in your question?
Idk how to incorporate math into the problem but I'm going to guess 5-10 times?

Next Questions: How many molecular biology teachers live in San Francisco?

[hmcginny]

ok so San Francisco is 1E6 people, lets say a little less than 10% are middle school/high school age so thats thats -E5 students. Around 5E3 students per high school/middle school combo and only maybe 2 or 3 molecular bio teachers per set of schools so lets say 2E1 schools and E2 molecular bio teachers, because you add in a handful for all the colleges in the area.

How many moles of carbon are there in a standard sized blimp?

On the computer question: Thats probably not the best fermi question, it's mainly a fact-based question with very little math or conversion necessary. Most questions it is possible to assume things, like how often people eat big macs or how many schools there are in San Francisco for example, but then you have to use those assumptions to determine an answer. I like the idea of the question and of course it's still a completely valid question, however if there is some mathematical way to solve it please share.

On the big mac question: Great job, you were very close with that logic. The internet says E10. I can't really think of a better way to determine it, I think your total sales number is a little low though, thats your only error, but thats unavoidable.

[Bogoradwee]

How many times more powerful are computer processors now than they were when Windows 98 came out?

{click for answer} (Click to Show Hidden Text)

{8}

Edit: idk where I got some of those numbers for big macs. I think my final answer is off

Am I missing something or can you explain the math in your question?
Idk how to incorporate math into the problem but I'm going to guess 5-10 times?

Next Questions: How many molecular biology teachers live in San Francisco?

I think I worded that wrong, but what I meant to say was like comparing what a micro-SD can do today to what something of its physical size could do then. Supposedly, storage size can roughly double every 6 months (or so I've heard) so you would take 2^26

[Schrodingerscat]

How many moles of carbon are there in a standard sized blimp?

Instead of a quick answer I feel like trying to estimate the lifting power for a blimp.

I will estimate about 50x10x10m=5E3m^3
Helium in air should provide lift somewhere around 0.7kg/m^3
so therefore the blimp could support about 3E3 kg.
I will also guess that the cabin is likely made largely out of light metals, but the rest of the blimp is made out of plastics, so A fraction of that will likely be carbon, so I will predict 1E3 kg of C
To do it quickly its something like 60 moles per kg, so I will say 6E4 moles of carbon or E5.

If the titanic sank in fresh drinkable water, how many people could be given drinking water for a day with all the water within it?

[hmcginny]

The titanic was like what E3 by E1 by E1 meters? so E5 cubic m. Lets just say that includes all the stuff in the titanic, so E5 cubic meters of drinking water. E11 cubic cm and E11 ml which is E8 liters. Each person drinks 2 liters a day so E8 people for a day.

How many jelly beans would fill the grand canyon?

[49ers]

The volume of the grand canyon is about 4.17 trillion cubic meters or 4.17*10^9 m^3 or 4.17*10^11cm^3. On average, the volume of a jelly bean is ~3.5 cm^3. So 4.17*10^11cm^3/3.5*10^1cm^3 is about 1.2*10^10 jelly beans. so is the answer 10?