Fermi Problems — Definition & Examples
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- Often, you might find it useful to estimate the size of something without very much information. Rather than to get a precise answer, you might aim to get an order of magnitude …
By Moor Xu, Liza Sulkin, Alex Federspiel, Joshua Siktar, Jonathan Heller
- Tips and Tricks for Fermi Problems: Use Nice Numbers One of the highlights of Fermi Problems is that you are asked to estimate a given quantity rather than find its exact value.…
By Joshua Siktar, Alex Federspiel, Caroline K, Jonathan Heller
- (Video) A Clever Way to Estimate Enormous Numbers by TED-Ed Here's a great video by TED-Ed that explains Fermi Problems and their uses. Summary\large{\text{Summary}}Summary The …
By Alex Federspiel, Jonathan Heller, Joshua Siktar
Problems 35
- Here is another famous Fermi Problem: How many drops of water are in all of the oceans on Earth? If you think there are DDD drops, round DDD to the nearest integer power of ten,…
- Try this one: How many AA Batteries could fit in a sphere of the same radius as the Earth? If you think the BBB batteries, round BBB to the nearest integer power of ten, 10N10^N…
- How many human hairs are lost every day? If you think there are HHH hairs lost every day, round HHH to the nearest integer power of ten, 10N10^N10N, and submit the value of NNN …
- How many gallons of gas would it take to drive to the moon? If you think it would take GGG gallons, round GGG to the nearest integer power of ten, 10N10^N10N, and submit the val…
- Given that 210=10242^{10} = 1024210=1024, how many digits does 2532^{53}253 have?
- How many taste buds are there on the average human tongue, to the nearest power of ten?
- Evaluate 9452945^29452 without a calculator. (Hint: 945945945 is between 900900900 and 100010001000.)
- Evaluate without a calculator: 7952795^27952. (Hint: 795795795 is close to 800800800.)
- Olivia Munn was selecting dresses for the Academy Awards, and one of her finalists was a full length gown covered in 6mm sequins. How many sequins are there in her dress? \\ (Th…
- The ozone layer is a region of the Earth's atmosphere with a high concentration of ozone that blocks most of the sun's harmful UV radiation. The ozone concentration is greatest …
- How many times more powerful is the radiation intensity at a distance equal to a palm's width, versus the radiation intensity at a distance equal to an arm's length?
- A U-2 spy plane's camera has the resolution of 2.52.52.5 feet at an altitude of 60,00060,00060,000 feet. If you were flying in the U-2 spy plane, what is the smallest object tha…
- If all of the 777 billion people in the world stood shoulder to shoulder, packed like sardines, what is the smallest country that they could fit inside?
- Ever wonder how large the bursts are in a fireworks displays? It turns out that the burst diameter is roughly 454545 feet per inch of the diameter of its shell. How wide will th…
- If the water from this storm was all collected (and purified), how many people could it support for one week?
- Pumpkin pie is a classic part of the American Thanksgiving dinner. Libby's produces 85%85\%85% of the canned pumpkin worldwide, which is enough for 909090 million pies. Each can…
- Suppose the dimensions of a city are "roughly 300030003000 times" the dimensions of a detailed city map. What can you conclude? Select all that apply.
- What is the order of magnitude of 106×π5×300−3?10^6\times \pi^5\times 300^{-3}?106×π5×300−3?
- How many cups of coffee do the Expii employees drink per year? Remember, for Fermi problems, the order of magnitude is more important than a precise value.
- If you stacked all the people in the world on top of each other, how tall would the stack be (in feet)? Remember, for Fermi problems, the order of magnitude is more important th…
- How many times does a person's heart beat in a day? Remember, for Fermi problems, the order of magnitude is more important than a precise value.
- How many times does a person blink in a year? Remember, for Fermi problems, the order of magnitude is more important than a precise value.
- Approximate the following expression without a calculator: 10!10!10!
- Approximate the following expression without a calculator: 7107^{10}710
- Approximate the following expression without a calculator: 108×299×20000−310^8\times 2^{99}\times 20000^{-3}108×299×20000−3
- How many digits does 99999\sqrt{99999}99999 have?
- How many problems are there on Expii? Remember, for Fermi problems, the order of magnitude is more important than a precise value.
- How much should you charge the Scottish government for you to drain the Loch?
- Approximately how many blades of grass are in the state of Pennsylvania?
- Assuming you can only use your ten-gallon hat as a cup to carry water from the ocean into the tank, how many trips do you have to make to fill the whole tank? Remember, for Ferm…
- An average tire on a new car lasts for 50,00050,00050,000 miles. Approximately how many times could a tire rotate before it is worn out?
- How many windows are in New York City?
- Approximate the number of ice cubes that can fit into a bathtub to the nearest order of magnitude.
- How many times does an average person’s heart beat in a lifetime?
- The U.S. State Route 505050 is exactly 3017.1973017.1973017.197 miles long, ranging from Ocean City, Maryland, to West Sacramento, California (Wikipedia). Let's say the gods hav…