The following questions and estimated solutions are presented by 8th graders at Harwood Union Middle School in honor of Enrico Fermi. The blog is inspired by a modern day Fermi geek, Dr. Aaron Santos, who writes his own blog, A Diary of Numbers. Check out his link in the side bar.
Monday, October 28, 2013
How many eye drops would it take to fill all of the pools in America?
1. Background Story: One day a thought came into my head “How many eye drops are in an eye dropper?” That led me to a different question “how many eye drops are in a pool?” and that gave me my final question “How many eye drops will it take to fill all of the swimming pools in America?” I thought this would be really complex and Interesting.
2. Ask Yourself This:
how many eye drops are in an eyedropper?
how many swimming pools are in america?
How many gallons of water does an average swimming pool have?
how many liquid oz are in an eye drop container?
how many liquid oz are in a gallon?
3. Helpful Hints:
there are approximately 10 million pools in the USA http://www.cdc.gov/healthywater/swimming/
The average pool is 21 feet and holds 25,000 gallons http://www.ask.com/question/how-many-gallons-of-water-does-the-average-21-ft-swimming-pool-hold
An eye drop container has .5 loz of water, this is common knowledge
there are 900 drops of liquid in a oz, I tested this.
1 gallon has 128 liquid ounces http://www.ask.com/question/how-many-ounces-are-in-a-gallon
b.
I estimated the amount of drops because there are approximatley 30 drops per millileter and about 30 millileters in an ounce.
4. Construct a Formula:
you multiply the loz in an eye dropper and the loz in a gallon
you take the eyedrops in a gallon and multiply that by the gallons in a pool
you then multiply the eyedrops in a pool by the number of pools in the usa
eyedrops per bottle x ounces per gallon
eyedrops per gallon x gallons per pool
eyedrops per pool x amount of pools in the USA
5. Messy Math: Plug in the numbers you need from the Helpful Hints or the assumptions you are making into your formula. One of your calculations must be performed with Scientific Notation. Check that your units cancel so you end with the correct final unit.
450 drops x 128 loz = 57600 drops per gallon
57600 drops x 25000 = 1440000000
1.44 * 10^7 x 1 * 10^7 = 1.44 x 10 ^14
6. Answer: There are 14,400,000,000,000,000 or Fourteen quadrillion four hundred trillion eye drops. If each eyedrop was a mile you could go around the earth 578,290,028,513 times
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