Monday, October 28, 2013

How many grains of salt does it take to fill up a kiddie pool?

Background Story:
 How many grains of table salt will it take to fill up a kiddie pool?
I chose this problem because I have realized how small a grain of salt really is. I was wondering how many grains of salt it would take to fill up a salt shaker. As I was thinking about that I was looking out the window into one of our neighbors yard and say a kiddie pool. That led me to think, how many grains of salt would it take to fill up a kiddie pool?
Ask Yourself:
Some questions I came up with to help me find the answer to the problem were:
How many cubic feet are in a kiddy pool?
How many grains of salt in a square foot?
How many layers of salt in a cubic foot?
How many grains of table salt fill up in a cubic foot?
Helpful Hints:
After doing some work I found answers to my questions, the answers were:
31.213 cubic feet in a kiddie pool.
about 1,900,000,000 grains of table salt in a square foot.
2 grains of salt in a millimeter
120 millimeters in a foot
240 grains of salt in a foot.
            456,000,000,000 grains of table salt in a cubic foot.
about 14,233,128,000,000 grains of table salt in a kiddie pool.
Construct a Formula:
The method I used to find out about how many grains of table salt were in a cubic foot was not that hard. What I did was I took a salt shaker and counted roughly how many grains of salt were on the bottom of the salt shaker, there were about . Then I counted how many grains of salt were stacked up to the top layer of salt. I multiplied them together and got 190,000,000. After that I poured them on the palm of my hand to see if they would fill it up, and they did. I then figured out that that about 10 of the palms of my hand could fit in a square foot. Then I multiplied 190,000,000x10=1,900,000,000. For the height of the the cubic foot I figure that there were about 2 grains of salt in a millimeter and there are 120 millimeters in a foot. So then I did 120 millimeters in a foot x2 grains of salt per millimeter =240[e] grains of salt in a foot. So I knew that 240 grains of salt fit the height of a cubic foot. Then I multiplied how many grains of salt were in a square foot by the number of layers of salt in a cubic foot and got about how many grains of salt are in a cubic foot.  
To find out the answer to my questions I could multiply the number of  grains of salt in a square foot by the number of layers of salt in a cubic foot. That answer would give me how many grains of salt in a cubic foot.[f]Then I could multiply the number of grains of salt in a cubic foot by the number of cubic feet in a kiddie pool to get how many grains of salt can fill up a kiddie pool.
The equation would look like this:
grains of salt layers of salt square feet grains of salt
 kiddie pool        square foot      1 kiddie pool    kiddie pool
Messy Math:
When I put all of my numbers in the equation and do the math this is what it all looks like:
31.213 cubic ft   120 mill 2 grains of salt 19.x10e8 Grains of salt = 1.4231128x10e14 grains of salt in a kiddie pool
1 kiddie pool             1ft               1mill                            1 square ft                     1 kiddie pool[h]
31.213 cubic feet in a kiddie pool.
about 1,900,000,000 grains of table salt in a square foot.
2 grains of salt in a millimeter
120 millimeters in a foot
240 grains of salt in a foot[c]                                                                                                                                          456,000,000,000 grains of table salt in a cubic foot.
about 14,233,128,000,000 grains of table salt in a kiddie pool.[d]   
1,900,000,000 grains in a cubic foot X 31.213 cubic feet in kiddie pool = 14,233,128,000,000 grains of salt in a kiddie pool.  
 I wanted to put my numbers in scientific notation so they were easier to work with.
This is how I did it:
14,233,128,000,000                            
1.4231128000000
decimal point moved 14 places
1.4231128
1.4231128x10e14 grains of salt in a kiddie pool.
1,900,000,000.
19.00000000
decimal point moved 8 spaces
19.
19.x10e8 grains of salt in a square foot
Conclusion:
In conclusion, after all of my calculations I found out that there are about
1.4x10e15 grains of salt in a kiddie pool.[i] To give a comparison there are only 2,000,000 grains of salt in a cup. So that number is 700,000,000 cups of 2,000,000 grains of salt.

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