SOLUTION: A grain of sand is placed on the first square of a chessboard, two grains on the second square, four grains on the third, eight on the fourth, and so on. Without a calculator, use

Algebra ->  Equations -> SOLUTION: A grain of sand is placed on the first square of a chessboard, two grains on the second square, four grains on the third, eight on the fourth, and so on. Without a calculator, use       Log On


   



Question 979142: A grain of sand is placed on the first square of a chessboard, two grains on the second square, four grains on the third, eight on the fourth, and so on. Without a calculator, use scientific notation to approximate the number of grains of sand required for the 64th square. (Hint: Use the fact that 2^10 ≈ 10^3.)
I got 9.2 x 10^18. The books answer was 8 x 10^18. I used the calculator for this problem. If I'm wrong, please help me.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

you got it right

2%5E0+=+1 grain on the first square
2%5E1+=+2 on the second square
2%5E2+=+4 on the third square
2%5E3+=+8 on the fourth square
...
2%5E63 on the 64th square
(exponent is always one less than the # of square 1 to 64)
Answer is 2%5E63=9.223372036854775808%2A10%5E18=9.2%2A10%5E18 grains of sand on the 64th square.
Note: Do not subtract 1.
2%5E63 is not the same as 2%5E%2864-+1%29