Question

A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.

Answer 1

Answer:

1,2,4,8,16,32,64,128,256,512

(2048 experience)

1023 grains of rice if you add it all up

Step-by-step explanation:

Answer 2

Hey there! I'm happy to help out!

As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.

However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:

$2^0, 2^1, 2^2, 2^3,2^4,... etc.$

So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!

$2^9=$ 2×2×2×2×2×2×2×2×2= 512

However, we want to find how much he has done in total! So, let's find how much he did on the other squares!

$2^8$= 256

$2^7$=128

$2^6$=64

$2^5$=32

$2^4$=16

2³=8

2²=4

$2^1$=2

$2^0$=1

Now, we add these all up to find the total grains of rice!

512+256+64+32+16+8+4+2+1=895

Therefore, George has placed a total of 895 grains of rice on the chess board.

I hope that this helps! Have a wonderful day!