How many numbers between 100 and 200 can be expressed as powers of 2??
geeeshhh! , oobleck gave you the answer in your previous post!!!
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
....
I wonder how many numbers in the right-side column fall between 100 and 200 ?
Could you explain it to me?
1. So I'm right.
Yes.
To find how many numbers between 100 and 200 can be expressed as powers of 2, we need to determine which powers of 2 fall within that range.
To begin, let's find the smallest power of 2 that is greater than or equal to 100. We can do this by repeatedly multiplying 2 by itself until we reach a number greater than or equal to 100.
Starting with 2, we have 2, 4, 8, 16, 32, 64, 128. We see that 128 is the smallest power of 2 greater than or equal to 100.
Next, let's find the largest power of 2 that is less than or equal to 200. Similar to the previous step, we can repeatedly multiply 2 by itself until we reach a number greater than 200. Then, the previous power of 2 will be our answer.
Continuing from 128, we have 128, 256. We see that 256 is the smallest power of 2 greater than 200. Thus, the previous power of 2 is 128.
Now we have the range of powers of 2 from 2^7 (128) to 2^8-1 (255).
To find how many numbers are in this range, we subtract the two powers:
2^8-1 - 2^7 + 1 = 256 - 128 + 1 = 129
Therefore, there are 129 numbers between 100 and 200 that can be expressed as powers of 2.