how many numbers between 100 and 200 can be expressed as powers of 2?
2^6 = 64
2^7 = 128
2^8 = 256
Your verdict is ??
Well, between 100 and 200, there are quite a lot of numbers that can be expressed as powers of 2. Let me count for you... 1, 2, 4, 8, 16, 32, 64, 128. Oops, I seem to have lost count. Let me try again... 1, 2, 4, 8, 16, 32, 64, 128. Oh no, I did it again! I just keep getting carried away with my powers of 2. Sorry, I'm just not good at counting, but I'm pretty sure there are more than a few numbers between 100 and 200 that can be expressed as powers of 2!
To find out how many numbers between 100 and 200 can be expressed as powers of 2, we need to determine the range of powers of 2 that fall within this range.
Step 1: Find the range of powers of 2 within the given range.
To do this, we need to find the smallest and largest powers of 2 that are less than or equal to 100 and 200, respectively.
The largest power of 2 less than or equal to 100 is 2^6 (64), and the smallest power of 2 greater than 200 is 2^7 (128). Therefore, the range of powers of 2 within the given range is from 2^6 to 2^7.
Step 2: Calculate the number of powers of 2 within the range.
To find the number of powers of 2 within this range, we subtract the smaller power from the larger power and add 1.
Number of powers of 2 = (7 - 6) + 1 = 2
Therefore, there are 2 numbers between 100 and 200 that can be expressed as powers of 2.
To find out how many numbers between 100 and 200 can be expressed as powers of 2, let's start by understanding what it means for a number to be a power of 2.
A number is said to be a power of 2 if it can be written in the form of 2^x, where x is an integer greater than or equal to 0. So, we need to find all the numbers between 100 and 200 that can be expressed as 2^x.
To solve this, we can start by finding the smallest power of 2 greater than or equal to 100, which is 2^7 = 128. We can continue raising 2 to higher powers until we reach a number greater than 200.
2^1 = 2,
2^2 = 4,
2^3 = 8,
2^4 = 16,
2^5 = 32,
2^6 = 64,
2^7 = 128,
2^8 = 256.
We can see that the powers of 2 that fall within the range of 100 to 200 are 2^7 (128) and 2^8 (256 is greater than 200, so we stop here).
Therefore, there is only one number between 100 and 200 that can be expressed as a power of 2, which is 128 (2^7).
So the answer is 1.