14.a) How many numbers between 100 and 200 can be expressed as powers of 2? Show the steps you follow.
b)Which power of 2 is the closest to 1000? Show your work.
what do you mean by square?
powers of 2 are numbers like
2^2, 2^3, 2^4 ... etc or
2,4,8,16,32,64 128 256 512 1024 ..
Now, which of those lie between 100 and 200 ?
BTW, before the size of memory chips got out of hand, they used to come in 128 MB, or 256 MB, etc
I am using a 512 MB chip in my Nikon camera.
soo the answer is
2,4,8,16,32,64 128?
a) answer I think is 1 which is 128 (2^7)
b) answer is 1024 (2^10)
a) To find the numbers between 100 and 200 that can be expressed as powers of 2, we can start by listing the powers of 2 until we reach the upper limit of 200. Then, we can identify the numbers that fall within the given range.
1. Start by listing the powers of 2:
- 2^0 = 1
- 2^1 = 2
- 2^2 = 4
- 2^3 = 8
- ...
Continue listing the powers of 2 until you reach a number just above 200.
2. Identify the numbers between 100 and 200:
Based on the list of powers of 2, we can see that the numbers between 100 and 200 that can be expressed as powers of 2 are:
- 2^6 = 64
- 2^7 = 128
- 2^8 = 256 (outside the range of 100 to 200)
Therefore, there are two numbers, 64 and 128, that can be expressed as powers of 2 between 100 and 200.
b) To determine which power of 2 is closest to 1000, we can start by listing the powers of 2 until we reach a value greater than 1000. Then, we can compare the distance between 1000 and each of the powers of 2 to find the closest one.
1. Start by listing the powers of 2:
- 2^0 = 1
- 2^1 = 2
- 2^2 = 4
- 2^3 = 8
- ...
Continue listing the powers of 2 until you reach a number just above 1000.
2. Compare the distance between 1000 and each power of 2:
The distances between 1000 and the powers of 2 are:
- 2^9 = 512 (distance: 1000 - 512 = 488)
- 2^10 = 1024 (distance: 1024 - 1000 = 24)
The distance is smaller for 2^10 = 1024, which is just 24 away from 1000. Therefore, the power of 2 closest to 1000 is 2^10.
a) Square the numbers starting with 10 and ending when you get an answer over 200.
b) Keep squaring numbers until you get to one that equals close to, but less than, 1000.
Hint: The square root of 1,000 = about 31.62.