The powers of 2 between 100 and 200 are 128 and 256. The only power of 2 that falls within the range of 100 to 200 is 128 (since (2^7 = 128)). Therefore, there is only one number between 100 and 200 that can be expressed as a power of 2.
There is only one solution: 44 = 256.
To determine the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888, we can use the Prime Number Theorem. This theorem states that the density of prime numbers around a large number n is approximately 1/ln(n). Therefore, the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888 can be estimated by dividing ln(8888888888888888888888888888888888888888888888) by ln(2), which gives approximately 1.33 x 10^27 prime numbers.
Any number that can be expressed as a fraction is rational and there are plenty of fractions from -1 to 0
There are 5,000 even numbers between 1 and 10,000. This is because even numbers in this range can be expressed as 2, 4, 6, ..., 10,000. The sequence starts at 2 and ends at 10,000, with a common difference of 2, resulting in a total of 5,000 terms.
There are only two different rational numbers although each of them can be expressed in infinitely many ways.
42
There is only one solution: 44 = 256.
To determine the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888, we can use the Prime Number Theorem. This theorem states that the density of prime numbers around a large number n is approximately 1/ln(n). Therefore, the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888 can be estimated by dividing ln(8888888888888888888888888888888888888888888888) by ln(2), which gives approximately 1.33 x 10^27 prime numbers.
Any number that can be expressed as a fraction is rational and there are plenty of fractions from -1 to 0
There are infinitely many rational numbers between any two consecutive rational numbers. This is because rational numbers can be expressed as fractions, and between any two fractions, an infinite number of other fractions can be found by taking the average of the two given fractions. Therefore, the set of rational numbers is dense, meaning there is no smallest gap between any two rational numbers.
There are 5,000 even numbers between 1 and 10,000. This is because even numbers in this range can be expressed as 2, 4, 6, ..., 10,000. The sequence starts at 2 and ends at 10,000, with a common difference of 2, resulting in a total of 5,000 terms.
There are only two different rational numbers although each of them can be expressed in infinitely many ways.
Infinitely many. there are infinitely many numbers between any two numbers.
There are infinitely many numbers between 8 and 9 that can be expressed in decimal form. For example, 8.00000000000000000001 8.000000000000000000010001 8.000000000000000000010002 8.0000000000000000000100038.00000000058.0000000005000000000018.0000000005000000000023and so on, and we have not even got to 8.00001 yet!
Infinity cannot be expressed in numbers. You can't count to it!
Seven thousand, expressed in decimal numbers as 7,000
There are infinitely many numbers between any two numbers. But there are only 9 integers between them.