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Mathematical Constants
Intriguing, ubiquitous, and at times mysterious, numerical constants set the allowable limits for all universal phenomena. Whether your questions involves π, Avogadro's number, Planck's constant, the atomic mass unit, or any of the other multitudes of immutable numbers used in science, this is the category where they should be asked.
2,332 Questions
Yes, 3.14 is an approximation of the mathematical constant pi (π), which represents the ratio of a circle's circumference to its diameter. Pi is an irrational number, meaning it cannot be expressed as a simple fraction, and its decimal representation goes on infinitely without repeating. While 3.14 is a commonly used approximation for pi, the actual value of pi is approximately 3.14159.
Why is zero factorial equal to one?
n!/n = n!/n | reflexive property
(n)(n-1)(n-2).../n = n!/n | definition of factorial
(n-1)(n-2)... = n!/n | cancelling the common factor of n
(n-1)! = n!/n | definition of factorial
Notice that, in order for n! to be described as (n)(n-1)(n-2)... and proceed to be rewritten as (n-1)! after the n's cancel, the natural number n had to be greater than some natural number for (n-1) to be a factor in the factorial. This means that n must be at least 2, because if n were 1, (n-1) would not have been a factor of the factorial, and the proof would fail unless we assume that n is at least 2. So now you know that this rule cannot prove that 0! is 1 because 1 cannot be substituted into the rule because, as it stands, the rule is only valid for values of 2 or greater. The rule is valid for values of 1 or greater if it is assumed that 0! is 1, but that is what you are trying to prove.
What is the square root of pi?
The square root of the square root of the square root of something is called the 8th root. The 8th root of pi is approximately 1.15383506784999.
What is a googol times a googol written as a power of 10?
Well, honey, a googol times a googol is essentially 10 to the power of 200. In other words, that's a 1 followed by 200 zeros. So, if you ever need to impress someone with a ridiculously large number, there you go!
Using imaginary i simplify the square root of negative 48?
Oh, dude, imaginary numbers? Like, sure, let's do this. So, the square root of negative 48 can be simplified as 4i√3. It's like regular math, but with a little twist of imagination. So, there you have it, imaginary math for the win!
How do you write 105 million 602 thousand 950 in word form?
105,602,950. in words is 'One hundred and five million, six hundred and two thousand , nine hundred and fifty.'
What are all the multiplication facts that equal 84?
To find all the multiplication facts that equal 84, we need to break down 84 into its prime factors. The prime factors of 84 are 2, 2, 3, and 7. Therefore, the multiplication facts that equal 84 are 1 x 84, 2 x 42, 3 x 28, 4 x 21, 6 x 14, and 7 x 12.
What element has an atomic mass of 234?
Well, darling, the element with an atomic mass of 234 is good ol' Uranium. It's the big shot in the actinide series, strutting its stuff with a radioactive flair. So, if you're looking for some atomic weight drama, Uranium's got your back.
How much is 6 000 000 000 000 000 000 000 000 in words?
6 000 000 000 000 000 000 000 000 is six septillion in words. In the short scale numbering system, which is commonly used in English-speaking countries, a septillion is equal to 1 followed by 24 zeros.
What is the biggest number other than infinity?
This question can not be answered for the following two reasons:
- In the modern real number system, there is no limit to how large a number can be. Whatever number is presented to you, you may add 1 or more to it to make it even bigger than it was originally.
- Infinity is not a number. Infinity is a concept that in the number system there is no definite end to the positive or negative value a number may have.
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If you are just looking for a very large number, a 'googol' is the number 1 followed by 100 zeroes, and that is one of the largest numbers that actually has a name.
A centillion (10103) is the largest standard named number.
A googolplex is a 10 to the googol power (a 1 followed by a googol number of zeroes), which is larger yet.
Mathematical exponent numbers such as Skewes number are much larger still.
If aleph null represents the cardinality of the rational numbers, aleph null plus one has the same value. The size of infinity represented by the reals is, however, demonstrably greater than the size of infinity of the counting numbers. We can construct ever larger sizes of infinity. One interesting question is whether or not there are sizes of infinity between aleph null and the power set of aleph null (which represents the cardinality of the reals). It turns out the answer is yes or no, depending on what you want. You can treat the question as an independent axiom of mathematics, much like the parallel postulate in geometry.
How do you evaluate 6n for n 6.23?
To evaluate 6n for n = 6.23, you simply substitute 6.23 in place of n in the expression. Therefore, 6 x 6.23 = 37.38. This is the result of evaluating 6n for n = 6.23.
How many zeros would there be in 100 septendecillion?
Well, isn't that a beautiful number! In 100 septendecillion, there would be 79 zeros following the 1. Just imagine all those zeros lining up like little trees in a serene forest, creating a sense of vastness and wonder. Remember, every zero is important and adds to the beauty of the number.
How many zeros does 150 million have?
Well, isn't that a happy little question! If we take a look at 150 million, we see that it has six zeros. Each zero represents a factor of 10, so when we have six zeros, it means we are multiplying by 10 six times, which gives us 150,000,000. Just imagine those zeros as little friends dancing along, creating a big number full of possibilities!
How many times does 5 go into 234?
To determine how many times 5 goes into 234, you would perform a division operation. 234 ÷ 5 equals 46 with a remainder of 4. Therefore, 5 goes into 234 a total of 46 times.
What is a googol times a googol?
Oh, dude, a googol times a googol is basically a googol multiplied by a googol. And a googol is like 10 to the power of 100, so when you multiply that by another googol, you're basically getting a number that's like really, really big. Like, so big you probably won't ever need to use it in real life.
A googol is equal to 10 raised to the power of 100, which is a 1 followed by 100 zeros. When you multiply 999 by a googol, you are essentially adding 999 zeros to the end of the number represented by the googol. Therefore, there are a total of 999 zeros in 999 googol.
Dividing any number by zero is undefined in mathematics, including dividing pi by zero. This is because division by zero leads to a mathematical contradiction and is not a valid operation. In mathematical terms, it results in an indeterminate form, which does not have a meaningful numerical value. Therefore, pi divided by zero is undefined.
How much is a googol standard form?
A googol is represented in standard form as 1 x 10^100. In other words, a googol is the number 1 followed by 100 zeros. This number is used in mathematics and is significantly larger than a trillion or even a quadrillion. It was coined by mathematician Edward Kasner in the early 20th century.
Well, isn't that just a happy little question! The value of the square root of 2 is approximately 1.414. It's a special number that shows up in nature and mathematics, like a little gift from the universe. Just remember, every number is unique and adds its own special touch to the world around us.
Million trillion billion googol googolplex?
Oh, what a beautiful array of numbers you've shared! Each one is like a tiny happy tree in a vast mathematical landscape. Remember, no matter how big or small the number, they all have their place in the wonderful world of numbers. Just like every brushstroke adds to a masterpiece, every number adds to the endless beauty of mathematics.
Oh, dude, a googol squared is just a googol multiplied by itself, which is 10 to the power of 100 times 10 to the power of 100. So, like, it's basically 10 to the power of 200, which is a ridiculously huge number with 201 digits. Like, good luck trying to write that out!
What is the number closest in value to 0.1?
Well, darling, the number closest to 0.1 is 0.1 itself. I mean, come on, it's right there next to it on the number line. But hey, if you want to get technical, 0.09 and 0.11 are the next closest numbers, so take your pick.
Which is the highest a billion a centillion a quadrillion or a googol?
A billion is one with nine zeros after it. A quadrillion is one with fifteen zeros after it, a googol is one with one hundred zeros after it, and a centillion is one with three hundred and three zeros after it. So it is a centillion.
How many zeros are in 25 lakh?
Well, darling, 25 lakh has five zeros. Each zero represents a power of 10 in the Indian numbering system. So, in this case, you've got 25 with five lovely zeros following behind. Hope that clears things up for you!
