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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
What are the first 40 numbers of pi?
The first 40 decimals of pi are
3.1415926535 8979323846 2643383279 5028841971
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To get a lot of decimals simple search "decimals of pi" in Google - there are many pages.
How many zeros in 0.5 million?
0.5 million equals 500 000, therefore there are five zeros in half a million.
It is not known. The Rhind Papyrus describes how the area of a circle is related to pi where pi was estimated as (4/3)4 ≈ 3.1605 (approx).
The Rhind Papyrus dates from around 1700 BCE. So either very ancient people used pi = 3 or else they were later people who were dogmatically required to use pi = 3.
How can you learn numbers 1 2000 in French in one night?
You can learn French numbers just by knowing how they work. The first thing, and the most difficult, is to know the numbers from zero to twenty:
0 zéro - 1 un - 2 deux - 3 trois - 4 quatre - 5 cinq - 6 six - 7 sept - 8 huit - 9 neuf - 10 dix - 11 onze - 12 douze - 13 treize - 14 quatorze - 15 quinze - 16 seize - 17 dix-sept - 18 dix-huit - 19 dix-neuf - 20 vingt.
Then learn the tens up to 100:
0 zéro - 10 dix - 20 vingt - 30 trente - 40 quarante - 50 cinquante - 60 soixante - 70 soixante-dix - 80 quatre-vingts - 90 quatre-vingt-dix - 100 cent.
Once you know them, you can combine them to count up to the million!
examples in the 1-100 range:
21 vingt et un - 23 vingt-trois - 35 trente-cinq - 40 quarante - 42 quarante-deux - 64 soixante-quatre - 70 soixante-dix - 72 soixante-douze -75 soixante-quinze - 79 soixante dix-neuf - 85 quatre-vingt-cinq - 91 quatre-vingt-onze - 92 quatre-vingt-douze - 93 quatre-vingt-treize - 94 quatre-vingt-quatorze - 95 quatre-vingt-quinze - 96 quatre-vingt-seize- 99 quatre-vingt dix-neuf -
...
numbers from 100 up to 2000 are written just as the first 100 ones, with just 'cent', 'deux cent', 'trois cent', 'quatre cent', 'mille', 'mille cent' etc., written in front.
examples in the 100-2000 range: 501 = cinq cent un, 601 = six cent un, 701 = sept cent un; 512 = cinq cent douze, 612 = six cent douze, 1612 = mille six cent douze, 1993 = mille neuf cent quatre vingt treize, 2000 = deux mille.
Zero
any number instead of 4 like 1234567890 and it will still be ZERO!!!!!!!!!!!!
How many zeros in factorial googol?
Googol is not a real number, but supposedly, it is a 1 with 100 zeros behind it. Which would not make sense since any significant type number would have the number of zeros divisible by 3. Such as the number 1 with 303 zeros behind it which is the number centillion.
* * * * *
Not true. A googol is a real number and it does have 100 zeros.
A hundred is a significant number the number of zeros is not divisible by 3!
What you need to do is as follows (G = googol):
The number of times 5 goes into G = 2*1099 - that gives 2*1099 0s.
The number of times 52 goes into G = 4*1098 - that gives another 4*1098 0s.
The number of times 53 goes into G = 8*1097 - that gives another 8*1097 0s.
and so on, all the way down to
The number of times 5143 goes into G = 100 = 1.11 - that gives another 1 0s.
All in all, that makes nearly 2.5*1099 or a quarter of a googol 0s.
Why the golden ratio is ideal ratio?
The golden ratio is the ideal ratio because it is consistent throughout many aspects in nature - proportions of the human body, the crests and troughs of a heartbeat, the stripes on a tiger's head, et cetera.
The value of the Golden Ratio is 0.5*[1 + sqrt(5)] = 1.61803 (to 5 dp)
What are some fractions that are almost equivalent to pi?
22/7 or 3 1/7 is the closest known fraction
Why is the atomic mass of an atom the average atomic mass?
It allows for the relative abundances of different isotopes.
What is the abbreviation of a imaginary number?
The letter i represents the imaginary unit [square root of -1]. It's added after the number. So 5i means 5 units in the positive imaginary direction, or just 5 times sqrt(-1).
In electrical engineering, often the letter j is used, because i represents current in electrical notation.
CommentIn electrical engineering, the operator 'j' is usually placed in front of a number, not behind it: i.e. (a+jb) not (a +bj).
How many digits do you need to write if you write all numbers from 0-1450?
You would need infinitely many digits to write all numbers. However, to write all whole number (integers) you would need 4243.
What does planck's constant state?
It makes no statement. It's just a number, with dimensions [ M L2 T-1 ]
See the Web Links for "Answers.com: Atomic mass" to the bottom for the answer. Atomic mass refers to the weight of an atom when compared to aribitary figure that is relative to other atoms.
The unit used is 1/12 the weight of a carbon atom (the most prolific around). Atomic mass is used to avoid using very small numbers that would otherwise result if you try to physically weigh an atom.
Note that atomic mass is not the same thing as atomic weight. See the Related Question to the left for more information.
Negative square roots are just the opposite of positive square roots. Since square roots (of positive numbers) are real, the negative square roots are also real.
Square roots of negative numbers are not real.
Note that -1 = exp(Pi*i), so (-1)^(1/2) = exp((1/2)*Pi*i) = i.
Note that exp(i*x) = cos(x) + i*sin(x), for instance by taking derivatives:
(d/dx)(exp(i*x)) = i*exp(i*x), and
(d/dx)^2(exp(i*x)) =(-1)*exp(i*x).
This means that the second derivative of exp(i*x) equals -exp(i*x).
The same property holds for cos(x) + i*sin(x):
(d/dx)(cos(x) + i*sin(x)) = -sin(x) + i*cos(x)
(d/dx)^2(cos(x) + i*sin(x)) = -cos(x) - i*sin(x) = -(cos(x) + i*sin(x)))
Hence cos(x) + i*sin(x)) = C + Dx + exp(i*x), for some C and D.
Comparing the values on both sides for x = 0, we find:
1 = C+1, so C = 0 and for the first derivative:
i = D + i, so D = 0.
So cos(x) + i*sin(x)) = exp(i*x) for all x.
by comparing x=0 for both functions and their first derivative. Since they coincide,
Yes. (But the correct descriptive term is "transcendental".)
Why is log i 0.682i Where i is the imaginary number sqr rt -1?
By Euler's formula, e^ix = cosx + i*sinx
Taking natural logarithms, ix = ln(cosx + i*sinx)
When x = pi/2, i*pi/2 = ln(i)
But ln(i) = log(i)/log(e) where log represents logarithms to base 10.
That is, i*pi/2 = log(i)/log(e)
And therefore log(i) = i*pi/2*log(e) = i*0.682188 or 0.682*i to three decimal places.
How much is Planck's constant?
To 3 significant figures: h = 6.63*10-34 J s If you have not encountered this type of notification, take 6.63 and divide it by 10 34 times. On your calculator type 6.63, then (usually) press "exp", then type "-34". ENSURE THAT UNITS ARE CONSTANT! This is done in SI units so energy is in Joules (Nm or Kgm2s-2) and seconds, so use: * Kilogrammes for Mass * Seconds for Time * Metres for Distance A suitable conversion system: * 1 parsec = 3.086333*1016 metres * 1 light-year = 9.46728*1015 metres * 1 astronomical unit (earth-sun distance) = 1.49*1011 metres * 1 year = 31557600 seconds * 1 day = 86400 seconds * 1 imperial ton = 1016.0416 kilogrammes * 1 short (US) ton = 907.18 kilogrammes * 1 mile = 1609.283 metres * 1 foot = 0.30479 metres * 1 yard = 0.914365 metres * 1 pound (lb) = 0.454 kilogrammes Hope this helps Paul Hurley
Which value of gas constant should be applied?
There are several values, most of which are related, but vary according to the units used. See //en.wikipedia.org/wiki/Gas_constant for details.
