A googol is the large number 10100. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
Then there is the Googolplex. It is 1 followed by Googol zeros. I can’t even write down the number, because there is not enough matter in the universe to form all the zeros: 10,000,000,000,000,000,000,000,000,000,000, … (Googol number of Zeros)
And a Googolplexian is a 1 followed by Googolplex zeros. Wow.
The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. mathematician Edward Kasner. He may have been inspired by the contemporary comic strip character Barney Google.
Kasner popularized the concept in his 1940 book Mathematics and Imagination. Other names for this quantity include ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.
What is the last number in the world?
There is no such thing as the biggest number or the last number. Why? Because the concept of infinity exists.
Simply put, numbers continue on and on indefinitely, and they never end. So, there could never be a final number.
Just like the highway that never ends, when we count numbers, no matter how high we go, there will always be another number that is larger than the number we have counted to. This idea is the very definition of the concept of infinity.
If you think you have found it, you can always add 1 and get a bigger one. The largest number that has a commonly-known specific name is a googolplex, which is 10 to the power of a googol, or 1 followed by a googol of zeros. A googol is 10 to the 100th power, which is 1 followed by 100 zeros.
Infinity is not a number but rather the number at the end of the real number line. It is bigger than all other numbers. There is no number before infinity, and there’s nothing larger than infinity except for infinity itself.
Some people believe that the last number in the world is 9,999,999,999. If you add one to that number, it becomes 10,000,000,000. That would be the next number in the world.
There is no such thing as the last number when it comes to the natural number system. By definition, every number has a number larger than it.
In the base-10 number system, every number has a number larger than itself. The concept of infinity relates to the idea that there is no last or largest number; there is always a bigger number than any number chosen. For example, if someone chooses any abstract number N, and then adds 1 to it, the resulting sum is larger than N. For any number N chosen, N is not the last number that is possible.
We know that Infinity is the idea of something that has no end. Therefore, we can say that there is no last number in the world. And we can call it an Infinity. Infinity is not a real number.
What is The Biggest Number In The World?
A googol is a large number that is equal to 10 to the power of 100, or 1 followed by 100 zeros. The term was coined in 1920 by a nine-year-old boy named Milton Sirotta, who was the nephew of mathematician Edward Kasner.
A googolplex is an even larger number that is equal to 10 to the power of a googol, or 1 followed by a googol of zeros. If all the matter in the universe was turned into paper, it still wouldn’t be enough paper to write down all the zeroes in a googolplex.
The term “googolplex” was popularized by mathematician Edward Kasner in his book “Mathematics and the Imagination”. While these numbers are incredibly large, there are still infinitely larger numbers than them.
Even if you tried to write out all the zeroes in a googolplex and could write two numbers per second, it would take you longer than the age of the universe to finish writing.
While there are infinitely many larger numbers than a googol and a googolplex, these two numbers were given names as didactic techniques used by mathematicians to pique the interest of laypeople in the differences between very large numbers and infinity.
Size of Googol Number
A googol has no special significance in mathematics. However, it is useful when compared with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game.
Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role, it is sometimes used in teaching mathematics.
To give a sense of how big a googol really is, the mass of an electron, just under 10−30 kg, can be compared to the mass of the visible universe, estimated at between 1050 and 1060 kg. It is a ratio in the order of about 1080 to 1090, or at most one ten-billionth of a googol (0.00000001% of a googol).
Carl Sagan pointed out that the total number of elementary particles in the universe is around 1080 (the Eddington number) and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be around 10128. He also noted the similarity of the second calculation to that of Archimedes in The Sand Reckoner.
By Archimedes’s calculation, the universe of Aristarchus (roughly 2 light years in diameter), if fully packed with sand, would contain 1063 grains. If the much larger observable universe of today were filled with sand, it would still only equal 1095 grains. Another 100,000 observable universes filled with sand would be necessary to make a googol.
The decay time for a supermassive black hole of roughly 1 galaxy mass (1011 solar masses) due to Hawking radiation is on the order of 10100 years. Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol year in the future.
A googol is considerably smaller than a centillion.
Properties of Googol
A googol is approximately 70! (Factorial of 70). Using an integral, binary numeral system, one would need 333 bits to represent a googol, i.e., 1 googol = 2(100/log102) ≈ 2332.19280949. However, a googol is well within the maximum bounds of an IEEE 754 double-precision floating-point type, but without full precision in the mantissa.
Using modular arithmetic, the series of residues (mod n) of one googol, starting with mod 1, is as follows:
0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 4, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 16, 10, 5, 0, 1, 4, 25, 28, 10, 28, 16, 0, 1, 4, 31, 12, 10, 36, 27, 16, 11, 0, … (sequence A066298 in the OEIS)
This sequence is the same as that of the residues (mod n) of a googolplex up until the 17th position.
Some Very Big, and Very Small Numbers
| Name | The Number | Prefix | Symbol |
| Septillion | 1,000,000,000,000,000,000,000,000 | yotta | Y |
| Sextillion | 1,000,000,000,000,000,000,000 | zetta | Z |
| Quintillion | 1,000,000,000,000,000,000 | exa | E |
| Quadrillion | 1,000,000,000,000,000 | peta | P |
| Quadrillionth | 0.000 000 000 000 001 | femto | f |
| Quintillionth | 0.000 000 000 000 000 001 | atto | a |
| Sextillionth | 0.000 000 000 000 000 000 001 | zepto | z |
| Septillionth | 0.000 000 000 000 000 000 000 001 | yocto | y |
All Big Numbers We Know
| Name | As a Power of 10 | As a Decimal |
| Thousand | 103 | 1,000 |
| Million | 106 | 1,000,000 |
| Billion | 109 | 1,000,000,000 |
| Trillion | 1012 | 1,000,000,000,000 |
| Quadrillion | 1015 | etc … |
| Quintillion | 1018 | |
| Sextillion | 1021 | |
| Septillion | 1024 | |
| Octillion | 1027 | |
| Nonillion | 1030 | |
| Decillion | 1033 | |
| Undecillion | 1036 | |
| Duodecillion | 1039 | |
| Tredecillion | 1042 | |
| Quattuordecillion | 1045 | |
| Quindecillion | 1048 | |
| Sexdecillion | 1051 | |
| Septemdecillion | 1054 | |
| Octodecillion | 1057 | |
| Novemdecillion | 1060 | |
| Vigintillion | 1063 | 1 followed by 63 zeros! |
All Small Numbers We Know
| Name | As a Power of 10 | As a Decimal |
| Thousandths | 10-3 | 0.001 |
| Millionths | 10-6 | 0.000 001 |
| Billionths | 10-9 | 0.000 000 001 |
| Trillionths | 10-12 | etc … |
| Quadrillionths | 10-15 | |
| Quintillionths | 10-18 | |
| Sextillionths | 10-21 | |
| Septillionths | 10-24 | |
| Octillionths | 10-27 | |
| Nonillionths | 10-30 | |
| Decillionths | 10-33 | |
| Undecillionths | 10-36 | |
| Duodecillionths | 10-39 | |
| Tredecillionths | 10-42 | |
| Quattuordecillionths | 10-45 | |
| Quindecillionths | 10-48 | |
| Sexdecillionths | 10-51 | |
| Septemdecillionths | 10-54 | |
| Octodecillionths | 10-57 | |
| Novemdecillionths | 10-60 | |
| Vigintillionths | 10-63 |