Most scientific and graphing calculators can only display up to 10 decimal places of accuracy. While sufficient for everyday use, this is limiting for applications where precision is paramount. Big number calculators are essential in fields such as cosmology, astronomy, cryptography, and statistical mechanics.
Big Numbers in Everyday Life
We encounter massive scales more often than we think:
- Bits on a modern computer hard drive.
- Neuronal connections in the human brain.
- Avogadro's constant: The number of constituent particles in one mole of a substance.
- Estimated number of atoms in the observable universe ($10^{80}$).
Special Notations
When numbers exceed standard scientific notation, mathematicians use specialized systems like Knuth's up-arrow notation, Conway chained arrow notation, or Steinhaus-Moser notation. For example, calculating 10,000 factorial (!) results in a number far too large for standard displays, but essential for understanding combinatorial limits.
Names of Large Numbers
| Power of 10 | Name (Short Scale) | Number of Zeros |
|---|---|---|
| $10^6$ | Million | 6 |
| $10^9$ | Billion | 9 |
| $10^{12}$ | Trillion | 12 |
| $10^{15}$ | Quadrillion | 15 |
| $10^{18}$ | Quintillion | 18 |
| $10^{21}$ | Sextillion | 21 |
| $10^{100}$ | Googol | 100 |
| $10^{googol}$ | Googolplex | Googol |