The
number 10googol,
or 1 followed by a googol number of zeros. This is reputed to be
the largest
number with a name.
Note: This can also be written 10(10^100).
Key Formula
googolplex=1010100
Where:
10100 = A googol, which is the exponent applied to the base 10
Example
Problem: Express a googolplex using repeated exponentiation, and compare its size to a googol.
Step 1: Start with a googol, which is 1 followed by 100 zeros.
googol=10100
Step 2: A googolplex uses that entire googol as the exponent on 10.
googolplex=10googol=1010100
Step 3:If you tried to write a googolplex out in full decimal form, you would write the digit 1 followed by 10100 zeros. A googol itself only has 100 zeros, so a googolplex has incomprehensibly more digits.
Answer:A googolplex is 1010100. Writing it out would require a googol digits — far more zeros than there are atoms in the observable universe (roughly 1080).
Why It Matters
A googolplex illustrates how quickly repeated exponentiation (also called tetration) produces numbers beyond any physical meaning. The observable universe does not contain enough particles to write out a googolplex digit by digit, making it a useful benchmark when discussing the limits of computation and the scale of large numbers.
Common Mistakes
Mistake:Confusing a googolplex (1010100) with a googol (10100).
Correction: A googol is 1 followed by 100 zeros. A googolplex is 1 followed by a googol zeros — an astronomically larger number. The googol serves as the exponent in a googolplex.
Mathwords