A googol is the number 10100 or a 1 followed by 100 zeros. It was coined by the American mathematician Edward Kasner in 1920 to illustrate the difference between an unimaginably large number and infinity. But what does such an enormous number actually look like when written out in full? In this article, we’ll explore what a googol looks like when written out completely and try to wrap our minds around just how massive it really is.
Defining a Googol
Let’s start by formally defining what a googol is:
A googol is the number 10100. In decimal notation, this number would have 101 digits. The full value of a googol is:
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
This is already getting lengthy! As we can see, a googol has 100 zeros after the initial 1. It’s hard for our human brains to comprehend just how huge this number is.
Writing Out a Googol
To get a true sense of the scale of a googol, let’s write it out completely in words:
Ten quindecillion, quattuordecillion, tredecillion, duodecillion, undecillion, decillion, nonillion, octillion, septillion, sextillion, quintillion, quadrillion, trillion, billion, million, thousand, hundred, ten, one.
That’s 101 digits expressed fully in words. As we can see, this number is far larger than anything we normally deal with. Some key facts about the size of a googol:
- A googol has more zeros than the estimated number of atoms in the observable universe, which is approximately 1080.
- It would take over 300,000 pages to print a googol in digits – more pages than many books!
- If you wrote one digit per Planck length, which is the smallest measurement of distance that has any meaning, it would take over 300 million kilometers to write out a googol. That’s 2.5 times farther than the distance from Earth to the Sun!
These analogies give us some sense of scale for just how massive a googol really is. It’s far larger than anything we normally conceptualize in math or physics.
Visualizing a Googol
Numbers this large can be nearly impossible for us to visualize accurately. But here are some ways we can try to wrap our minds around the scale of a googol:
Counting to a Googol
Let’s try counting to a googol out loud, one number per second. How long would this take us?
If we count non-stop, 24 hours a day, it would take over 3.1 quadrillion years to count to a googol! That’s over 200 million times longer than the current age of the universe, which is 13.8 billion years. Needless to say, we’d never make it even remotely close.
Paper and a Googol
Let’s say we printed out every digit of a googol on pieces of paper. How much paper would we need?
If we use standard printer paper, each sheet has around 4000 digits printed on both sides. At this rate, it would take over 2.5 billion sheets of paper to write out a full googol.
| Size of paper | Sheets needed |
| Standard printer paper | 2,500,000,000 |
| A4 paper | 8,300,000,000 |
| US Letter size | 3,900,000,000 |
That’s enough paper to build a pillar 400 km high – over twice the height that commercial jets fly at!
Clearly, it’s impossible to truly visualize the scale of a googol in our everyday lives. It dwarfs any quantities or measurements we actually contend with.
Reaching a Googol
Let’s consider how long it would take to count up to a googol starting from 1, if we could count one number per second.
Counting nonstop, 24 hours a day, it would take over 3.1 quadrillion years to reach a googol. That’s over 200 million times longer than the age of the universe!
Here is a table showing how long it would take to reach certain milestones on the way to a googol at one number per second:
| Milestone | Time to Reach |
| 1 million | 12 days |
| 1 billion | 32 years |
| 1 trillion | 32,000 years |
| 1 quadrillion | 32 million years |
| 1 quintillion | 32 billion years |
| 1 googol | 3.1 quadrillion years |
As we can see, it quickly becomes utterly implausible to conceptualize reaching numbers even remotely close to a googol at this pace. The number is simply far too gigantic relative to human scale.
Uses of a Googol
Given how inconceivably massive it is, a googol may seem like an abstract and impractical concept. But googols do have some legitimate (if still somewhat whimsical) uses:
- In mathematics, googols illustrate the difference between unimaginably huge finite numbers and actual infinity.
- In physics and cosmology, googols help put immense quantities like the number of particles in the universe in perspective.
- The name ‘googol’ inspired the name of the technology company Google. The company name is a misspelling of googol.
- Googols are used in puzzles, riddles, trivia and factoids to dazzle people with an immense number.
- Googolplex, or 10googol, is an even larger number, based on a googol.
So while perhaps not the most practical numeric concept, googols do help quantify our notion of “a really huge number” in math and culture.
Conclusion
A googol is an extremely large number – 10100 digits long. When written out completely in words or digits, it becomes clear just how massive this number is relative to anything we can properly conceive or visualize.
While we can make analogies and comparisons to grasp the scale, numbers like a googol remain firmly in the abstract and conceptual realm. Their size dwarfs everyday quantities and spans of time. Nevertheless, huge numbers like googols are mathematically legitimate entities and can help contextualize topics in science and culture. Being able to name and symbolize inconceivably huge quantities is powerful, even if we can’t fully visualize them intuitively.
