What Is A Googol? How Big It Really Is
The short version
- A googol is 10100, which is a 1 with 100 zeros written after it. That’s 101 digits in all.
- The name came from a nine year old. Milton Sirotta made it up for his uncle, the mathematician Edward Kasner, who put it in print in 1940.
- A googol is bigger than the estimated number of atoms in the observable universe, which most estimates put near 1080.
- A googolplex is 10 raised to a googol, so it’s a 1 with a googol zeros after it. You could never write it out, even with the whole universe as paper.
- The search company Google took its name from googol. The usual story is that the spelling got changed along the way.
A googol is the number 10100: a 1 followed by one hundred zeros. Written the long way it looks like 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. It isn’t a special or magic number in math. It’s just a very big round number with a fun name, and it’s a great way to see what exponents actually do.
Kids usually meet the googol in fourth or fifth grade, right when place value stretches past the millions. If your child asked what a googol is, they’re really asking a place value question, and that’s worth answering well.
How to write a googol without writing 100 zeros
Nobody writes a googol out by hand. We write it as a power of 10.
10100 means 10 multiplied by itself 100 times.
101 = 10
102 = 100
103 = 1,000
106 = 1,000,000
Here’s the shortcut that makes powers of 10 easy: the exponent tells you how many zeros follow the 1. So 106 has six zeros, and 10100 has one hundred zeros. That also means a googol has 101 digits total, because the 1 in front counts as a digit too. Kids miss that one constantly.
| Power of 10 | Name | Zeros after the 1 |
|---|---|---|
| 103 | Thousand | 3 |
| 106 | Million | 6 |
| 109 | Billion | 9 |
| 1012 | Trillion | 12 |
| 1015 | Quadrillion | 15 |
| 10100 | Googol | 100 |
Notice there’s no standard name for most of the sizes between a quadrillion and a googol. That’s part of why the word stuck.
Where the word googol came from
In the 1920s the American mathematician Edward Kasner wanted a name for 10100. As the story is usually told, he asked his young nephew, Milton Sirotta, who was around nine years old, and the boy said “googol.” Kasner kept it. He and James Newman published the word in their 1940 book Mathematics and the Imagination, and that’s how it reached the rest of us.
The boy also came up with googolplex. His first idea was that it should be a 1 followed by zeros until you got tired of writing. Kasner tightened that into something fixed: a googolplex is 10 raised to a googol.
How big is a googol, really
Big numbers stop meaning anything past a point, so compare the googol to things that are already absurd.
| Thing | Rough size |
|---|---|
| Seconds since the Big Bang | about 4 × 1017 |
| Grains of sand on Earth (a commonly quoted estimate) | about 7 × 1018 |
| Stars in the observable universe | estimates near 1022 |
| Atoms in the observable universe | estimates near 1080 |
| A googol | 10100 |
Look at that last gap. A googol isn’t a little bigger than the atom count. It’s roughly 1020 times bigger, which is about 100 quintillion times bigger. If you gave every atom in the universe its own private universe of atoms, you’d still be short of a googol.
This is the real lesson hiding in the googol: each step up in the exponent multiplies by 10 again. 1081 is ten times 1080. Going from 1080 to 10100 is twenty more of those jumps, and twenty jumps of ×10 is a factor of 100 quintillion.
Googol vs googolplex
These get mixed up all the time, and the difference is enormous.
| Number | Meaning | Digits |
|---|---|---|
| Googol | 10100 | 101 |
| Googol squared | 10200 | 201 |
| Googolplex | 10 raised to a googol | a googol plus 1 |
A googolplex is not a googol times a googol. Googol × googol is only 10200, which is still a number you could type out in an afternoon. A googolplex is a 1 with a googol zeros after it. Writing one zero per second, you’d need about 10100 seconds, and the universe has only been around for about 4 × 1017 seconds. There isn’t enough matter in the universe to print it, even one digit per atom.
Is Google a number?
No. The number is the googol. Google is the search company, and it was named after the number. The widely reported version of the story is that the founders meant to use googol, the spelling got garbled while they were checking whether the name was available, and Google is what ended up registered. The company later leaned into it: its headquarters is called the Googleplex.
So if your kid writes “google” on a math worksheet, the number they mean is spelled g o o g o l.
Common mistakes
Counting 100 digits instead of 100 zeros. A googol has 101 digits. The exponent counts zeros, not total digits.
Thinking a googol is the biggest number. It isn’t close. Add one and you get a bigger number. There is no biggest number.
Reading 10100 as 10 × 100. That’s 1,000. The exponent is not a multiplier. 10100 means a hundred copies of 10 multiplied together.
Assuming 10010 and 10100 are the same. They’re wildly different. 10010 = (102)10 = 1020.
Calling a googolplex “a googol googols.” A googol googols is 10200. The googolplex is in a different league.
Practice problems
1. Write 105 as a whole number.
2. How many zeros come after the 1 in 1012? How many digits does the whole number have?
3. Which is larger, 10100 or 10010?
4. Write 10100 ÷ 1097 as a power of 10, then as a whole number.
5. A googol × a googol equals which power of 10?
6. If you could write one zero every second without stopping, how long would it take to write the zeros in a googol?
7. How many times bigger is a googol than 1080?
8. True or false: a googolplex equals a googol × a googol.
Answers
1. 100,000
2. 12 zeros, and 13 digits in all.
3. 10100 is larger. 10010 = (102)10 = 1020, and 10100 is far past that.
4. 10100 ÷ 1097 = 10100 – 97 = 103 = 1,000
5. 10100 × 10100 = 10200
6. 100 seconds, so under two minutes. The googol is easy to write. The googolplex is the impossible one.
7. 10100 ÷ 1080 = 1020, which is 100 quintillion times bigger.
8. False. A googol × a googol is 10200, a 201 digit number. A googolplex is 10 raised to a googol, so it has a googol plus 1 digits. The two aren’t in the same league.
What it means if your kid is stuck here
Almost no child is stuck on the googol itself. They’re stuck on what’s under it: place value and exponents. If a fifth grader can’t say how many zeros are in 107, the missing piece is usually the pattern that each place to the left is ten times the one before. That pattern starts in second grade and gets reinforced every year after.
Watch for a couple of tells. A kid who reads 104 as “ten times four” hasn’t built the meaning of an exponent yet, and that will hurt badly in pre algebra. A kid who can’t line up 1,000,000 against 100,000 and say which is bigger is missing place value, not big number trivia. Our guide to 12 signs your child is behind in math by grade level lists the specific things to watch for, and math skills by grade level for grades 3 to 5 shows where place value and powers of ten are supposed to land.
The good news is that this gap is small and fixable. Ten minutes on the powers of ten pattern usually clears it up, as long as you find it. If your child clams up whenever numbers get big, that’s often nerves rather than skill, and math anxiety in children covers what that looks like and what actually helps.
Frequently asked questions
How many zeros are in a googol?
One hundred. The number is written as a 1 followed by 100 zeros, which makes 101 digits total.
Is a googol bigger than infinity?
No. Infinity isn’t a number you can count to, so nothing finite is bigger than it. A googol is finite. Add 1 to it and you get a bigger number, and you can keep doing that forever.
What is bigger than a googol?
Plenty. A googol plus 1, 10101, a googol squared, a googolplex, and named giants like Graham’s number, which is used in a real mathematical proof and dwarfs the googolplex.
Who invented the googol?
The name was coined by Milton Sirotta, the young nephew of mathematician Edward Kasner. Kasner and James Newman published it in 1940. The number 10100 existed before it had a name, of course.
What grade do kids learn about a googol?
Usually grades 4 to 6, as a fun extension while students work on place value, powers of ten, and exponents. It rarely appears on tests. It shows up because it makes kids curious.
Is a googolplex the largest number?
No. There is no largest number. A googolplex is just a large number with a memorable name, and mathematicians work with numbers far past it.
Find the actual gap
When a kid asks about a googol, they’re showing you they like big numbers. When a kid freezes on 104, they’re showing you something else. Math Anon starts every student with a short adaptive assessment that works out which skills are actually solid and which ones are missing, and you get a written report naming them.
After that it’s targeted practice on the gaps, about 20 minutes a day, with a progress report each week so you can see what moved. Start the assessment for $49, credited back in full against your first month if you continue. The pricing page has the rest of the details.
