What’s the biggest number you can think of? A million? A billion? A trillion? A gazillion? Infinity?

Long ago, mathematicians came up with an easy way of representing very large numbers. They created exponents (also called powers) to represent the mathematical function of multiplying a number by itself a certain number of times.

Let’s look at some examples. If you see 10^{2}, 10 is the base and the ^{2} is the exponent or power. 10^{2} means 10 to the second power or 10 multiplied by itself twice. Thus, 10^{2} is the same as 10 X 10 or 100.

Likewise, 10^{3} is the same as 10 x 10 x 10, which equals 1,000. Do you see a pattern? When 10 is the base, the exponent will be the number of zeroes after the 1 in the answer. So, 10^{6} would be a 1 with 6 zeroes, or 1,000,000 (1 million).

Exponents work with any base. For example, 4^{2} is the same as 4 x 4 (16) and 4^{3} is the same as 4 x 4 x 4 (64).

How would 1 billion and 1 trillion be represented as exponents? One billion is 1 followed by 9 zeroes, or 10^{9}. One trillion is 1 followed by 12 zeroes, or 10^{12}.

Believe it or not, mathematicians use numbers much bigger than 1 trillion. In 1938, a 9-year-old boy named Milton Sirotta, who was the nephew of American mathematician Edward Kasner, invented a new number that he called a googol. According to Milton, a googol is 10^{100}, or 1 followed by 100 zeroes!

How big is a googol? Really, really big! Mathematicians believe a googol is bigger than the number of subatomic particles in the universe. Despite its size, a googol is still smaller than the total number of possible different games of chess (approximately 10^{120}).

Not content with the mind-blowing size of the googol, Milton also invented an even bigger number: the googolplex. A googolplex is 10^{googol}, or 1 with a googol of zeroes after it.

How big is a googolplex? 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. 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 write it down!

Googol and googolplex aren’t used very often, except to show the difference between an incredibly large number and infinity…or to remind students how exponents can be used to generate huge numbers quickly.

These terms did inspire one of the most famous and successful companies in the world today, though. Technology giant Google chose its name based upon a purposeful misspelling of googol.

The company wanted to convey that its Internet search engine could provide huge quantities of information for its users. Google’s current headquarters in Mountain View, California, has come to be known as the Googleplex.

Google now processes over 1 billion search requests every day. The main Google search engine is the Internet’s most-visited website.

The Google search engine — a noun — has become so associated with Internet searching that google — a verb — was added to the dictionary. It means “to use the Google search engine to obtain information on the Internet.”

Dear Wonderopolis,

Googolplex is a BIG number! We were excited to learn that Googol is connected to exponents! In our Math class, we just finished studying about exponents! So, this is a great connection for us to make! This WONDER made us WONDER what will be the name of the number after Googolplex?

TEAM CAISSE 5th grade Reading class

What a WONDERful comment you left for us today, TEAM Caisse! We’re really glad that today’s Wonder aligned so well with what you just finished studying in math class! We love to hear about our Wonder Friends’ personal connections to the Wonders of the Day®!

Hey, I can’t believe this wonder about google. You know what? Here is a really cool wonder…what is the biggest number in the whole world, and you already have that wonder! Here is one more…where is the center of the earth? Well, I hope you like my wonders.

Your ideas for Wonders are GREAT, Kate! Thank you so much for sharing them with us and for being such an awesome Wonder Friend!

Class was fun today, Mrs. Caisse!!!! I loved every bit of it! You’re a great teacher. By the way, I’m in your reading class.

We’re so glad you like learning in Mrs. Caisse’s class, PinkSocks! We think she’s a really awesome teacher for sharing Wonderopolis with her students every day, don’t you?

We want to know why everybody dies.

That really is something LOTS of Wonder Friends WONDER about, Shane! Thank you for visiting Wonderopolis today and leaving us this comment! We appreciate you!

If you bang anything on a metal pot why does it make noise?????????

That’s a GREAT question, Luke! Check out this past Wonder of the Day® for a little more insight into sound:

Wonder #161 – What Makes Sounds Louder? http://wonderopolis.org/wonder/what-makes-sounds-louder/

Hey there Wonderopolis!

This is an amazing wonder! I learned a lot about the (number) googol. I learned two new words from this wonder. They are convey and quantities. I never knew that from the (number) googol they got the name for the website Google, except they spelled it wrong. I also never knew that googol was a specific number. I thought it was just saying that something is really, really big. Why did Google choose to have googol as their logo? Anyways, I learned a lot about the (number) googol. I will never stop WONDERing!:)

It ROCKS that you said you will never stop WONDERing, Team Unger 7! It makes us SUPER happy to hear that! We won’t, either…we LOVE to WONDER! We really liked hearing all the cool things you learned by visiting this Wonder of the Day®!

If you were wondering, I will show you how big one googol is without comas:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

MAN, isn’t that big or what! Most people think googol is the last number but, numbers never end!

That really is a SUPER BIG number, Jacob! Thanks for sharing your comment with us today and helping us see what a googol looks like without commas! YOU ROCK!

Yes,yes you do.

Thanks for WONDERing, Michael!

100 zeros. no problem

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

TA DA.

(gosh that a huge number. So a googolplex is 100 times that. I’ve got a lot of 0′s to type).

Well, I will try it

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

OH MY GOSH MY FINGER IS TIRED.

(You may want to highlight it to see it.)

WOW, we are impressed with your diligent work, Tyler J! We are proud of you– thanks for WONDERing about the googol with us today! Phew!

Yes Googol is indeed a big number. But the thing is numbers are endless, and possibilities are also endless. So my wonder is…Is it possible to give every number a name? Like googol, trillion, billion….

Hi Jasmine! Thanks for WONDERing with us! What a WONDERful Wonder! It is possible, but perhaps we haven’t discovered the largest number yet! Keep WONDERing!

WOW! I didn’t know it’s this big:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000!

Hi Michael! Thanks for WONDERing with us! It it very big! What’s the largest number of stuff that you’ve seen in real life? 100 pizzas? 20,000 people? We’re having so much fun WONDERing with you!

900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 times 900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Wow, Jace, that would be a big number! Thanks for WONDERing with us!

I think googol would be something like

100000000000000000000000000000000000000000000000000000000000000000000000000000.

Great try! However, we think you may need more zeros, Wonder Friend!

Trying to Understand BIG numbers – Part 2

I would like to offer an explanation:

Consider a grain of sugar, and how many of them are in a teaspoonful of sugar that you might add to your cup of coffee. I know that sugar grains may vary in size, depending on which sugar refinery produced them, but let’s just suppose that we have a large supply of sugar where the grains are exactly one millimetre in size.

Now, we could get a tweezers to pick up sugar grains, one at a time, to make a row of ten grains, which would be one centimetre long.

If we now made nine more rows of sugar crystals alongside the first row, we would have a layer of ten rows which each had ten crystals, making one hundred crystals in all.

If we could now add another nine layers on top of the first layer, we would have a sugar cube one centimetre wide and one centimetre high, which contained one thousand crystals. One thousand, as we all know, is written as a digit 1 followed by three zeroes, “1000”, or “ten to the third power”.

Trying to Understand BIG numbers – Part 3

We could make a packet of sugar cubes, with ten layers of sugar cubes, where each layer was made up of ten rows, and ten sugar cubes in each row. This packet, measuring ten centimetres wide, and ten centimetres high, would be exactly one litre in size, containing 1000 sugar cubes – and actually 1000000 – one million sugar grains.

Let’s suppose that we are in the warehouse, and want to load a pallet for delivery to a supermarket. We could make a stack of packets (each of one litre) which has ten rows of ten packets making up a layer, and then adding more layers until it was ten layers high. This stack would be one metre wide, and one metre high, and would contain one thousand packets of sugar, and this stack would contain one million sugar cubes – and actually one billion sugar grains – the digit 1 followed by nine zeroes, which can also be written as ten to the ninth power.

Trying to Understand BIG numbers – Part 1

When we hear mention of large numbers, it is often difficult to comprehend exactly how big they are. There are much bigger numbers than a million, a billion, or a trillion.

A trillion is “a million lots of one million”, and is quite a large number – just think how impossible it might be for one person to earn a trillion dollars.

But when it comes to really large numbers, such as a googol, how can we imagine just how big that number is?

A googol, which is “ten to the power of one hundred”, can be written as a digit 1 followed by one hundred zeroes, but for most of us that does not give any real indication of how big it is.

Trying to Understand BIG numbers – Part 4

Now we start the interesting bit. It’s taking a bit longer than I wanted to. However, I think it’s quite important that we can appreciate that I am trying to explain something bigger than you may have really understood.

Let’s suppose that we have a large paddock, a kilometre square – that’s more than enough for a thousand soccer fields – and we get pallets of sugar from the warehouse. We will need thousands of truck loads of these pallets of sugar, because I want us to imagine a thousand pallets side by side, making a row one kilometre long, along one side of our paddock. After we complete that first row, we need to make another 999 rows, because I want us to imagine the whole paddock covered with a layer of sugar pallets. That’s right, 1000 rows of sugar pallets, each 1000 pallets long, making a layer of one million pallets. We need to use a bit more imagination now, because I want us to imagine building a tower now, containing 1000 layers of pallets, and each layer containing one million pallets. To be sure, nobody has ever built such a big tower of sugar pallets, and it would contain a billion sugar pallets – “ten to the ninth power”

Trying to Understand BIG numbers – Part 5

Can we comprehend how many sugar grains are in this kilometre high sugar stack? Well, the answer is one billion lots of one billion – “ten to the eighteenth power”. It’s quite a big number, but it’s quite small really when we compare it to a googol.

Well, how can we imagine something bigger? We have already imagined in our mind’s eye a cubic kilometre, and found that it was far too small. Let’s imagine our planet earth, with a circumference of 40,000 kilometres or 25,000 miles around the equator. The diameter of the earth is about 12,800 kilometres or 8,000 miles, and we can do a bit of maths to calculate how many cubic kilometres are equivalent to the volume of the earth. The earth is approximately 10 to the 12th cubic kilometres in volume, and is definitely not made of sugar cubes!!

Trying to Understand BIG numbers – Part 6

I am still trying to show how big a googol is, and I want you to be a bit imaginative now. Can you imagine that you are an astronaut, looking down at an amazing sight – a sugar planet the size of the earth! This sugar planet would contain 10 to the 30th grains of sugar. You can trust me that the maths are correct. Can you believe it when I say that we have hardly started yet in visualising a googol? 10 to the 30th is huge, but a googol is 10 to the 70th times bigger!!!!

Trying to Understand BIG numbers – Part 7

Astronomers tell us that our galaxy, the Milky Way, is about 100,000 light years in diameter, which is approximately 10 to the 13th kilometres. The Milky Way galaxy is not very thick, when compared to its diameter, but we have been on a fantasy voyage, viewing a sugar planet from the comfort of a spaceship. If we could possibly imagine that the Milky Way was a giant sphere, 100,000 light years in diameter, it would have the volume of approximately 10 to the 38th cubic kilometres, big enough to contain 10 to the 26th sugar planets, and would contain about 10 to the 56th grains of sugar.

And so, lamentably, I think I am going to have to give up on trying to explain how big a googol is, because it is still 10 to the 44th times bigger than our Sugary Galactic monster planet.

WOW! We are so proud of you for sharing and trying to show what a googol is! You’re AWESOME! We hope you join us again soon!