Understanding Very Large Numbers

Have you ever wondered what number comes after a trillion? Or how many zeros there are in a vigintillion? ​Some day you might need to know this for a science or math class, or if you happen to enter one of several mathematical or scientific fields. 

Numbers Bigger Than a Trillion

The digit zero plays an important role as you count very large numbers. It helps to track these multiples of 10 because the larger the number is, the more zeros are needed.

Grouping Zeros by Threes

Many people find it easy to understand that the number 10 has one zero, 100 has two zeros, and 1,000 has three zeros. These numbers are used all the time in daily living, whether it is dealing with money or counting something as simple as our music playlist or the mileage on our cars.

When you get to million, billion, and trillion, things become a little more complicated. How many zeros come after the one in a trillion? It's hard to keep track of that and count each individual zero, so these long numbers have been broken down into groups of three zeros.

Read More

Numbers of Zeros in a Million, Billion, Trillion, and More

By Anne Marie Helmenstine, Ph.D.

For example, it's much easier to remember that a trillion is written with four sets of three zeros than it is to count out 12 separate zeros. While you might think that one's pretty simple, just wait until you have to count 27 zeros for an octillion or 303 zeros for a centillion. Then you will be thankful that you only have to remember nine and 101 sets of three zeros, respectively.

Powers of 10 Shortcut

In mathematics and science, you can rely on the "powers of 10" to quickly express exactly how many zeros are needed for these larger numbers. For example, a shortcut for writing out a trillion is 10¹² (10 to the power of 12). The 12 indicates that the number needs a total of 12 zeros.

You can see how much easier these are to read than if there were just a bunch of zeros:

Quintillion = 10¹⁸ or 1,000,000,000,000,000,000

Decillion = 10³³ or 1,000,000,000,000,000,000,000,000,000,000,000

The Enormous Numbers: Googol and Googolplex

You are probably very familiar with the search engine and tech company Google. Did you know that the name was inspired by another very large number? Though the spelling is different, the googol and the googolplex played a role in the naming of the tech giant.

A googol has 100 zeros and is expressed as 10¹⁰⁰. It is often used to express any large quantity, even though it is a quantifiable number. It makes sense that the largest search engine that pulls a large quantity of data from the internet would find this word useful.

The term googol was coined by the American mathematician Edward Kasner in his 1940 book, "Mathematics and the Imagination." The story goes that Kasner asked his then 9-year-old nephew, Milton Sirotta, what to name this ridiculously long number. Sirotta came up with googol.

But why is a googol important if it's actually less than a centillion? Quite simply, a googol is used to define a googolplex. A googolplex is 10 to the power of googol, a number that boggles the mind. In fact, a googolplex is so large that there's really no known use for it. Some say that it even exceeds the total number of atoms in the universe.

The googolplex is not even the largest number defined to date. Mathematicians and scientists have also devised "Graham's number" and "Skewes number." Both of these require a math degree to even begin to understand.

Short and Long Scales of a Billion

If you thought the concept of a googolplex is tricky, some people cannot even agree on what defines a billion. In the U.S. and most of the world, it is accepted that 1 billion equals 1,000 million. It is written as 1,000,000,000 or 10⁹. This number is used often in science and finance, and it is called the "short scale."

In the "long scale," 1 billion is equal to 1 million million. For this number, you will need a 1 followed by 12 zeros: 1,000,000,000,000 or 10¹². The long scale was first described by Genevieve Guitel in 1975. It is used in France and, for a time, was accepted in the United Kingdom as well.