How Many Zeros in a Million, Billion, and Trillion?


How many zeros in...?
Here are the names of numbers of zeros using the short scale. (Todd Helmenstine, sciencenotes.org)

Have ever wondered how many zeros are in a million, billion, or trillion? Do you know how many zeros are in a vigintillion or a googol? Knowing how to write ordinary large numbers is useful for science or math class (or your bank account, if you are rich). Use your knowledge of the gigantic numbers to impress your friends. 

Numbers Based on Groups of Three Zeros

While ten and a hundred get their own name, larger numbers are based on groups of three zeros. This table gives the name for the groups of zeros in a number.

NameNumber of ZerosGroups of (3) Zeros
Ten1(10)
Hundred2(100)
Thousand31 (1,000)
Ten thousand4(10,000)
Hundred thousand5(100,000)
Million62 (1,000,000)
Billion93 (1,000,000,000)
Trillion124 (1,000,000,000,000)
Quadrillion155
Quintillion186
Sextillion217
Septillion248
Octillion279
Nonillion3010
Decillion3311
Undecillion3612
Duodecillion3913
Tredecillion4214
Quatttuor-decillion4515
Quindecillion4816
Sexdecillion5117
Septen-decillion5418
Octodecillion5719
Novemdecillion6020
Vigintillion6321
Centillion303101

What the Numbers Look Like Written Out

A table can be useful to look up how many zeros large numbers have. But, if you need to know how to write them, it helps to see them written out in all their glory.

Ten: 10 (1 zero)
Hundred: 100 (2 zeros)
Thousand: 1000 (3 zeros)
Ten thousand 10,000 (4 zeros)
Hundred thousand 100,000 (5 zeros)
Million 1,000,000 (6 zeros)
Billion 1,000,000,000 (9 zeros)
Trillion 1,000,000,000,000 (12 zeros)
Quadrillion 1,000,000,000,000,000 (15 zeros)
Quintillion 1,000,000,000,000,000,000 (18 zeros)
Sextillion 1,000,000,000,000,000,000,000 (21 zeros)
Septillion 1,000,000,000,000,000,000,000,000 (24 zeros)
Octillion 1,000,000,000,000,000,000,000,000,000 (27 zeros)
Nonillion 1,000,000,000,000,000,000,000,000,000,000 (30 zeros)
Decillion 1,000,000,000,000,000,000,000,000,000,000,000 (33 zeros)

Zeros Grouped in Sets of 3

The larger a numeral gets, the harder it becomes to count the digits. So, digits in large numbers are grouped in sets of three. Write numbers with commas separating sets of three zeros so that it’s easier to read and understand the value. For example, write one million as 1,000,000 rather than 1000000. The set of three starts as you move to the left of a decimal point (the last zero). So, you write 10,000 rather than 100,00. Commas aren’t commonly used after the decimal point, unless you’re dealing with a value containing a large number of digits, like pi. Sometimes a space is used instead of a comma to separate digits.

As another 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 zeroes. While you might think that that one is pretty simple, just wait until you have to count 27 zeros for an octillion or 303 zeros for a centillion. It is simpler to remember nine and 101 sets of zeros, respectively.

Numbers With Very Large Numbers of Zeros

The number googol (termed by Milton Sirotta) has 100 zeros after it. Here’s what a googol looks like, written out with all of its zeros:

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

What is a googol?
A googol is 10 raised to the 100 power.

You may notice the number googol bears a resemblance to the company name Google. This isn’t by accident. Google is a mis-spelling of googol and fits the company’s goal of being an extremely large search engine.

Do you think the googol is big? How about the googolplex, which is a one followed by a googol of zeros. The googolplex is so large its value exceeds the number of atoms in the known universe.

Yet, a googolplex isn’t the largest number described to date. Graham’s number is so enormous it can’t even be described using everyday mathematics. When Graham’s number was described in 1977, it was the largest positive integer used in a mathematical proof. Since then, even larger numbers have been described, such as TREE(3).

Short Scale and Long Scale

The names given to large numbers based on powers of ten vary between different countries. The two main naming systems are the short scale and the long scale. The United States uses the short scale, in which a billion is 1,000 million and is written as a one followed by nine zeros.

The long scale is used in France and was previously used in the United Kingdom. In the long scale, a billion means one million million. According to this definition of a billion, the number is written with a one followed by 12 zeros. Both the short scale and long scale were described by French mathematician Genevieve Guitel in 1975.

References

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.