Managing our finances can be quite complex and daunting especially while dealing with bigger amounts. But it is not such a thing to worry about!! To manage the bigger amount finances, we just require or must be aware of sound knowledge of various terms that shows a great impact on your financial well-being.

Well, not only in the field of finances but in various fields where math calculation is required, we are in need of using large numbers. Large numbers include Nonillion, Millard, and Virgintillion. We all are very familiar with million, billion, and trillions but I hope we rarely hear these names of large numbers like Nonillion, Millard, etc. So, today we are going to learn more about our bizarre terms and what exactly they mean. In this article, we are going to discuss on usage and derivation of large number names. If possible we will also try to learn about their potential extensions. Let’s begin.

Understanding Very Large Numbers

Understanding large numbers helps to think in terms of groups of zeros. For ex: 1,000,000,000,000. As I already told you, understanding names of large numbers is very much useful when you enter in one of several fields that deal with big mathematical calculations, including scientific fields. Have you ever think of what number comes after trillion? I would expect the answer, which might be, ‘Yes Of Course’. But not frequently used right!

You all know the value of ‘zero’ in calculations. Without zero, there is no value to the mathematical calculations and of course the value of zero is calculated depending on its place and position. Coming to our modern calculus, there is no modern electronics, no modern automation and engineering, no modern world, etc. So, we should keep on teaching our next generations about the importance of ‘Zero’.

Coming to our topic, if we are asked to name or write a large number or any simple number, firstly, we concentrate on the place of zero and how many times it is repeating in a number. A good way to do this is knowing about place-value chart. Here I have shown some examples to make you understand easier.

Example-1: Ten Million

	Millions	Thousands	Ones
Hundreds
Tens	1
Ones	0

 

	Millions	Thousands	Ones
Hundreds		0	0
Tens	1	0	0
Ones	0	0	0

To write ‘Ten Million’, we need to write 10 in the millions family as shown in the first table. And then we need to fill the rest of the places (Thousands and one’s family) with zeroes. Finally, writing a ‘Ten Million’ is done.

Example-2: Six Million and Fifteen Thousand

To write 6 Million and Fifteen Thousand, we need to enter six in millions family at one’s place and fifteen at thousands family at ten’s and one’s place. Rest of the places in thousands and one’s family are filled with zeroes. That’s it! We are done with writing 6,015,000. We used comma in the space between the families.

	Millions	Thousands	Ones
Hundreds
Tens		1
Ones	6	5

 

	Millions	Thousands	Ones
Hundreds		0	0
Tens		1	0
Ones	6	5	0

In this way, we can learn the importance of zeroes and especially children’s understand the concept of place value holders and zeroes placement values.

Reading large numbers

Naming and reading big numbers is relatively easy! In the above table, consider reading the number in each family box followed by name of the family itself, suppose starting with millions then followed by thousands and lastly by one’s family. This is the standard way to read a large number. Give some examples in table formats to your children and ask them to read out the numbers. It would be a good practice for children to understand and learn very big numbers.

Now let us discuss about Naming Very Big Numbers…

The following table helps us to track multiples of 10 as the larger the number is, the more zeroes are required.

Name	Number of Zeros	Groups of 3 Zeros
Ten	1	0
Hundred	2	0
Thousand	3	1 (1,000)
Ten thousand	4	1 (10,000)
Hundred thousand	5	1 (100,000)
Million	6	2 (1,000,000)
Billion	9	3(1,000,000,000)
Trillion	12	4 (1,000,000,000,000)
Quadrillion	15	5
Quintillion	18	6
Sextillion	21	7
Septillion	24	8
Octillion	27	9
Nonillion	30	10
Decillion	33	11
Undecillion	36	12
Duodecillion	39	13
Tredecillion	42	14
Quattuordecillion	45	15
Quindecillion	48	16
Sexdecillion	51	17
Septen-decillion	54	18
Octodecillion	57	19
Novemdecillion	60	20
Vigintillion	63	21
Centillion	303	101

Generally, naming very large numbers is done using two main systems i.e. scientific notation and naming by grouping. Let us understand with an example:

In scientific notation, 700 000 000 000 000 000 000 is denoted as 7 x 10²⁰ as there are 20 zeroes after number 7. If the same large number is asked to name by grouping, then it is denoted as ‘five hundred quintillion’ (American) or Trillion (European). Don’t panic, I will tell you the detailed naming system of large numbers in American, European, and British form.

The American way of naming large numbers is different from the Europeans and British. Americans use ‘short form’ where as Europeans use ‘long form while naming very large numbers. The main reason behind this is America’s finance. Based on thousands, Short form is designed and based on millions, Long form is designed in calculations. We will see an example to understand this easily.

A Billion is read or written as ‘One Thousand Millions’ i.e. 10⁹ in short form while the same is written and read as ‘One Million Millions’ I.e. 10¹² in long form. In the below table I am going to show you all how large numbers are denoted and called in American British, and European countries. After that I will also explain about Australian Naming system of very large numbers.

Scientific Notation	British Name (Long Form)	European Name (Long Form)	American Name (Short Form)
1099	Thousand sexdecillion	Sexdecilliard	Duotrigintillion
1096	Sexdecillion	Sexdecillion	Untrigintillion
1093	Thousand quindecillion	Quindecilliard	Trigintillion
1090	Quindecillion	Quindecillion	Novemvigintillion
1087	Thousand quattuordecillion	Quattuordecilliard	Octovigintillion
1084	Quattuordecillion	Quattuordecillion	Septenvigintillion
1081	Thousand tredecillion	Tredecilliard	Sexvigintillion
1078	Tredecillion	Tredecillion	Quinvigintillion
1075	Thousand duodecillion	Duodecilliard	Quattuorvigintillion
1072	Duodecillion	Duodecillion	Trevigintillion
1069	Thousand undecillion	Undecilliard	Duovigintillion
1066	Undecillion	Undecillion	Unvigintillion
1063	Thousand decillion	Decilliard	Vigintillion
1060	Decillion	Decillion	Novemdecillion
1057	Thousand nonillion	Nonilliard	Octodecillion
1054	Nonillion	Nonillion	Septendecillion
1051	Thousand octillion	Octilliard	Sexdecillion
1048	Octillion	Octillion	Quindecillion
1045	Thousand septillion	Septilliard	Quattuordecillion
1042	Septillion	Septillion	Tredecillion
1039	Thousand sextillion	Sextilliard	Duodecillion
1036	Sextillion	Sextillion	Undecillion
1033	Thousand quintillion	Quintilliard	Decillion
1030	Quintillion	Quintillion	Nonillion
1027	Thousand quadrillion	Quadrilliard	Octillion
1024	Quadrillion	Quadrillion	Septillion
1021	Thousand trillion	Trilliard	Sextillion
1018	Trillion	Trillion	Quintillion
1015	Thousand billion	Billiard	Quadrillion
1012	Billion	Billion	Trillion
109	Thousand million	Milliard	Billion
106	Million	Million	Million
105	Hundred thousand	Hundred thousand	Hundred thousand
104	Ten thousand	Ten thousand	Ten thousand
103	Thousand	Thousand	Thousand
102	Hundred	Hundred	Hundred
101	Ten	Ten	Ten
100	One	One	One

We got to know that even the British used ‘Long Form’ to name large numbers. But the change in United Kingdom (UK) from long form to short form had happened in 1974. Currently, short form is the most common way of naming very large numbers in most English speaking countries.

Googol is another mathematical term used to denote a huge quantity, which is a one followed by one hundred zeroes i.e. 10^100.  Googolplex and Googolplexian are the number names, which are even bigger out there. Googolplex is a number ten followed by googol of zeroes i.e. 10^google In scientific form, Googolplex is denoted as 10^{Ten duotrigintillion} or 10^{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.} The world’s second largest number with a name is Googolplexian. It is a number with googolplex of zeroes.

Milton Sirotta invented the names googol and googolplex. Interestingly, these names for larger numbers inspired an internet company, Google along with its corporate headquarters, the Googleplex.

Number	Number of Zeros	Name
10100	100	googol
10googol	a lot more zeros than I can fit here	googolplex

Standard Dictionary Numbers

Name	Short Scale (US, Eastern Europe,English Canadian, Australia, and Modern British)	Long Scale (Western, Central Europe, Older British, and French Canadian)
Centillion	10303	10600
Vigintillion	1063	10120
Novemdecillion	1060	10114
Octodecillion	1057	10108
Septendecillion	1054	10102
Sexdecillion	1051	1096
Quindecillion	1048	1090
Quattuordecillion	1045	1084
Tredecillion	1042	1078
Duodecillion	1039	1072
Undecillion	1036	1066
Decillion	1033	1060
Nonillion	1030	1054
Octillion	1027	1048
Septillion	1024	1042
Sextillion	1021	1036
Quintillion	1018	1030
Quadrillion	1015	1024
Trillion	1012	1018
Billiard		1015
Billion	109	1012
Milliard		109
Million	106	106

 

Name	Value	Authorities
		AHD4	CED	COD	OED2	OEDnew	RHD2	SOED3	W3	UM
Googol	10100	✓	✓	✓	✓	✓	✓	✓	✓	✓
Googolplex	10googol (1010100)	✓	✓	✓	✓	✓	✓	✓	✓	✓

The words in the above list that are ending with ‘–illion’ apart from million are derived from Latin by adding prefixes such as bi, tri, etc. to the stem –illion. In dictionary form, ‘Centillion’ is the highest name ending with –illion. The Oxford English Dictionary remarks that the names, Googol and Googolplex are not in formal mathematical use.

Australian Naming System of Large Numbers

There are many types of naming systems in the world for integer powers of ten, among them Short Scale and Large Scale are two important and main naming systems. These two types of scales are identical for whole number smaller than 1,000,000,000 (10⁹), such as one thousand or one million and they are different for larger numbers starting from 10⁹ Considering identical names, short scale form uses one thousand where as long scale uses multipliers of one million. For instance: a billion is denoted as 10³ million in short scale and 10⁶ million in long scale.

Long Scale system is very much handy in introducing new terms for intervening multipliers and especially shows its importance in replacing the typical words ending with –ion and –iard.

Easy to Remember Derivations for Short and Long Scales

Short Scale

A Billion is denoted as 10⁹ in short scale form i.e. 1,000,000,000, a Trillion is written as 10⁹ i.e. 1,000,000,000,000, and so on. From this, an n –illion can be derived or equals to 10^3n+3.

Long Scale

In long scale, a billion is denoted as 10⁹   i.e. 1,000,000,000,000 and a trillion is denoted as 10¹⁸ i.e. 1,000,000,000,000,000,000 and so on. Thus, an n –illion is equal to 10⁶ⁿ

Usage of Naming Systems of Large Numbers in different Countries

Does it really make a difference while naming large numbers in different countries across the world!? Absolutely Yes! In one country a billion is denoted with nine zeroes whereas the same billion is denoted with twelve zeroes in some other country.  Therefore, there is a huge difference in between large and short scale system of naming large numbers.

Different countries use different scale system while naming very big numbers. Number names from any country seems like they are rendered in their respective country language but according to shared etymology, they are similar.

Actually, short scale naming system is used in Arabic-speaking and English-speaking countries like Brazil and several other countries. The long scale system is used in most countries of Continental Europe, Spanish speaking (except Spanish speakers born in English countries and culture, for example: Puerto Rico), French speaking, Portuguese speaking countries (except Brazil).

Some languages especially in South Asia and East Asia, use large number naming system which is different from long and short scale systems. The best example is Indian Numbering System.

Australia along with English-speaking Canada, USA, New Zealand, Ireland, Brazil, UK (after 1974), and most other English-speaking countries use Short Scale System of Naming Large Numbers. Long Scale System of Naming Large Numbers is used in countries including UK (before 1974), France, Germany, Denmark, Finland, Sweden, Poland, Italy, Spain, etc. Some countries like India, Japan, China, Korea, and Greece use neither scales.

Final Conclusion

Things become complicated when you go counting numbers beyond million, billion, and trillion. We might get confused on how many zeroes do we need to put in a trillion, counting each and every individual zero, etc. Therefore, these large numbers are broken down into groups of three zeroes. For example; it is easy to read and write a trillion with four sets of three zeroes than counting out twelve separate zeroes. However, somehow if you manage counting and writing twelve zeroes for a trillion, just imagine about reading and writing out an octillion with 27 zeroes and a centillion with 303 zeroes. Now, you must have realized the importance of using Naming large number system and definitely be thankful to the naming large numbers since you only need to remember nine and 101 sets of three zeroes.

Using ‘Powers of 10’ in Mathematics and Science, you can easily express or write how many zeroes are exactly needed for these large numbers. You can understand how easier it is to read and write a bunch of zeroes using powers of 10 in a very big number like below.

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 short cut for writing a billion is 10⁹ that means ten to the power of nine. Nine indicates the total number of zeroes required to write a billion.