Millions, Billions & Trillions: Understanding Large Numbers

Whether you are buying a tiny amount of bitcoin and have to face a huge decimal; or whether you are doing stats at Shoprite and have to collate all the sales figures from Zambia Zambia in Kwachas – at some point you are going to have to deal with large numbers. Don’t be left stranded, check out this easy cheat sheet below.

XLS SPREADSHEET

Grouping by zeros

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

Increments

From 1 to a million, our naming convention adds a single trailing zero each time:

  • One=1
  • Ten=10
  • Hundred=100
  • Thousand=1,000
  • Ten-thousand=10,000
  • Hundred-thousand=100,000

But from 1 million upwards, we add a set of 3 trailing zeros each time:

  • Million=1,000,000
  • Billion=1,000,000,000
  • Trillion=1,000,000,000,000
  • Quadrillion=1,000,000,000,000,000
  • Quantillion=1,000,000,000,000,000,000

In summary:

  • Million has 2 sets (of 3 zeros)
  • Billion has 3 sets (of 3 zeros)
  • Trillion has 4 sets (of 3 zeros)
  • Quadrillion 5 sets (of 3 zeros)
  • Quantillion 6 sets (of 3 zeros)
  • Etc

To the power of ten

Millions, Billions and Trillions are sill fine, but even a Quadrillion becomes cumbersome with it’s 15 zero’s. In this case a different way of presenting the total number of zero’s would be greatly appreciated. Enter The Powers of Ten.

In Maths & Science, it is common to quickly express the amount of zeros required in large numbers by this convention. A million would be written as 106, or ten to the power of six, indicating that there are six zeros. This saves a lot of time. So now, for a quantillion, in stead of  1,000,000,000,000,000,000 – just write 1018.

Powers of Ten are written as:

Million:     =106
Billion:     =109
Trillion:    =1012
Quadrillion: =1015

The Excel formula would simply be:

Million:     =1*10^6
Billion:     =1*10^9
Trillion:    =1*10^12
Quadrillion: =1*10^15

And a calculator with limited screen size might display:

Million:     1E+6
Billion:     1E+9
Trillion:    1E+12
Quadrillion: 1E+15

What is a googol?

We all know google. Their name is inspired by a large number, the googol. A googol has 100 zero’s, so 10100. Even though you can clearly measure it, many people use the word googol for describe any really large number. The word googol originates from American Mathematician Edward Kasner, when he asked his 9 year old nephew the name a very large number. The little guy, Milton Sirotta, said ‘googol’.

And a googolplex?

Ten to the power of googol, So 101E+100. And this isn’t the largest number defined as of yet. See Graham’s number and Skewe’s number. It’s so big that I cannot tell you how big it is.

Different definitions of a billion

The short scale and the long scale.

There are two definitions of a billion. I know it as a thousand-million (1,000,000,000) or 109. This is the number we all use in science and finance and it is referred to as the short scale. The short scale is the most widely used definition of a billion, used in South Africa, the USA and most of the rest of the world. South Africa United States

Enter the French. They refer to a billion as a million-million (1000,000,000,000) or 1012, ie what we would know as a trillion. This is known as the long scale up until recently was used in the UK as well. France United Kingdom

PS, the long scale version of a million is called a milliard, admittedly something we also often heard in the South African news, in Afrikaans ‘n Miljard, so defining a billion might become blurry, especially with the older population.

More on wiki.

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