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Duodecillion — Definition, Formula & Examples

A duodecillion is the number 1 followed by 39 zeros, or 103910^{39}, in the American (short scale) naming system used in the United States. It sits between undecillion (103610^{36}) and tredecillion (104210^{42}) in the sequence of large number names.

In the short scale system, a duodecillion is defined as 103910^{39}, representing the 13th power of one thousand beyond unity: 1,000131{,}000^{13}. In the long scale system used in some European countries, duodecillion instead denotes 107210^{72}.

Key Formula

1 duodecillion=1039=1000 000 000 000 000 000 000 000 000 000 000 000 000⏟39 zeros1 \text{ duodecillion} = 10^{39} = 1\underbrace{000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000}_{39 \text{ zeros}}
Where:
  • 103910^{39} = Ten raised to the 39th power, the value of one duodecillion in the short scale

Worked Example

Problem: How many duodecillions are in one tredecillion?
Write each value as a power of 10: One duodecillion is 103910^{39} and one tredecillion is 104210^{42}.
Divide: Divide tredecillion by duodecillion using exponent rules.
10421039=1042−39=103=1,000\frac{10^{42}}{10^{39}} = 10^{42-39} = 10^{3} = 1{,}000
Answer: There are 1,000 duodecillions in one tredecillion.

Why It Matters

Large number names like duodecillion appear in scientific contexts such as estimating the number of atoms in massive objects or distances in astronomy. Knowing how these names map to powers of ten helps you read and compare extreme quantities without getting lost in strings of zeros.

Common Mistakes

Mistake: Confusing the short scale (American) and long scale (European) values.
Correction: In the U.S. short scale, a duodecillion is 103910^{39}. In the long scale used in parts of Europe, it means 107210^{72}. Always check which system is being used.