Duodecimal facts for kids

The duodecimal system (also known as base 12 or dozenal) is a way of counting that uses twelve as its main number, or "base". In this system, numbers are grouped by 12s. For example, the number fifty (which we usually write as 50) would be written as 42 in the dozenal system. This is because 50 is the same as 4 groups of 12, plus 2 left over (4 × 12 + 2 = 50).

The number 12 is special because it can be divided evenly by many small numbers: 2, 3, 4, and 6. This is more than the number 10 (which can only be divided evenly by 2 and 5). Because of this, the duodecimal system can handle fractions better than our usual decimal system. For example, if you divide 12 by 3, you get a whole number (4). If you divide 10 by 3, you get a repeating decimal (3.333...).

How We Write Numbers in Base 12

In our everyday decimal system, we use digits from 0 to 9. But in the duodecimal system, we need symbols for ten and eleven. Since we don't have single numbers for 10 and 11, special letters are used.

• The letter X is often used to represent the number ten. This comes from the Roman numeral for ten.
• The letter E is often used to represent the number eleven. This comes from the first letter of "eleven".

Some people also use A for ten and B for eleven, similar to how it's done in the hexadecimal system.

A mathematician named Edna Kramer, in her 1951 book The Main Stream of Mathematics, suggested using * for ten and # for eleven. She chose these symbols because they were easy to find on typewriters and push-button telephones.

In this article, we will use "X" for ten and "E" for eleven.

Comparing Numbers: Decimal vs. Duodecimal

This table shows how some numbers look in both our usual decimal system and the duodecimal system.

See also

In Spanish: Sistema duodecimal para niños