# What does the colon use in the decimal place mean?

When I type into wolfram the query, exp(1) in base 100, the answer comes back "2.71:82:81...."

What does the colon (:) mean?

• I would guess that the base-100 digits are the pairs separated by colons. For example, the first base-100 digit past the radix point is 71. – MPW Jul 17 '14 at 21:31
• to expand on what MPW said, you'd need 100 different characters to not need colons – Jam Jul 17 '14 at 21:33

You are asking for a number to be expressed in base $100$. That means the first "place" after the "decimal" point is in units of $1/100$, the second "place" after the "decimal" point is in units of $(1/100)^2$, and so on. Each "place" is populated by a whole number ("digit") from 0 to 99. Because we do not have distinct symbols for each of those possible digits, each one of those base-100 "digits" is actually written using a pair of base-10 digits. This makes reading the number hard, so it is helpful to use a delimiter to keep the place values separated for readability's sake.
The particular number you are looking at is $$2 + 71(1/100) + 82(1/100)^2 + 81(1/100)^3 + \dots$$
• When we write 1000 in base 3, we write it as $1101001$. We interpret this as $1 \cdot 3^6 + 1 \cdot 3^5 +1 \cdot 3^3 + 1$, but that is actually a base 10 expression -- which you can tell because it contains not just the symbol 6, but also a 5 and a 3, none of which are legal symbols in base 3. If we wanted to write the same expanded form using only base 3 symbols, we would write it as $1 \cdot 10^{20} + 1 \cdot 10^{12} + 1 \cdot 10^{10} + 1$. – mweiss Jul 18 '14 at 23:13