# Related Bases 1

## We don't care at all about base 100, but we start here because you are familiar with
base 10, so the arithmetic is easy, and the result is pretty obvious anyway.

### Let's convert 12345 decimal to base 100.

- start at the right side of the page
- divisor (always 100 in this case) is yellow; dividend is aqua; quotient is purple; remainder is green
- divide the original numeral (12345) by the new base (100), which gives you a quotient (123) and a remainder (45)
- long division procedure guarantees that the remainder will be less than the divisor (100 in this case)
- now repeat until the quotient is zero
- move to the left
- write down the quotient from the last division (arrows)
- make it a new division problem using the same divisor
- do the division, getting another quotient and remainder

- the answer is the string of remainders read left to right (1, 23, 45 in this case)
- I hope that you find it obvious that we didn't need to do the division procedure to get this answer
- all we needed to do is start at the right and bunch the digits into groups of 2
- we wanted groups of 2 because 100 = 10
^{2}
- likewise, groups of three would convert to base 1000
- whenever one base is a power of the other, we can convert just by grouping like this
- and we don't have to do any arithmetic
- this is going to be
**really** handy