jamie.j1989 said:
This is the type of calculation I don't understand, it seems a bit messy?
Dr Claude is writing down the place value expansion of the number 4 using a radix of e. The system is described here:
https://en.wikipedia.org/wiki/Non-integer_representation
The algorithm to convert a number to a base e representation is tedious but straightforward.
Edit: This will yield
a base e expansion. Some tweaks would be required to produce
the canonical base e expansion.
Divide your number by e. If the result is greater than e, keep dividing by e until you have a number between 1 and e. Keep track of how many times you divided. This is the number of places you will need to move the radix point to the right. For small numbers you will multiply by e instead and keep track of the number of places to move the radix point to the left.
In this case, 4 divided by e is 1.41930... That result is between 1 and e. So there will eventually be a one place shift of the radix point.
Write down the integer part of this number (a digit which will be either 1 or 2).
In this case, we write down "1".
Subtract the integer part and multiply the remainder by e.
In this case, we multiply .41930... by e giving 1.13978...
Repeat, writing down the integer part of the number (a digit which will be 0, 1 or 2), subtracting and multiplying the remainder by e.
As per Dr. Claude, the resulting digit string is 1102001...
When you have as many digits as you please, insert a radix point and shift it the appropriate number of digits. The default position is to the right of the first digit.
In this case, one division by e to start means a one place right shift. 11.02001...
