$1\mathrm{.}2\mathrm{.}4$ Arbitrary accuracy

Download the file

expand.py from the VLE which contains the code for the three methods: expand, expand$\_$integer$\_$part and expand$\_$fractional$\_$part. Place them in the Rational class and check you understand how they are used to convert a rational number to any base $($like decimal$),$ and to any number of digits. For example,

In $[1]$: Rational $(1,4).$expand $(10,4)$

Out $[1]$: $10\mathrm{.}25($base $10)\text{'}$

$10$

CHAPTER $1.$ COMPUTATIONAL ACCURACY

In $[2]$: Rational $(1,7).$ expand $(10,30)$

Out $[2]$ : $\text{'}0\mathrm{.}142857142857142857142857142857($base $10)\text{'}$

Experiment with these conversion functions. What is the $100$th decimal place of $e?$ How many terms in the partial sum are necessary to establish this?