source: https://timroderick.com/floating-point-introduction/
- Computer use binary numbers instead of decimal numbers
- Standard Form (Scientific Notation)
- we can do the exact same thing with binary
- based on the significant digits and the placement of the fractional point relative to said digits
- Floating point is a binary standard-form representation of numbers!
- $(sign)\times(significant digits)\times(base)^{(some power)}$
- Why floating point always with errors
- Recurring Fractions
- any fraction $\cfrac{x}{y}$. If $y$ has a prime factor that isn't also a factor of the base, it will be a recurring fraction.
- we can't easily represent all numbers in a finite number of digits.
- we store an approximation accurate to finite places.
- Easter egg
- We all know the answer is ~~42~~