부동소수점 내용같은데


Note that the bounds for the relative error using k-digit arithmetic are independent of number being represented. 

this result is due to the manner in which the machine numbers are distributed along the real line.

because of the esponential form of the characteristic, the same number of decimal machine numbers is used to represent each of intervals [10^(-1),1],

[1,10],[10,100]. in fact, within the limits of the machine, the number of decimal machine numbers in [10^n,10^(n+1)] is constant for all integers n.



내가 생각한바로는 부동소수점 연산에서 k digit rounding을 했을때 오차가 5*10^(-k+1)로  bounded 되있으니까


이것은 어떤숫자가 되었든 k반올림오차는 동일하게 bounded 되있다는 소리같은데  [10,100] 구간은 왜 언급하는건지 해석이 안되네