how do we know that there is a subtraction of two close numbers thus making loss of significance?
there is no close numbers there is variable X
it could give use a close result or otherwise
and why multiplying and dividing by
makes it go away?
how do we know that there is a subtraction of two close numbers thus making loss of significance?
there is no close numbers there is variable X
it could give use a close result or otherwise
and why multiplying and dividing by
makes it go away?
I presume this means for x close to 0. For example, if x= 0.001, . If you are rounding to, say, 6 decimal places, That would be just 0. As for multiplying and dividing by the result, of course, will be the same but I presume that this is talking about it being some intermediate result in a further calculation- where the " " you would get in the numerator will be canceled.
I think you have already figured out that
The point of the exercise is that in this form the value can be computed without the catastrophic loss of significant figures that occurs in the original computation when x is small due to the subtraction of two almost-equal numbers.
Or, to put it another way, No Subtraction!