1
$\begingroup$

Searching for some help with the following questions:

Given the $3$ numbers $0.1329, 1.543, 23.21$,

$1$ ) Add the $3$ numbers in both ascending and descending order rounding all calculations to $4$ digits.

My workings: I am a little confused with the ascending and descending order, wouldn't these two calculations be equivalent?

Ascending $0.1329+1.543+23.21 = 24.89$
Descending $23.21 + 1.543+ 0.1329 = 24.89$

$2$) Compute the relative errors:

What relative errors do i need to calculate? if i was to calculate the erors for each number individiually wouldnt they be $0$ since they lost no accucary when rounded to 4 digits.

$3$) Which is more accurate and why?

$\endgroup$
1
$\begingroup$

Your second sum is wrong (you forgot to round to $4$ digits): $23.21 + 1.543 = 24.753 \rightarrow 24.75$ and $24.75 + 0.1329 = 24.8829 \rightarrow 24.88.$

This intermediate round is the reason why the order of summation may give different results.

The true sum is $s=24.8859.$ Compute the relative error: Ascending $(s-24.89)/s = -0.00016475$ and decending $(s-24.88)/s = 0.000237082.$

Therefore the ascending sum is more accurate.

$\endgroup$
  • $\begingroup$ should the relative errors be done in absolute values? making them both positive? $\endgroup$ – jh123 Sep 20 '18 at 20:47
  • $\begingroup$ and I didn't know you had to add one to another then add that sum to the final number you needed to add, that's where I was going wrong in my calculation. Thanks for pointing that out! $\endgroup$ – jh123 Sep 20 '18 at 20:48
  • 1
    $\begingroup$ If not otherwise stated, I would use signed relative errors. If you use signed errors you compare the magnitude to get the smaller one. $\endgroup$ – gammatester Sep 20 '18 at 20:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.