# Relative error in numerical analysis

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?

Your second sum is wrong (you forgot to round to $$4$$ digits): $$23.21 + 1.543 = 24.753 \rightarrow 24.75$$ and $$24.75 + 0.1329 = 24.8829 \rightarrow 24.88.$$
The true sum is $$s=24.8859.$$ Compute the relative error: Ascending $$(s-24.89)/s = -0.00016475$$ and decending $$(s-24.88)/s = 0.000237082.$$