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Let's say i calculated a mean to be 2.475, but the data values had the least significant figure in the tenths place (i.e Like why when adding or subtracting we keep the same number of decimal plac. 2.6, 2.8 etc.) so i round the mean value to 2.5 for correct sig figs

The following link how to determine significant figures involving radicals and exponents mentions that if you have 5.1^4 "the 4 is (probably) exact, so we ignore that for deciding precision, s. I wanted to know how do we know that the rules that we follow when doing arithmetic with significant figures are correct Are you asking about the number of significant figures in the answer or how to do the calculations to arrive at the answer?

So one sig fig is added to the value and one is removed from the uncertainty

(28,3 ± 0,05) ÷ 4 = 7,075 ± 0,0125 rounded to 7,08 ± 0,01 here the number of sig figs for both the value and the uncertainty is maintained, but the value is rounded to one more decimal place I am confused as to what the rules are supposed to be here. I can't seem to find anything about this but i thought that for every 10 samples (of the same thing) that you averaged together you gained 1 significant figure You'd maybe need 100 samples to gai.

These percentages come not from measurements but from dividing integers (numbers of elements in a set that satisfy a property over the cardinal of the set) Since exact numbers have infinitely many significant figures, and since your dividend and divisor are exact numbers, therefore your quotient also has infinitely many significant figures If i ask for a percentage with 2 significant figures. In other words, i took 3.1 (2 sig figs) to calculate 0.018

I have a question about what the sig figs for the standard deviation

Do i follow the rules for the addition, and get 12 because there can't be decimals Or do i need to round to three sig figs because 101 is three sig figs? I have a question about sig figs and decimals If you start off with an exact value like 8.00 m which is 3 sig fig and you multiply by 100 cm so 800 cm

Then you divide by 2.54 cm and get 314.96 in.

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