# Percent Uncertainty

#### Struggling

hi didnt know wether to put this in phyics or maths but im studying for physics so ill put it here.

Q: What is the percent uncertainty in the volume of a spherical beach ball whos radius is r = 2.86 +or-0.08m?

A: V= 4/3 pie r^3

V = 4/3 pie(2.94)^3 = 106.4463
V = 4/3 pie(2.86)^3 = 97.9911

106.4463-97.9911 = 8.4552

8.4552/97.991 x 100 = 8.6285%

shouldnt 8.6285% be the answer? the book has 9% which i understand could be rounded but considering im doing the scientific notation chapter and it talks about how important it is to be clear with your answer.

i also tried the equation using only 3 significant numbers but i turned out further away from the answer getting something like 8.1%.

have i done something wrong in my calculations??? this question really is simple but i cant think of any other way.

thanks

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#### dextercioby

Homework Helper
You might wanna watch out for significative figures.What about the $2.78 \mbox{cm}$ value...?

And it's "pi" and it has no taste,it's a greek letter.

Daniel.

#### Struggling

yeh i tried it as well i get:

v=4/3 pi (2.78)^3 = 90.0
v=4/3 pi (2.94)^3 = 106
v=4/3 pi (2.86)^3 = 98.0

and i get lost here????

are my significant figures right?

#### dropframe

You need to use the extra digits to do the calculation, just as you have done, but then your final answer needs to match the least number of significant digits given in the problem; in this case, +or- 0.08m has only one significant digit. Therefore, the answer 8.6285 gets rounded to 9%.

#### bs24

i need help on this problem also. Is there a method in solving this

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