what is the area, and its approximate uncertainty, of a square of side 3.1x10^4 cm?
(3.1*10^4)^2 = 9.6*10^8
3.1^2 ----> 9.6 to two significant figs
but it might have been
3.05^2 ----> 9.3
or maybe
3.1499999999...^2 ---> 9.9
so
9.6 + or - .3 * 10*8
To find the area of a square, you need to square the length of its side. In this case, the length of the side is given as 3.1x10^4 cm.
So, the area A of the square is calculated by squaring the given side:
A = (3.1x10^4 cm)^2
To simplify this calculation, square the numerical part and multiply it by the square of the exponential part:
A = (3.1)^2 x (10^4)^2 cm^2
A = 9.61 x (10^8) cm^2
Therefore, the area of the square is 9.61 x 10^8 cm^2.
Regarding the uncertainty, you haven't provided any information about it. But usually, if the uncertainty in a measurement is given, you need to consider the maximum and minimum values for the length of the side. By finding the areas corresponding to these values, you can calculate the range of uncertainty in the area.