I have a question that asks to find the result (in sig figs) as well as the standard deviation for the following
$$(23\pm 8)\times(99\pm 11)\times(11\pm 3)\times(8\pm 4)$$
I began this question by multiplying out the numbers, which gets $200376$. This value, to 1 sig fig (since $8$ is 1 sig fig) gives $200000$. I have a bit of trouble with the standard deviation, however.
I researched and found the formula for propogation of error in multiplication to be
$$\frac{\Delta z}{z}=\left(\left(\frac{\Delta x}{x}\right)^2+\left(\frac{\Delta y}{y}\right)^2\right)^{1/2}$$
I used this, and once I calculate the right side I multiply by $200000$. This yields a number like $135308$.something. For one sig fig, I get $100000$. So my answer comes out to $200000\pm 100000$. I feel as if maybe my standard error is too big, or even I may be doing it wrong. So I was wondering if someone could point me in the right direction or such. Thanks.