Find the number of significant figure in the approximate number $0.49865$ for the given relative error of it as $0.2\times 10^{-2}$.
MY TRY: Let $x_A$ denote the approximate and $x_t$ denote the true value of $x$. Also let $E_A$ be absolute error and $E_r$ be the relative error. Then, we have $x_A=0.49865$ and $E_r=0.2\times 10^{-2}$.
Also $E_r=\dfrac{x_A-x_t}{x_t}\implies 0.2\times 10^{-2}=\dfrac{0.49865-x_t}{x_t}$
I am confused about what the question is actually asking me to find out. Is it asking me to find out $x_t$ by solving the above question?
Can someone please help me to figure out how to do it?
We have $$x_t = (1 + 0.2 \times 10^{-2}) x_A = 0.4996473.$$ When we compare $x_A$ and $x_t$ we find the first two significant figures are identical. It is very likely that the required answer is $2$.
There is a small point to note regarding the original question. Specifically, the number of significant figures in the real number $y =0.49865$ is (by definition) equal to 5. Therefore the phrasing of the question is at odds with the established definition. This issue may well be the result of a translation error. This conjecture is supported by the presence of the string "of it as" which is, well, unusual.
However, pedagogically, this is a fine problem! It is designed to wean students of reporting final results with a number of significant figures that is far larger than supported by the available accuracy.