A metal wire has mass ( 0 . 4 ± 0 . 002 ) g , radius ( 0 . 3 ± 0 ....

Density$= \dfrac{\text{mass}}{\text{volume}}$

$⇒ ρ = \dfrac{m}{\pi{r}^{2}l}$

Therefore, percentage error can be written as

$⇒ \dfrac{dρ}{ρ} \times 100 = \left[\dfrac{dm}{m} + 2\left(\dfrac{dr}{r}\right) + \dfrac{dl}{l}\right] \times 100 = \left[\dfrac{0 . 002}{0 . 4} + 2\left(\dfrac{0 . 001}{0 . 3}\right) + \dfrac{0 . 02}{5}\right] \times 100 \approx 1 . 6$