(a) Density of water in `CGS` system is `g//cm^(3)`. Convert it into `SI` unit.
(b) Young's modulus of steel is `2 xx 10^(11) N//m^(2)` (`SI` unit). Convert in into `CGS` unit (in `"dyne"//cm^(2)`).

Explanation

The dimension of density are `[ML^(-3)]`
`1 kg//cm^(3) = (1 g) (1 cm)^(-3)`
`1 g//m^(3) = (1 kg) (1m)^(-3)`
`(1 g//cm^(3))/(1 kg//m^(3)) = ((1 g)/(1 kg)) ((1 cm)/(1 m))^(-3)`
`= ((1)/(1000)) ((1)/(100))^(-3)`
`= (1)/(100) xx (100)^(3) = 1000`
`1 g //cm^(3) = 1000 kg//m^(3)`
(b) The dimensionks of Young's modules
`[Y] = (F)/(L^(2)) = (MLT^(-2))/(L^(2)) = ML^(-1) T^(-2)`
`1 N//m^(2) = (1 kg) (1 cm)^(-1) (1 s)^(-2)`
`1 "dyne"//cm^(2) = (1 g) (1 cm)^(-1) (1 s)^(-2)`
`(1 N//m^(2))/(1 "dyne"//cm^(2)) = ((1 kg)/(1 g)) ((1 m)/(1 cm))^(-1) ((1 s)/(1 s))^(-2)`
`= (1000) ((100)/(1))^(-1)`
`= (1000) xx (1)/(100) = 10`
`N//m^(2) = 10 "dyne"//cm^(2)`
or `2 xx 10^(11) N//m^(2) = 2 xx 10^(12) "dyne"//cm^(2)`