Solution:

Growth rate Of hair in nm $s^{-1}$ = Imm per day

Growth rate of hair in one day = $24\times 60 \times$ 60 s

(Since 1 mm $10^{-3} m and one day = 24 \times 60 \times 60 s)$, hence

1 mm per day = $I\times 10^{-3} m \times \frac{1}{24} \times 60 \times$ 60 s
        = $I \times 10^{-3}  m \times \frac{1}{8400} m s^{-1}$
        = $I \times10^{-3}  m\times 0.00001157$
        = $I \times 10^{-3} m \times1157 \times 10^{-8} ms^{-I}$
        = $1157 \times 10^{-2}m \times 10^{-9}ms^{-1}$

        =$11.57 \times10^{-9} ms^{-1}$
1 mm per day =$11.57  nms^{-1}$ 
(because $10^{-9} ms^{-1} = 1n ms^{-1})$.