metric system conversions

1. how many micrograms make 1kg?

=1×10^9 µg  (micrograms)

2. how many nanometers are there in 1cm?

=1×10^7 nm  (nanometers)

1. how many micrograms make 1kg?             1 kg = 1 000 000 000 µg

$\small{ \begin{array}{rcl} 1~ \text{kg} &=& 10^3 g \\ 1~ \mu g &=& 10^{-6} g \\ \\ \hline \\ \frac{ 1~ \text{kg} }{1~ \mu g } &=& \frac{10^3 g}{ 10^{-6} g } \\ \frac{ 1~ \text{kg} }{1~ \mu g } &=& \frac{10^3}{ 10^{-6} } \\ \frac{ 1~ \text{kg} }{1~ \mu g } &=& 10^3 \cdot 10^6\\ \frac{ 1~ \text{kg} }{1~ \mu g } &=& 10^9 \\ 1~ \text{kg} &=& 10^9~ \mu g \\ \end{array} }$

2. how many nanometers are there in 1cm?  1 cm =     10 000 000 nm

$\small{ \begin{array}{rcl} 1~ \text{cm} &=& 10^{-2} m \\ 1~ \text{nm} &=& 10^{-9} m \\ \\ \hline \\ \frac{ 1~ \text{cm} }{1~ \text{nm}} &=& \frac{ 10^{-2} m }{ 10^{-9} m } \\ \frac{ 1~ \text{cm} }{1~ \text{nm}} &=& \frac{ 10^{-2} }{ 10^{-9} }\\ \frac{ 1~ \text{cm} }{1~ \text{nm}} &=& 10^{-2} \cdot 10^9\\ \frac{ 1~ \text{cm} }{1~ \text{nm}} &=& 10^7 \\ 1~ \text{cm} &=& 10^7~ \text{nm} \\ \end{array} }$

heureka's answer is the correct one.