#### Answer

See the answer below.

#### Work Step by Step

1 ppb = 1 part per billion= $\frac{1}{10^{9}}=\frac{10^{-6}}{10^{3}}= \frac{10^{-6}\,g}{10^{3}g}$
( Multiplying and dividing by gram does not make any difference).
Prefix for $10^{-6}$= micro or $\mu$
Prefix for $10^{3}$=kilo or k
Then, 1 ppb= $\frac{10^{-6}g}{10^{3}g}=\frac{1\,\mu g}{1\,kg}$