The speed of gamma rays in air is approximately $2.983\times 10^{10}$ cm/s.

1. Convert the speed from cm/s to m/s and express in standard form.

Since $1\text{ m}=100\text{ cm}$,

$2.983\times 10^{10}\text{ cm/s}\div 100=2.983\times 10^{8}\text{ m/s}.$

1. Calculate the time in seconds using distance divided by speed.

Using the speed from part (a),
$\text{time}=\frac{10000}{2.983\times 10^8}$
$=3.35232987\times 10^{-5}\text{ s}$

2. Convert the time from seconds to microseconds.

Since $1\ \mu\text{s}=10^{-6}\text{ s}$,
$3.35232987\times 10^{-5}\text{ s}=\frac{3.35232987\times 10^{-5}}{10^{-6}}\ \mu\text{s}$
$=33.5232987\ \mu\text{s}\approx 33.5\ \mu\text{s}$