Answer:
a) K^-1
Step-by-step explanation:
You want the units of the quantity defined as ...
e = (increase in length)/((original length) × (temperature rise))
Units analysis
The units of the parts of the ratio are ...
increase in length = (length - length) ⇒ length units (m)
original length = length ⇒ length units (m)
temperature rise = (temperature - temperature) ⇒ temperature units (K)
Then the units of the ratio are ...
e = (m)/(m × K) = 1/K . . . . . . . . m cancels
e = K^-1 . . . . units of e