The Rydberg's constant is $1.097373177\times {10}^7{ m}^{-1}$. It can be expressed to three significant figures as:

1. If the no to be rounded off is greater than 5 then preceding digit is increased by 1

2. If the no to be rounded off is lesser than 5 then preceding digit is remained unchanged.

Using the following rule and rule of judging sig figures(i.e Exponential form( power form) doesn't affect the no of significant figures) the number can be expressed as$1.10\times {10}^7{ m}^{-1}$

Hence option (C) is the correct answer to the question.