IPA: /ˈrɪɡərəsli/
KK: /ˈrɪɡərəsli/
In a very strict and careful way, ensuring that all details are considered and nothing is overlooked.
The experiment was conducted rigorously to ensure accurate results.
Rigorously → It is formed from "rigor" (from Latin "rigor", meaning stiffness or severity) and "-ously" (a suffix meaning in a manner characterized by). The word "rigorously" means in a manner characterized by strictness or severity.
Think of 'rigor' meaning strictness or severity, and remember that 'rigorously' describes doing something in a strict or severe manner.