One Address, Several Representations
An IPv4 address is fundamentally a single 32-bit number, and dotted-decimal notation (like 192.168.1.1) is just the most human-readable of several equally valid ways to write that same underlying value (see IP Address Notations for the full breakdown of why each format exists). Binary reveals exactly what a CIDR/subnet prefix operates on — a count of fixed leading bits — which is far more transparent when written out in binary than reasoned about in decimal.
The packed 32-bit integer form matters specifically for anywhere IP addresses are stored or compared at scale — many databases and geolocation datasets store addresses as a single integer rather than four separate octets, since a single integer is both more storage-efficient and trivially comparable for range queries ("is this address between X and Y") — a comparison that's awkward to express directly across four separate decimal octets.
Converting between these representations by hand is genuinely error-prone (each octet's positional weight in the integer form is a power of 256, not 10), which is exactly the kind of mechanical conversion worth automating rather than risking a manual arithmetic mistake in something like a firewall rule or database query.