There are a number of ways to have RIP advertise a default route.
see
formatting link
RIP advertises a route to 0.0.0.0 if a gateway of last resort is selected using the ip default-network command. This network specified in the ip default-network command need not be explicitly advertised under RIP
In earlier versions of RIP, the default route created using the ip route 0.0.0.0 0.0.0.0 was automatically advertised by RIP routers. In Cisco IOS Software Release 12.0T and later, RIP does not advertise the default route if the route is not learned via RIP. It may be necessary to redistribute the route into RIP.
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router rip redistribute static network 192.168.1.0
ip route 0.0.0.0 0.0.0.0 Null0
*Mar 1 00:06:31.681: RIP: build update entries
*Mar 1 00:06:31.681: subnet 0.0.0.0 metric 1
*Mar 1 00:06:59.547: RIP: sending v1 update to 255.255.255.255 via FastEthernet1/0 (192.168.1.1)
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router rip network 192.168.1.0
ip default-network 192.168.2.0
MERV1#debug ip rip RIP protocol debugging is on MERV1#
*Mar 1 00:15:45.717: RIP: sending v1 update to 255.255.255.255 via FastEthernet
1/0 (192.168.1.1)
*Mar 1 00:15:45.717: RIP: build update entries
*Mar 1 00:15:45.717: subnet 0.0.0.0 metric 1
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router rip network 192.168.1.0 default-information originate
*Mar 1 00:18:06.220: RIP: sending v1 update to 255.255.255.255 via FastEthernet
1/0 (192.168.1.1)
*Mar 1 00:18:06.220: RIP: build update entries
*Mar 1 00:18:06.220: subnet 0.0.0.0 metric 1