2000 is a leap year, February 29th. In a leap year of four years, Grandpa was born on February 29th, 1940.

Non-leap year has 365 days in a year and 28 days in February.

There are 366 days in leap year and 29 days in February, which is 29 days more.

So Xiaoming's grandfather was born on February 29th, so he only has his birthday once every four years. In 60 years, he just had 60÷4= 15 birthdays. Grandpa was born on February 29th, 1940.

He only has 15 birthdays, but he is 60 years old, which means that his birth date only happens once every four years. Through the analysis of the whole year, it is found that he was born on February 29, and then he was 60 years old in 2000, which means that he was born on February 29, 1940.

Because 2000 was a leap year, there were 2.29 in that year. There is only one leap year in four years, so he was born on February 9, 1940.