1099
To the nearest hundred, 1100 To the nearest thousand, 1000
Observe that: 100+999 =1099, 101 + 998 = 1099 up to 549+550=1099. So 1099 * (1000-100/2) or 1099 * 450 (450 pairs of numbers that sum to 1099) or 494,500. This is a variant of the method exposed in the "Gauss Anecdote"
The next integer is 1100.
The year 1031 was the 11th century (years 1000-1099).
The year 1066 was the 11th century (years 1000-1099).
1000
The first crusade took place in the year 1000.
2000 (1000+1000=2000)
2000
2000
= 2000