To round to the nearest hundred and ten both being 200 it leaves 9 possibilities. 195,196,197,198,199,201,202,203, and 204. The only one with digits adding up to 19 is 199.
555
-12
0
199 If it's 200 rounded to nearest ten, then the number must be between 195 and 205. Only 199 has the correct digit sum.
The number 47 does not have a digit in the hundreds place. It only has digits in the ones and tens places. The four is in the tens place and the seven is in the ones place. Therefore it cannot be rounded to the nearest hundreds place. The number 47 is between zero hundred and one hundred. It is nearer to zero hundred than it is to one hundred. When rounded to the nearest hundred, it becomes zero, since zero hundred is nearer to it than one hundred is.
5600
199
The number would be 2666. 6 is repeated 3 times. Rounded to the nearest hundred is 2700 and rounded to the nearest thousand is 3000.
The mystery number is 155. When rounded to the nearest hundred, it rounds to 200. The sum of its digits is 1+5+5=11 which is greater than 10, so we must adjust the digit in the hundreds place. When rounded to the nearest ten, 155 rounds to 160, which has digits summing up to 1+6+0=7.
If you're talking about whole numbers, then it's 6,049 .If you're talking about any number, including decimals and fractions, then there's no "greatest possible" one.
555
555
600
2722
-12
3200
0