Smallest: 79500
Largest: 80500
Although many schools teach you to round 5 up, the IEEE (Institute of Electronic and Electrical Engineers) standard 754 is to round up or down so that the new "last" digit is even. See link for more.
The problem with always rounding up from 5 (or more is that it introduces an upward bias. Thus,
If the number is 0.0 you don't need to round
If the number is 0.1, 0.2, 0.3 or 0.4 you round down
If the number is 0.5, 0.6, 0.7, 0.8 or 0.9 you round up
So for a random last digit, 5 times out of 10 you round up and 4 times out of 10n you round down: (and one out of ten is no change). The net result is an upward bias
One possible solution is to round up from 0.5 half the time, round down the other half. That satisfies the bias problem but introduces another - that of reproducibility. If someone else were to look at your data would they round up/down the same way you did? Unlikely. You need a system which will round 0.5 up half the time and down half the time but where the decision is made for you.
Hence the best solution is the answer given above: Round up or down so that the new last digit is even. See link for more.
5500 to 6499
To solve this, you have to consider what the largest and smallest numbers could be to cause the ten thousand's place to round to a 0.404,444 is the largest, because if you round to the ten thousand's place, it will still be 400,000. If any of the 4s becomes a 5, it will round up to 410,000.394,445 is the smallest, because if you round to the ten thousand's place, it will round up to 400,000
8,500 and 9,499
50
The answer depends on the degree of rounding. To the nearest fifty, the range is 325 < X < 375.
29500 to 30499
5500 to 6499
The smallest number would be 29500. The largest number would be 31499.
8000
85000 and 94999
The wording of this question seems confusing. 5700 rounded to the nearest thousand would be 6000. So you appear to be looking for the largest and smallest whole numbers that would round to 6000.The smallest whole number that would round to 6000 would be 5500. 5499 if rounded to the nearest thousand would be 5000.The largest whole number that would round to 6000 would be 6499. 6500 if rounded to the nearest thousand would be 7000.
Any number in the interval [29500, 30500].
I believe the answers are 165,000 and 174,999
6000
70
45 to 54
To solve this, you have to consider what the largest and smallest numbers could be to cause the ten thousand's place to round to a 0.404,444 is the largest, because if you round to the ten thousand's place, it will still be 400,000. If any of the 4s becomes a 5, it will round up to 410,000.394,445 is the smallest, because if you round to the ten thousand's place, it will round up to 400,000