Lets suppose it says: half. Is the estimate reasonable or rough, or is it wrong altogether?That depends on how you are rounding the readings to get the estimate.
Put the estimate in perspective of what its comparable to. The estimate is half in our example, so its comparable to quarter and three-quarters. If the estimate was one-third then it would be comparable to one-sixth and half. If 8000 then 4000 and 12000.
The estimate along with its comparables can be called markers. Markers stretch on both sides. If estimate is half the markers are zero, quarter, half, three quarters, full; and it can go beyond zero and full. For estimate that is one-third the markers are zero, one-sixth, one-third, half, two-third, five-sixths, full. For 8000 0, 4000, 8000, 12000, 16000 and so on.
If the reading is within 0.4375 and 0.5625 then its reasonable to round it to half. Its nearer to half than the middle point (0.375 or 0.625) between 0.50 and 0.25 or 0.75.
If its nearer to 0.375 than 0.50 then its reasonable to round it to 0.375, not 0.50.
Only when estimating roughly can anything nearer to 0.375 than 0.50 be rounded to 0.50, ofcourse only when the reading getting rounded is between 0.375 and 0.50.
The difference between reasonable and rough rounding is respecting the middle point between markers.
Both reasonable and rough rounding are correct. Rough rounding is not wrong, its just unusual, we dont normally go there. We do rough rounding only out of necessity, that is, when other option is not available. If the result has only options: zero, quarter, half, three-quarters, full; and reading is 0.35 then we are forced to unreasonably round it to quarter. Its a long way away from quarter. Its reasonable rounding is 0.375. Since that option is not available we are forced to roughly round it to quarter. Its not wrong. Depending on the situation it may work. If our readings are always in tens, never in units then it may be ok to let go of this much accuracy.
If you need significant amount of accuracy you have to do reasonable rounding, you cannot do rough rounding. If you only need a general spray of bullets to keep your enemies' head down while your other team make a close approach you dont need a rifle, you need a machine gun, even as inaccurate as a klashinkov will do. Quick and dirty approach may work. Depends on the situation.
Having said that there are estimates that are wrong altogether. Anything between 37.5 and 50 cannot in our example be rounded to 25. That would not be rough rounding, that would be wrong rounding.
Back to correct rounding no matter its type, the numbers are ofcourse on number line. The number line extends infinitely at both sides so wherever you are on the number line you have two sides. Each marker being basically a number has its sphere of influence, which expand on both sides. 50s sphere of influence, for example, is between 43.25 and 56.25. 75s between 68.75 and 81.25. The left over middle space between the markers 50 and 75 goes entirely to the middle point between the markers:62.5 as its sphere of influence cover that entirety.
What to do about the exact middle point: 37.5, 62.5 etc when doing rough rounding? Just use the rounding rule about it. Round it above. Round 37.5 to 50, 62.5 to 75 and so on.
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