I was reading in my maths gcse book that when something is to the nearest measurement you half the unit and add it either side of the rounded number, like say 9m is to the nearest metre, the actual measurement could be from 8.5m to 9.5 metres, but wouldn't you round up at 9.5 metres? It said that 9.5 metres would be the highest value it could be. And also, how come you don't do the same with normal numbers, like say if 460 is to the nearest 10, then why can't the highest possible value of the original number be 465? I would appreciate it so much if you could help, thanks!
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I know what you mean. You are theoretically correct.
eg for 9m measurement could be between 8.5 and 9.499999999etc etc
However, for simplicity it is taken as 9.5 as 9.49999reoccuring is practically 9.5
It is the same with numbers like 460. To nearest 10 means it could be anywhere between 455 and 465
eg for 9m measurement could be between 8.5 and 9.499999999etc etc
However, for simplicity it is taken as 9.5 as 9.49999reoccuring is practically 9.5
It is the same with numbers like 460. To nearest 10 means it could be anywhere between 455 and 465
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The measurements on the tape which you are using for the first example are presumably 8m, 9m, 10m, 11m, 12m, and so on. So the NEAREST MEASUREMENT which you can get is 8 or 9 or 10 or whatever. So something which is 9m TO THE NEAREST MEASUREMENT tells you only that it COULD be 0.5 m to either side. But you are not talking about "rounding up". That would be incorrect. There are NO 0.5m marks on the tape, so 8.5 and 9.5 are NOT "nearest measurements". That is only the range of possible error.
Similarly, "to the nearest 10" means that the marks on the measuring device are 440, 450, 460, 470, and so on. So "460 to the nearest 10" does indeed mean that the actual value could be anywhere from 455 to 465. But you cannot "round up". Why not "round down" instead ? You do NOT know whether the actual measurement is nearer to 465 than it is to 455. I do not really understand what you mean by "you don't do the same with normal numbers". You do. Exactly the same. You appear to have a misunderstanding somewhere. You should provide an example of what it is that confuses you.
Similarly, "to the nearest 10" means that the marks on the measuring device are 440, 450, 460, 470, and so on. So "460 to the nearest 10" does indeed mean that the actual value could be anywhere from 455 to 465. But you cannot "round up". Why not "round down" instead ? You do NOT know whether the actual measurement is nearer to 465 than it is to 455. I do not really understand what you mean by "you don't do the same with normal numbers". You do. Exactly the same. You appear to have a misunderstanding somewhere. You should provide an example of what it is that confuses you.