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# maths rounding workk watch

1. a root for an equation is within the interval [2.97114, 2.97115]
what would the root be rounded to 5sf?
is it 2.9711 or 2.9712?
thank you
2. EDIT- See ghostwalker post(Better explained)
3. All numbers in that interval round to 2.9711, with the exception of 2.97115 which will round to 2.9712.

So if you know the root is not actually equal to 2.97115, then its rounded value must be 2.9711, otherwise it could be either.
4. (Original post by jit987)
2.97114 = 2.9711
2.97115 = 2.9712
I think I just died inside.
5. (Original post by ghostwalker)
All numbers in that interval round to 2.9711, with the exception of 2.97115 which will round to 2.9712.

So if you know the root is not actually equal to 2.97115, then its rounded value must be 2.9711, otherwise it could be either.

i think that makes sense, because i have to do the error bounds and when i use 2.9712 there is no change of sign so there is no root, but when i use the error bounds for 2.9711 there is a change of sign showing there is a root.
thanksss
6. (Original post by nuodai)
I think I just died inside.
lool.
when i use 2.9711 and find the error bounds there is a change of sign indicating a root present, but when i use 2.9712 there is no change of sign, so is it correct to put down 2.9711?
7. (Original post by sssm)
lool.
when i use 2.9711 and find the error bounds there is a change of sign indicating a root present, but when i use 2.9712 there is no change of sign, so is it correct to put down 2.9711?
Yes. The idea is that [2.97114, 2.97115] is the range of numbers given by . Every number in this range rounds down to 2.9711 except for when x=2.97115, in which case it rounds up to 2.9712. If, the root is in the range and is not equal to 2.97115, then, it must round down to 2.9711.
8. (Original post by nuodai)
Yes. The idea is that [2.97114, 2.97115] is the range of numbers given by . Every number in this range rounds down to 2.9711 except for when x=2.97115, in which case it rounds up to 2.9712. If, the root is in the range and is not equal to 2.97115, then, it must round down to 2.9711.
thank you clever cambridge dude.

9. Lol.
10. (Original post by ghostwalker)

Lol.
and thank you too babe x
11. (Original post by sssm)
and thank you too babe x
12. (Original post by nuodai)
Yes. The idea is that [2.97114, 2.97115] is the range of numbers given by . Every number in this range rounds down to 2.9711 except for when x=2.97115, in which case it rounds up to 2.9712. If, the root is in the range and is not equal to 2.97115, then, it must round down to 2.9711.
Thanks, I needed that

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