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secondary 2 | Maths
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Hi appreciate help to let me know what should be the correct answer as the answer sheet provided is actually 100+0.5g = 100.5g which I think it is incorrect because if you round it to nearest gram , it should be 101g. Should the answer be 149g or 100.4g?. Thks
Date Posted: 4 years ago
Views: 560
We actually call 100.5 the “upper bound”.
Having a maximum of 100.4 is technically incorrect. Because 100.49 is also rounded off to 100. So does 100.499, 100.4999 and so on. There is never an end.
Recurring numbers such as 0.999999... can be considered as 1; there is a proof to this. Thus, the 100.5 that is given is actually referring to 100.499999... without limit.
Having a maximum of 100.4 is technically incorrect. Because 100.49 is also rounded off to 100. So does 100.499, 100.4999 and so on. There is never an end.
Recurring numbers such as 0.999999... can be considered as 1; there is a proof to this. Thus, the 100.5 that is given is actually referring to 100.499999... without limit.
Hi sorry but the question asked ‘the weight is measured 100g correct to the nearest grams’ If we indicate answer as 100.5g as the greatest possible weight, doesn’t it become 101g if it is corrected to the nearest gram?..
Could we indicate the answer as 100.49g as the greatest possible weight?
In reality, numbers ending in 5 are not always rounded up. You can read up some links on this, but this is meant to be beyond your syllabus.
The 100.5 here does not exactly mean 100.5 sharp, but it’s more of 100.4999..... which is definitely rounded down. However, rather than writing 100.49999, we simply denote this by 100.5 (I would rather write 100.5 than 100.499999...)
So, we call 99.5 the lower bound and 100.5 the upper bound. For numbers being rounded off to 101, we have 100.5 as the lower bound and 101.5 as the upper bound.
The 100.5 here does not exactly mean 100.5 sharp, but it’s more of 100.4999..... which is definitely rounded down. However, rather than writing 100.49999, we simply denote this by 100.5 (I would rather write 100.5 than 100.499999...)
So, we call 99.5 the lower bound and 100.5 the upper bound. For numbers being rounded off to 101, we have 100.5 as the lower bound and 101.5 as the upper bound.
It could go 100.49 yes, but it could go even further 100.4999999, or even 100.49999999999, or even more. Hence, we cannot end anywhere at all.
If, however, the masses are measured in accuracy terms of 0.01 g, then 100.49 g is correct.
If, however, the masses are measured in accuracy terms of 0.01 g, then 100.49 g is correct.
You can read up
https://www.factmonster.com/math-science/mathematics/rounding-numbers-rules-examples-for-fractions-sums
to see how this rounding off of a digit 5 works.
https://www.factmonster.com/math-science/mathematics/rounding-numbers-rules-examples-for-fractions-sums
to see how this rounding off of a digit 5 works.
Ok. Thks for the explanation.
105g because 100.4999999999999999999 will be rounded off to 100.5,just show the working of rounding off 100.49(with a dot above 9) then it will be correct(i think) (because i got the same type of question wrong last time)
Hi can I ask what about a case the weight of 100g is corrected to the nearest hundred grams. For such case the greatest possible weight is it 100g + 100/2 = 150g? Or should it be 149g?. Thks
I don't really put working last time so I am notnsure if the working is valid but I think if you show it correctly the answer should be 150g(?)
Yup, for the same reason I would put 150. Again, it is more of 149.999999... than an exact 150.
If, however, the numbers are integers, then we should put 149 and not 150 as the largest possible number.
If, however, the numbers are integers, then we should put 149 and not 150 as the largest possible number.
Understand. Thks!
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100.5 is correct because nearest g not nearest 10 g. Even though the precise answer should be 100.499.... but 100.5 will be acceptable.
Date Posted:
4 years ago
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