Maths teacher or maths whizz? This way please!

Taking both numbers (45.49R & 45.5) and rounding them to the nearest whole number would not give you the same answer!
Yes it would, because they are the same number! 45.49999 [any number of 9s] rounds to 45, but 45.49recurring rounds to 46.

Perhaps what may help is to say that what is a convention is what you do with a number which is precisely half way between two whole numbers. It's fairly common, with conventions, that looking at it one way suggests one answer and looking at it another suggests another answer, and you just have to go with one. In this case, looking at the midway number notated as 45.49recurring suggests we should round it down, whereas looking at the same number notated as 45.5 suggests we should round it up.

I still vividly remember the classroom I was sitting in, aged 11, when our maths teacher taught us an algorithm for rounding that would sometime give you the wrong answer. I no longer remember precisely what her wrong algorithm was - I suspect it was "start from the right hand end and dispose of each number in turn: if it's 4 or less, just discard it, if it's 5 or more, bump up the next digit to the left as you discard this one; stop when you have the precision you want", which often works, but fails, for example, on 0.45. I do remember the anxiety of trying to convince her she was wrong without being rude!

let's talk English here not physics :-)

The thing is though, physics teachers have enough trouble trying to explain the difference between mass and weight, without maths test papers confusing the issue by using incorrect terminology. What are the pupils to make of it all?

And in South African English, people do refer to their mass being a certain number of kilograms (correct) and not their weight (incorrect).

Yes, I'm a pedant.

Bounds and error intervals are often expressed in inequality notation so your original answer would be 44.5

Atia and Relax,

Two elegant proofs (induction and deduction (?)) demonstrating the power of Maths as a subject!

Orange, I hope this enthuses your son.

No worries. Pass it on to your friends You're ok, I'm going out to walk the dog now, I'll shut up for a bit!

Ok,

Point taken. Thanks

I think 45.49 recurring tends to 45.5

No, they are the same thing!
Right.
Let a = 45.49999999.....
10a = 454.9999999......
So 9a = 10a -a
= 409.5
And a = 409.5/9
= 45.5

The sequence
45.49
45.499
45.4999
45.49999
etc
tends to 45.5. However, the notation 45.49recurring means the limit of that sequence. Which is 45.5. That's why 45.49recurring is equal to 45.5.

though oh gawd, looks as though GCSE may have its very own terminology:

www.bbc.co.uk/schools/gcsebitesize/maths/number/roundestimaterev5.shtml

In proper maths 12.5cm is an upper bound, but so is 27.48km :-) 12.5cm is the least upper bound, but that is still not the same as the highest possible value, and I very much hope a GCSE question wouldn't ask for the highest possible value and expect 12.5cm as an answer.

Well yes, you can't give a highest possible value! That's why we have the concept of upper bounds We need the question verbatim, and the teacher's explanation to give a full analysis here

Orange,

Excellent point. I think 45.49 recurring tends to 45.5. Mathematical semantics really, but examination boards are v pedantic, so best to just write what they want.

Atia is of course right, but it's a point that is very often misunderstood; it would not be in the least surprising if a primary teacher assumed 45.49recurring was a different number from 45.5, and sadly I wouldn't be surprised to get that mistake from a secondary maths teacher either. (If you doubt it, ask yourself what 45.5 - 45.49recurring should be...)

In fact, without more context, this is an unanswerable question. I expect, though, that there was an unspoken assumption about how precise measurements of Joe's weight (let's talk English here not physics :-) we're talking about. If Joe's scales only weigh to the nearest tenth of a kilo, and we interpret the question as:

Joe weighed himself, and then said, correctly, "My weight is 45kg to the nearest kilo". What are the highest and lowest possible values for the number he saw on his scales?

then the answers are 44.5 and 45.4.

People talking about upper bounds are confusing the issue, because an upper bound is a very different thing from a highest possible value.

(Goodness I'm in an assertive mood today.)

If the weight is 45 to the nearest kilo, then the actual weight is greater than or equal to 44.5 and less than 45.5.

If the weight is 46 to the nearest kilo, then the actual weight is greater than or equal to 45.5 and less than 46.5.

It is impossible to write down an actual highest possible value, so we use 45.5 as the upper bound, whilst knowing we mean less than 45.5. That's what your ds needs to accept and remember.

There's not a convention that you can write 45.5 for 45.49 (recurring) because 45.49 recurring is exactly 45.5

I think upper bound is 45.49(recurring)...cannot do the dot here. I agree with others that 45.5 would be rounded up.

If there is a convention that you can write 45.5 for 45.49 (recurring), that is possible (and kind of reasonable) but 45.5 itself would be rounded up.
Is it a new convention?

Ok, so what would you give as the highest possible value? You can't. Because for whatever value you give, I can suggest one that's higher, but is still less than 45.5.

So the convention is that we say the upper bound is 45.5.

The upper bound is 45.5, as it is any number less than this. He should have been taught this and the reasons why.

Also, 45.49 recurring is equal to 45.5, so technically he's right anyway, although probably didn't mean to be!