Maths teacher or maths whizz? This way please!

[Orangeplastic]

A recent question in a Maths test.....

Joe weighed 45kg to the nearest kilo. What is the highest and lowest possible value of his weight?

Ds got this question wrong - he thought he was right, he questioned the teacher but she insisted he was wrong and we are not sure why.

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

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.

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.

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

Ok,

Point taken. Thanks

So ds would have been correct with his 45.49 recurring because it equals 45.5 - but would he get it marked wrong in his GCSE?

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!

Atiao thank you for the proof, I’ll need it to convince Ds!

Atia and Relax,

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

Orange, I hope this enthuses your son.

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

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.

It has been an interesting discussion and he has accepted that he has to jump through the hoops to get maximum marks in his GCSE and he won't forget the right answer to this question in a hurry. He would feel happier with the inequality notation. Getting his head around 45.49R = 45.5 was too much. Taking both numbers (45.49R & 45.5) and rounding them to the nearest whole number would not give you the same answer!

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!