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.

Lowest 44.5kg? Highest 45.49999kg?

44.51 kg or 45.49 kg

44.5. 45.5

Being a total pedant here, but the question is incorrectly worded. It should say "Joe's mass was 45 kg."

As above - a value of 45.5 would actually round up but it’s the closest number we can use to 45.49recurring. So we use this as the upper bound.

44.5 and 4.499r

His weight is not 45 kg. His weight on Earth is 441 N.

His lowest possible mass is 44.5 kg. His highest possible mass is 45.49 with the 9 recurring.

As TheFallenMadonna and others have said.

well, no others said actually apart from MustTidyUp.

Best written as an inequality

45.5

What answer was he told was correct?

Ok so ds gave an the lower bound as 44.5kg which was marked correct.

And he gave 45.49 recurring for the upper bound, which was marked incorrect, the teacher wrote 45.5 as the correct answer.

I would have thought if the child weighed 45.5Kg it would have been rounded up to 46kg not rounded down to 45kg?

Well, Joe could weigh more than 45.49 kg - 45.494378655 kg for example, so as a convention we say 45.5kg. I'd assume that was covered in the teaching bit before answering the questions?

As Frendo says, think of it as an inequality.

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

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

But he was asked the highest possible value - not the upper bound. So if the the upper bound is 45.5, as it is any number less than this - the highest possible value could not be 45.5 it would have to be less than 45.5?

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.

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?

I would say the highest value is 45.49 with the 9 recurring. If I was given a figure of 45.5 and asked to round it to the nearest kilo I would round it up to 46.

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

I was wondering that too Larry has convention changed? I'm sure I would have right 30 years ago. Anyway ds just needs to know what gives him a right answer in his GCSE - you can't argue with the examiner.

45.49 recurring is exactly 45.5 So why doesn't 45.5 get rounded down to 45 then?

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.

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.)

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.