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**paulb203****Member**- Registered: 2023-02-24
- Posts: 264

Error Intervals (Bounds)

The weight of a bag of potatoes is 15kg to nearest kg.

a)Write down the smallest possible weight of the bag of potatoes

Answer; 14.5kg (any smaller, e.g, 14.499999999998kg would be rounded DOWN to 14kg.

14.5kg is correctly rounded UP to 15kg

b)Write down the largest possible weight of the bag of potatoes

My answer; Greater than 14.5kg but less than 15.5kg; but a specific weight can't be given.

Their answer; 15.5kg

My question; How can it be 15.5kg? If it was 15.5kg it would have been rounded UP to 16kg (?).

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,544

Mostly .5 is rounded up but as its exactly halfway between the options you could make a case for rounding down.

Why is round up preferred?

(1) there only has to be one non zero digit after the 5 to tip the number over to round up.

(2) if you round down when the tenths digit is 0 1,2 3 or 4 and up if it's 6, 7 , 8, or 9 then that's 5:4 so choosing up for .5 gives even ups and downs. In a company such as an electric supplier this means bills are rounded up as often as down so the regulator is kept happy.

Example of rounding down. Various cupboards have to be pushed through a narrow gap. We know the gap is 50cm. Each cupboard is measured for width to see if it will fit through the gap. Round the widths down to the nearest cm

Why?

Bob

.

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**paulb203****Member**- Registered: 2023-02-24
- Posts: 264

Bob wrote:

Mostly .5 is rounded up but as its exactly halfway between the options you could make a case for rounding down.

Why is round up preferred?

(1) there only has to be one non zero digit after the 5 to tip the number over to round up.

(2) if you round down when the tenths digit is 0 1,2 3 or 4 and up if it's 6, 7 , 8, or 9 then that's 5:4 so choosing up for .5 gives even ups and downs. In a company such as an electric supplier this means bills are rounded up as often as down so the regulator is kept happy.

Example of rounding down. Various cupboards have to be pushed through a narrow gap. We know the gap is 50cm. Each cupboard is measured for width to see if it will fit through the gap. Round the widths down to the nearest cm

Why?Bob

.

Thanks, Bob. I hear you regards rounding up is only preferred, not written in stone, and a case can be made for rounding down; but I'm surprised that at GCSE level, where you're taught to round up for .5, that this answer (from MathsGenie) is given without an explanation.

Also, what might the case be here for saying that the bag could have been 15.5kg, i.e, that rounding down is appropriate?

Regards your cupboards example; I'm not sure. If a cupboard was 50.5, and it was rounded down to 50 (instead of the usual rounding up to 51) it would be deemed acceptable, only for someone to be frustrated later (with a cupboard that doesn't fit in the gap), no?

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**Phrzby Phil****Member**- From: Richmond, VA
- Registered: 2022-03-29
- Posts: 47

Conventions only work if everyone agrees. Rounding up has been the convention. For most situations, everyone agrees.

That having been said, there are special cases when many would consider, or the actual rules say, that rounding up wrong.

If a baseball player's average is .3995, that may round to the coveted .400, but I don't think there are bragging rights here.

In bowling, from the internet (!), "If the result is a decimal, you typically round down to get to a whole number."

*Last edited by Phrzby Phil (2024-05-29 09:15:28)*

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,544

I've just thought again about my 'example' and I said it incorrectly. It's the gap that needs rounding down else a cupboard might appear to be ok but will not fit due to rounding. eg true gap is 50.6 cupboard is 50.8

I have a vague memory that a question like this did come up years ago and the mark sceme said award full marks for 14.5 or 14.4999999999...

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**paulb203****Member**- Registered: 2023-02-24
- Posts: 264

Thanks, Bob.

Sorry for the late reply.

Ah, yes, the cupboard example makes sense now.

As for full marks for 14.5; would that mean that they are implying that 14.5, in some (rare?) instances would be rounded down? If so, why might rounding down be appropriate for a bag of potatoes?

P.S. I'm picking this up again because I've come across more examples of this.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,544

The grower bags up the pots and weighs them. He puts the rounded down amount on the bag so no customer can complain they are being undersold.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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