rounding numbers

[richmal]

This is not really homework as I home educate, but it was a question asked me by dd.

If you had .499999(......recurring) at the end of a number, would you round the units up or down?

Depends which place you were needing to round to. ie if rounding to the nearest unit the answer would rounded down to 1. If rounding to the nearest 10th answer would be rounded up to 1.5. If rounding to the nearest 100th the answer would be 1.50.

I may be a little late but I've only just seen this :-)

Depends how many places of decimal. To one place of decimal you round up to 0.5.

I know this is a bit late, but just to confirm richmal and Cornflake you have ended up in the right place.

0.49999... is identically equal to 0.5 and so if you were rounding it using the convention that 0.5 rounds to 1 you would round it to 1.

But there is no area of study where you can encounter both infinitely recurring decimals and the need for rounding so this does not come up in practice.

BTW for another proof that 0.999... = 1 which some find more convincing compare 1/3 + 1/3 + 1/3 with 0.333... + 0.333... + 0.333..

Oh I meant to ask - how old is the pupil?

Thank you for your reply.

But there is no area of study where you can encounter both infinitely recurring decimals and the need for rounding so this does not come up in practice.

I was right: There was a mathematician somewhere who could put it a lot better.

Dd is 10.

we had this discussion recently over homework.

1.4999 rounded to no decimal places = 1
rounded to one decimal place = 1.5
rounded to 2 decimal places = 1.50 (I think??)

but we had another discussion about whether you always round 5 up. I remember (from distant past) something in university science about a convention of rounded some 5's up and some down, so even number plus 5 went up and odd number plus 5 goes down.

3.5 = 3
4.5 = 5

Is this a figment of my imagination? Dh just gave me the look and laughed!

Oh come on, don't all disappear, come and tell me I am not mad (of course I won't be letting on to dh if he is right!)

Yes steppenmum that convention does exist among the various tie breaking methods, although it is more common to round to an even number rather than an odd (so 3.5 and 4.5 would both round to odd).

Note that like most Wikipedia maths articles that one has some flaws but it is OK on the main points. Note however that the comment on bookkeeping does not apply in the UK - the most common place that rounding is encountered in UK bookkeeping is in VAT calculations where the regulations state that you can round VAT down ignoring fractions of a penny.

"so 3.5 and 4.5 would both round to odd"

Oops - I meant "so 3.5 and 4.5 would both round to 4".

... and I also meant to say that unless a particular convention is specified, the default tie break is to round away from 0, so 1.49 rounds to 1, 1.50 rounds to 2 and -1.50 rounds to -2 so whilst other conventions exist, it is wrong to use them in an exam unless told to.

Yey!

I knew I hadn't dreamt it.

I think we had to use it in certain statistical things to do with logging experiment results to prevent a bias, but couldn't for the life of me tell you when and how (dim and distant other life)

"I think we had to use it in certain statistical things to do with logging experiment results to prevent a bias"

Yes, before the days of calculators and when instruments had analogue readings so that you could estimate 0.5 of a unit but not 0.4 or 0.6 that used to be common. Now it is unlikely that there is any reason not to record and use in statistical summaries whatever level of precision the instrument displays.