## Friday, 7 November 2014

### Rounding to the nearest

I occasionally find myself having a disagreement with teachers and others involved in assessment who want to set children a test question in which to get the mark you have to assume that, for example, 148.5  rounded to the nearest whole number is 149. My argument is that in this situation there is no nearest whole number. The number 148.5 is as near to 148 as it is to 149. The only way you could decide which to round it to (if at all) would be to look at the context that gave rise to the number 148.5.

There is a myth that the convention is that if it ends in a 5 you round it up. I won't go along with this, because it is unnecessary and unjustified. Here's an example that illustrates my point.

I have a discount card from Waitrose that allows me 10% off any purchase. I buy a packet of biscuits that costs £1.65. For convenience, I'll write this in pence, as 165p. So ...

original price = 165p
discount = 16.5p
reduced price = 148.5p.

So let's assume we are to round the results to the nearest penny, because we can only deal in whole numbers of pence in Waitrose. If we use the rule of 'rounding up when it ends in a 5', we get:

original price = 165p
discount = 17p (to the nearest penny)
reduced price = 149p (to the nearest penny).

This is plainly impossible! A discount of 17p gives a reduced price of 148p.
So if the discount is rounded up, the reduced price has to be rounded down; or vice versa. So, assuming the generosity of Waitrose, I would expect:

original price = 165p
discount = 17p (rounded up)
reduced price = 148p (rounded down).

This is why I refuse to accept the so-called convention! Context is everything.

I suggest that we just do not set a context-free maths assessment question about rounding a number ending in a 5 to the nearest something, if in fact there is no nearest something.

Bad assessment questions (but good for class discussion):
1. Round 6.05 to 1 decimal place.
2. Round 125 to the nearest ten.
3. Round 3500 g to the nearest kilogram.
4. Round 3 minutes 48.65 seconds to the nearest tenth of a second.