Are GCSE upper bounds correct?

Question

Is the upper bound of 10 to 1sf really 15, or is it 14.98 recurring? If so, am I being taught incorrect information? For example if a box can take 70g (accurate to 1sf), what is the maximum number of exact 1.5g masses could I place into it? I have been taught 50 but is it 49.

Answer 1

When rounding to one significant figure, the convention is to round 15 up to 20. This means 10, 11, 12, 13, 14 are rounded down to 10, and 15, 16, 17, 18, 19 are rounded up to 20. This choice makes sense because then there are five numbers in each category, so there isn't too much bias towards one direction.

So in your problem, 50 lots of 1.5 make 75, which to 1 significant figure would be 80.

Answer 2

It is correct.

If we have 3.5 rounded to 1 decimal place, the upper bound is 3.55 and the lower bound is 3.45.

You might say, "the upper bound should be 3.5499999999999....", but "0.049999999..." converges to 0.05 (in fact, they are equal - try using recurring decimals to prove this). It is a bit like the 0.9 recurring = 1.

So in all essence, it is the same thing.

However, you are wrong when you say the upper bound is 14.98 recurring, as this is 14.99, but 14.991 still rounds down to 10, rather than up to 20. You would be correct to stay 14.99 recurring is an upper bound, but by what I said above, this is a bit pointless, given that it is exactly the same thing as 15.