Question

Can someone explain to me upper and lower bounds?

I just don't understand when to add or subtract and what to add and what to subtract from the numbers given in the question...!!!

Answer 1

If you are talking about bounds the lower bound is the same as when you are rounding numbers normally. The smallest number that rounds up ends in 5 or .5 but the upper bound is different to 'normal' rounding. The largest number that rounds down to 46 would be 46.4 as 46.5 would round up to 47. Now when you are talking about bounds there are all the numbers BETWEEN 46.4 and 46.5 like 46.44, 46.48123, `46.dot4` etc. The upper bound takes all these values into account .

If you round a length to the nearest cm and the answer is 46 cm then the lower bound is 45.5 cm. The upper bound is 1 cm more than the lower so it is 46.5 cm. If you were using inequalities it would be `45.5<=X<46.5` . Notice it does not include 46.5

If you round to the nearest 5cm and the answer is 745 cm then the lower bound would be 742.5 cm. The upper bound would be 5 cm more than the lower `=>`747.5

So work out the lower bound as the smallest number that would normally round up from. Then add on the number that you are round to. So if you are rounding to the nearest cm, add 1 cm on. If rounding to the nearest 5cm , add 5 cm on etc.

Hope this helps.